Twist Error Response of Periodic Lattices to Strain Energy Distribution
by
Lauren Amy Chai
S.B. Mechanical Engineering
Massachusetts Institute of Technology, 2012
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
OCT 0 12015
September 2015
LIBRARIES
2015 Massachusetts Institute of Technology
All rights reserved.
Sigrnature of Author..
Signature redacted
partment of Mechanical Engineering
August 26, 2015
Certifiedby...
.eSignature redacted .................................
Martin L. Culpepper
Professor of Mechanical Engineering
Thesis Supervisor
Accepted by.............
Signature redacted
David E. Hardt
Professor of Mechanical Engineering
Graduate Officer
Twist Error Response of Periodic Lattices to Strain Energy Distribution
by
Lauren Amy Chai
Submitted to the Department of Mechanical Engineering
on August 26, 2015 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Mechanical Engineering
ABSTRACT
Periodic lattices, when used as assembly scaffolds, can augment pre-existing 2D
manufacturing techniques to fabricate 3D structures with heterogeneous materials, components
and architecture such as human organs for transplant patients, and micro batteries. Periodic lattices
are first preformed and then folded using externally actuating walls that properly constrain the
lattice edges. Angular errors of the actuation walls cause the lattice to distort, misaligning
components on the lattice panels. Research into the response of a lattice to geometric errors
imposed on the lattice edges does not account for how much strain energy is put into the lattice
during folding and its impact on the lattice distortion response and magnitude.
This thesis shows how design parameters of the lattice can change the magnitude and shape
of the twist response of the lattice when external geometric errors are applied to the lattice during
folding. A Buckingham Pi analysis was used to show how the twist response of the lattice due to
an external angular wall error depends on the torsional stiffnesses of the panels, the initial fold
angle of the preformed accordion unit in the lattice and the angular wall error. A FEA simulation
study quantified the Buckingham Pi results by varying the torsional stiffness ratio of the panels,
the initial fold angle and the final lattice length after folding. The results showed that increasing
the ratio of the torsional stiffnesses by two orders of magnitude decreases the magnitude of the
response by as much as an order of magnitude and increases the asymmetry by 0.5 to 1.5 orders
of magnitude. Increasing the initial fold angle by 50% increases the magnitude of the result by as
much as 250% and decreases asymmetry by 26%.
Thesis Supervisor:
Title:
Martin L. Culpepper
Professor of Mechanical Engineering
3
Acknowledgements
This work was made possible through the financial support of the NSF EFRI-ODISSEI
Award for Origami and Assembly Techniques for Human-Tissue-Engineering (OATH). I would
like to thank the Principal Investigator Professor Carol Livermore and Co-Principal Investigators
Dr. Robert Lang, Professor Sangeeta Bhatia and Professor Roger Alperin of the OATH Project for
their collaboration in the OATH Project.
I am extremely grateful to Professor Martin Culpepper who provided invaluable motivation
and mentorship for this project and my professional development throughout the past two years.
His insights and recommendations have made me a more thoughtful and thorough engineer and
researcher.
Thanks should also be expressed to my lab mates and housemates who provided vital
advice and feedback these past two years. Last but not least, a huge hug to my family whose
unwavering support has sustained me throughout my entire academic career and without whom I
would not be where I am today.
Contents
Abstract..........................................................................................................................................
3
A cknow ledgem ents .......................................................................................................................
5
C ontents .........................................................................................................................................
7
Figures............................................................................................................................................
9
Tables ...........................................................................................................................................
11
1
13
2
3
Introduction.........................................................................................................................
1.1
M otivation.....................................................................................................................
13
1.2
Technology and Know ledge Gap ...............................................................................
18
1.2.1
A dditive M anufacturing ........................................................................................
18
1.2.2
Prior Art on Folding Technologies.........................................................................
20
1.2.3
D istortion of Passive Lattice Structures ...............................................................
22
1.3
Chapter Sum m ary ......................................................................................................
23
1.4
Thesis Sum mary ........................................................................................................
23
D esign of Periodic Lattice ...............................................................................................
25
2.1
D esign Considerations and Perform ance Evaluation................................................
25
2.2
Periodic Lattice Constraints......................................................................................
29
2.2.1
Buckling in Under-constrained Elastic M echanism s .............................................
30
2.2.2
Folding Uniform ity in Underconstrained Lattices ...............................................
32
2.3
M aterial Selection......................................................................................................
33
2.4
Strategies for M itigating Actuation Side W all Errors ...............................................
35
2.5
Chapter Sum mary ......................................................................................................
38
M odeling of A ccordion Lattice ......................................................................................
41
3.1
G eom etric Param eters for model and analysis ..........................................................
41
3.2
Geom etric Lim its and M odel Assum ptions ...............................................................
43
3.2.1
Elastic M odulus Range...........................................................................................
44
3.2.2
N um ber of Lattice Units in M odel........................................................................
44
3.2.3
Thin Panels and Hinges.........................................................................................
45
3.2.4
Stiff Actuation W alls.............................................................................................
45
3.2.5
Initial and Final Fold Angle Range.........................................................................
48
3.2.6
Sum m ary of Param eter V alues used in Analysis ....................................................
52
3.3
Buckingham Pi A nalysis...............................................................................................
53
3.4
FEA Setup .....................................................................................................................
55
3.4.1
Contact Setup ...........................................................................................................
57
3.4.2
M esh Elem ent Size in M odel .................................................................................
58
3.4.3
Convergence Analysis...........................................................................................
59
Chapter Sum m ary ......................................................................................................
62
Discussion of R esults...........................................................................................................
63
3.5
4
5
4.1
Variation in Twist Magnitude Oe* with Stiffness Ratio Sr* and Initial Fold Angle yi* .. 64
4.2
A symm etry of Lattice D eform ation...........................................................................
66
4.3
Chapter Sum m ary ......................................................................................................
74
Conclusion ...........................................................................................................................
75
5.1
Introduction...................................................................................................................
75
5.2
Sum mary .......................................................................................................................
76
5.3
Future W ork ..................................................................................................................
78
References....................................................................................................................................
79
Appendix A : D ata Processing M A TLAB Code....................................................................
81
8
Figures
Figure 1.1 Accordion (left) and Miura Ori (right) are two examples of periodic lattices. ........ 13
Figure 1.2 Preformed lattice unit with fold angle yj . Folded lattice unit with fold angle yf......... 14
Figure 1.3 Accordion lattices are displaced by different magnitudes of Ay in response to wall
15
angu lar error (p.. ............................................................................................................................
Figure 1.4 Twist response of lattice for varying stiffness ratio Sr* and starting fold angles yi.... 16
Figure 1.5 Selected biofabrication processes using 'bioinks'. (Reproduced with Permission
18
Wiley and Sons License # 3691560403539) ............................................................................
Figure 1.6 Schematic of 3D Microbattery design (a) gold current collector. (b-c) printing of
electrode materials. (d) packaging. [4] (Reproduced with Permission Wiley and Sons License
19
# 369 1560 59 1502) ........................................................................................................................
Figure 1.7 Examples of active hinges. Top left: reprogrammable lattice showing two
configurations that it can fold into [11]. Top right: popup robot [12] bottom - artery stent
21
exp an ding [13] ..............................................................................................................................
Figure 2.1 Schematic of two panels connected by a hinge with points Al and BI .......
........ . . .
26
Figure 2.2 ( Figure 1.1 reproduced here for convenience) Accordion (left) and Miura Ori (right)
29
are tw o exam ples of periodic lattices........................................................................................
Figure 2.3 Buckled M iura Ori lattice ........................................................................................
31
Figure 2.4 Upper and lower Z walls used during folding prevent large displacements in the Z
31
direction that result from buckling.............................................................................................
Figure 2.5 Miura Ori lattice being pressed by points at the center of the lattice. The hinges close
to the actuation points are much closer to folding completion that than those furthest from the
32
actu ation p o ints.............................................................................................................................
Figure 2.6 Side walls used to fold lattice. The walls enable even folding through lattice. ...... 33
Figure 2.7 Polypropylene scaffold with passive hinges.............................................................
34
Figure 2.8 Schematic of lattice with external walls restricting displacement in Z. Side walls (not
shown here) make a line contact with the lattice. The line contact runs parallel to the Y axis.... 36
Figure 2.9 Impact of wall angular error about z axis.................................................................
37
Figure 3.1 Geometric Parameters of Accordion unit: width w, panel length Lp, hinge length Lh,
42
thickness t and starting fold angle y ..........................................................................................
Figure 3.2 Geometric parameters of lattice...............................................................................
42
Figure 3.3 Final model setup with external walls......................................................................
46
Figure 3.4 Close up of external side walls...............................................................................
47
Figure 3.5 Schematic of rigid panel with torsional spring of stiffness K at hinge....................
49
Figure 3.6 Schematic of rigid body model of assembly unit ...................................................
50
Figure 3.7 (Reproduced here from Figure 3.3 for convenience) Lattice in FEA study............ 56
Figure 3.8 No Penetration condition applied to faces of hinges and external walls..................
57
Figure 3.9 No Penetration condition applied to adjacent faces of lattice .................................
58
Figure 3.10 Effect of' no penetration' condition. .....................................................................
58
Figure 3.11 Mesh control applied to highlighted faces. These areas are the lattice side (left),
lattice upper-lower face (center) and lattice hinges (right)........................................................
59
Figure 3.12 Convergence analysis for the lattice upper-lower flat faces..................................
61
Figure 3.13 Convergence analysis for the lattice side faces ......................................................
61
Figure 3.14 Convergence analysis for the lattice hinge faces....................................................
62
Figure 4.1 Nodes used for data measurement highlighted........................................................
64
Figure 4.2 (Figure 1.4 reproduced here for convenience) Twist response Oe* of lattice for varying
stiffness ratio Sr* and starting fold angle yi*. ................................................................................
65
Figure 4.3 Single Surface plotted as Twist magnitude vs stiffness ratio...................................
66
Figure 4.4 Asymmetry of twist response lattice deformation during folding...........................
67
Figure 4.5 Schematic showing the angle between the side walls (gray) and the actuation path
(d ash ed lin e)..................................................................................................................................
67
Figure 4.6 Graph showing displacement along lattice face for different values of Sr* ............. 69
Figure 4.7 Symmetry results for all lattice datasets with yi*= 90 degrees.................................
70
Figure 4.8 Symmetry results for all lattice datasets with i* = 105 degrees...............................
71
Figure 4.9 Symmetry results for all lattice datasets with yi*= 120 degrees...............................
71
Figure 4.10 Symmetry results for all lattice datasets with yi*= 135 degrees............................
72
10
Tables
Table 2.1 First order estimates for design considerations of periodic lattices used as assembly
26
scaffo ld s ........................................................................................................................................
Table 2.2: Mitigation of four of six side wall errors.................................................................
37
Table 3.1 List of geometric and material parameters ..............................................................
43
Table 3.2 Elastic moduli of traditional scaffold materials........................................................
44
Table 3.3: Percentage difference between schematic and simulation part values for X. ............. 52
Table 3.4: Parameter limits for FEA simulation study ............................................................
52
Table 3.5: Non-dimensionalized parameters limits from Table 3.4. .........................................
53
Table 3.6 Derived variables for Buckingham Pi analysis........................................................
54
Table 3.7 Non-dimensionalized Buckingham Pi variables......................................................
55
Table 3.8: Actuation steps in simulation study........................................................................
56
Table 3.9: Mesh control for the lattice faces.............................................................................
59
Table 3.10 Element sizes used in convergence analysis...........................................................
60
Table 4.1 a averaged across Sr* for each value of yi*...............................................................
73
11
CHAPTER
1
INTRODUCTION
1.1 Motivation
Periodic lattices are a type of folding structure formed from a single repeating unit.
Figure 1.1 shows two examples of such lattices. The repeating unit is outlined in red.
Figure 1.1 Accordion (left) and Miura Ori (right) are two examples of periodic lattices.
This purpose of this research is to understand how the design parameters of periodic
lattices modify the sensitivity of the lattice's shape to its folding behavior. The import to
engineers is that they can deterministically design and optimize the performance of
periodic lattices to be used as assembly scaffolds. The impact is that these lattices are
envisioned to enable the creation of viable human organs for transplant and micro-batteries
for the flexible electronics industry.
Periodic lattices are first preformed from an initially flat state before being folded.
The left image of Figure 1.2 shows a pre-formed unit of the lattice. The right image is the
folded lattice unit.
Yf
vi
Y, >> Yf
Figure 1.2 Preformed lattice unit with fold angle yi. Folded lattice unit with fold angle 7f
The hinges of the lattice are pre-formed so that they have an initial fold angle yi. The lattice
can then be folded by controlling its edges until the hinges have a final fold angle yf.
Angular errors of externally actuating walls that control these edges will cause undesired
displacements and twisting of the lattice. The purpose of this research was to understand
how design parameters in periodic lattices change the shape of the lattice distortion
resulting from these errors.
Figure 1.3 shows two examples of a periodic lattice subjected to identical angular
error qpo and final distance Xf and responding with a Y-axis displacement Ay. X* is the final
length Xf normalized to the length of the flat lattice. Ay* is Ay normalized to the length of
the flat lattice.
14
Ayj
I
Xf
I
I
Xf
Figure 1.3 Accordion lattices are displaced by different magnitudes of Ay in response to wall
angular error (po.
Changing the starting fold angle yi of the lattice prior to actuation and the stiffness
ratio S,* of the panels and hinges modifies the magnitude and distribution of strain energy
in the lattice and therefore the magnitude and symmetry of the lattice twist response. The
twist response Oe* is calculated as a ratio of Ay* and X*. Oe* was measured over a range of
S,* and yi to produce the 3D plot in Figure 1.4.
15
Magnitude of lattice twist error 0,* as function of y and S.
Each surface Is for difference value of Xf
6050
~40easing
30
w20
10
0
20
09
400120
60
80---14
140
80
130
-
Sr
(Degrees)
Figure 1.4 Twist response of lattice for varying stiffness ratio S,* and starting fold angles yi.
Figure 1.4 shows that decreasing X* leads to increased twist response 0e*. The figure
also shows that preforming the lattice to a 50% larger initial fold angle yi increases Oe* by
as much as 250%. Increasing the ratio of the stiffnesses Sr* by two orders of magnitude
reduces the 9e* by as much as an order of magnitude.
Components such as battery electrodes or cells are deposited on the surface of a
preformed but unfolded lattice. The lattice is then folded, assembling the panels and
components into a 3D structure. The twisting on the lattice misaligns points on adjacent
panels within the lattice.
This research explains how design parameters modify the sensitivity of the lattice
misalignment to the wall angular error Vo. Engineers may use this knowledge to
deterministically design and optimize the performance of periodic lattices in order to
manufacture 3D structures. Periodic lattices, if used as assembly scaffolds, can augment
16
pre-existing 2D manufacturing techniques to create 3D heterogeneous structures such as
human organs for transplant patients, and micro batteries.
Assembly scaffolds are envisioned to enable the manufacture of human organs for
transplant through its ability to create macroscale organs with the required heterogeneous
tissue organization necessary for proper function. The U.S. Department of Health and
Human Services reported that as of 2011 [1], there were 15,700 people waiting for liver
transplants, including 200 children under the age of five years. 2,500 people died waiting
for a liver. In the same year, there were 87,000 people waiting for kidney transplants and
3114 people waiting for hearts. 5,155 and 3,113 people died in 2011 waiting for kidneys
and hearts respectively. Assembly scaffolds thus have the potential to save at least 23,000
liver per year. Hundreds of thousands of people also suffer from chronic non-life
threatening conditions that would also experience an improved quality of life from organ
transplants. In the electronics industry, the use of periodic lattices as assembly scaffolds
are envisioned to enable manufacture of 3D micro-batteries. The micro battery industry is
estimated to be worth up to $1.5bn by 2017 [2]. This does not include the revenue generated
by the micro- and flexible electronics industry that use these micro-batteries.
Chapter 1 explains the technology gap and knowledge gap that this research fills,
design considerations for lattices used as assembly scaffolds and two metrics for evaluating
performance of folding assembly scaffolds.
17
1.2 Technology and Knowledge Gap
The following section describes the features and limitations of pre-existing 3D
manufacturing techniques, most notably, additive manufacturing, as well as alternative
lattice folding techniques.
1.2.1 Additive Manufacturing
Additive manufacturing, also known as 3D printing, is a fabrication technique that
builds a structure layer by layer. Additive manufacturing technology has been used to print
living issue [3] and batteries [4]. Figure 1.5 shows schematics of printing of living tissue,
also known as bioprinting. Figure 1.6 is a schematic of printing batteries.
Inkjet printing
Laser-induced forward
transfer
thermal
piezoelectric
Robotic dispensing
pneurnatic
piston
Wrew
.-Jet
energy aibsurbirtg laye
Figure 1.5 Selected biofabrication processes using 'bioinks'. (Reproduced with Permission Wiley
and Sons License # 3691560403539)
18
a)
Current
Nozzle
b)
collecto r (A u)
(30 pm)
Glass
C)
d)
LTO
Packaging
LF P
#
Figure 1.6 Schematic of 3D Microbattery design (a) gold current collector. (b-c) printing of
electrode materials. (d) packaging. [41 (Reproduced with Permission Wiley and Sons License
3691560591502)
Bio-printing and printing batteries are examples of material extrusion and/or
material jetting. These are two categories of additive manufacturing techniques as defined
by the ASTM [5]. Both methods have the following disadvantages:
*
Material/Components are subjected to destructive shear forces from internal
tubing and nozzles [6]
*
Material choice is limited to what can be deposited [7]
" Resolution is limited by fluid properties of the materials printed [7]
"
Serial process leading to long fabrication processes
19
In contrast, periodic lattices can take advantage of the maturity of current 2D
fabrication techniques to create 3D heterogeneous layered structures. The advantages of
this process are:
* Many 2D manufacturing techniques are already parallelized, resulting in
relatively rapid assembly of components [8]
* Material and components are no longer limited to what can be deposited and
extruded [6, 9]
* More benign process for components [10] [8]
1.2.2 Prior Art on Folding Technologies
Active hinges are an alternative option for folding lattices. These mechanisms
enable the lattice to fold and/or unfold themselves without external constraints. Figure 1.7
shows active hinges in reprogrammable lattices, popup robots and heart stents.
20
Figure 1.7 Examples of active hinges. Top left: reprogrammable lattice showing two
configurations that it can fold into [111. Top right: popup robot [121 bottom - artery stent
expanding [131
Active hinges are ideal for lattices or devices that have one or more of the following
qualities:
" Actuation of complex geometries and folding processes [14]
* Devices expected to fold/unfold many times [15]
* Hinges fold sequentially
* Devices need to be actuated in locations that are difficult to access, such as
in space or within the body. [16, 17]
This is in contrast to periodic lattices that use externally actuating walls to fold.
They have the following features:
21
*
Geometry is periodic, so that a single actuation motion is sufficient to fold
up the lattice (described in more detail in Chapter 2). Heterogeneous
architecture arise from the placement of components on the scaffold, not the
scaffold itself.
*
The 3D structures are not required to unfold. The mechanism need only be
one-directional
*
The application of periodic lattices as assembly scaffold means that folding
will take place in a highly controlled manufacturing environment. Folding
will be followed by a packaging step.
Examples of active hinges are hydrogels [18], shape memory materials [14], lorentz
force actuation [19] [20], ion implantation [21], magnetic saturation [22], carbon nanotubes
[23].
1.2.3 Distortion of Passive Lattice Structures
Current research into the distortion of passive lattices only examine static lattices.
That is, the experiments do not measure the response to the lattice at different points during
its actuation or the response of the lattice to errors from externally actuating walls. One
such example is a paper by Evans, et al, discussing how to design lattices to absorb energy
when used as a packaging layer for delicate structures [24]. This paper focuses on how the
variation of the stiffness ratios between the panel and hinge change the lattices ability to
expand or contract when energy is applied at the center of the lattice. Another paper
conducted an experiment where a local deformation was imposed on the edge of a paper
22
lattice of a static fold angle [25]. The research by Schenk looks at the shape of lattices as
the stiffness ratios and the fold angle of the configuration. He also looked at the impact of
geometric distortions. However, like Evans, he does not consider how strain energy added
to the lattice during folding may change the magnitude and shape of the lattice response.
1.3 Chapter Summary
Periodic lattices are structures with a folding unit that is repeated periodically. The
vision is that these lattices, when used as assembly scaffolds, will enable engineers to create
viable human organs for transplant patients, saving at least 23,000 lives per year. They are
anticipated to also enable the fabrication of micro batteries, an industry estimated to be
work up to $1.5bn by 2017. Current fabrication techniques for these devices are limited by
material choice, destructive shear forces and slow process times. Periodic lattices as
assembly scaffolds have more material choices for fabrication, faster assembly times and
are more benign to components. Current research into the distortion of passive lattices do
not consider the effect of folding on the response of the lattice. Therefore, an unexplored
area of research is how the strain energy added to the lattice during actuation may amplify
and distort the lattice response to geometric errors.
1.4 Thesis Summary
23
This research provides the groundwork for constraining periodic lattices with
passive hinges and analyzing the parameters that dominate the response to geometrical
errors of the actuation walls. Chapter 2 discusses the actuation constraints, considerations
for choosing the material for the scaffold and errors in the actuation constraints, how they
might affect the lattice and mitigating strategies. Chapter 3 explains how the lattice is
modeled and parameters analyzed to examine the errors form the actuation constraints.
Chapter 4 presents and discusses the results of the analysis.
24
CHAPTER
2
DESIGN OF PERIODIC LATTICE
This chapter discusses the design considerations and performance criteria for
periodic lattices used as assembly scaffolds. Then the chapter describes how the constraints
for folding periodic lattices were chosen, considerations for choosing lattice materials,
sources of error from these constraints and strategies mitigating for these errors. The
discussion here provides the justification for modelling choices described in chapter 3.
2.1 Design Considerations and Performance Evaluation
The design considerations of the scaffold for assembly are i) alignment accuracy
and precision, ii) areal coverage, and iii) panel strain. The final values for the design
considerations are determined by the specific application. However, first order estimates
may be estimated made for each. These estimates are described in Table 2.1.
Table 2.1 First order estimates for design considerations of periodic lattices used as assembly
scaffolds
Requirement
Estimation
Justification
Alignment
Liver cell diameter -25 microns [26]
Li-ion Battery layer thickness ~ 30
microns [4]
Characteristic length of liver
cell, micro-battery layer
thickness.
Areal Coverage
>50% Lattice Surface Area
Maximum permissible
Panel Strain
< 10% in cells [27]
Minimum 50% of total scaffold
onas compot
volum c
volume contains components
Cell Strain can change cell
function
Performance of the lattice is determined by how well the lattice meets the estimates in
Table 2.1.
Alignment accuracy is the lattice's ability to predictably align components.
Component alignment is measured as the distance between two points on different panels.
Figure 2.1 is a 2D schematic of two panels connected by a hinge in its post-folded state.
.
Figure 2.1 Schematic of two panels connected by a hinge with points A1 and B 1
26
The vector
xi
joins points Ai and Bi. Its magnitude, lxil, is the desired distance
between points A and B. x1* is the measured vector post folding where the lattice has some
alignment error. Equation (2.1) is the calculation for the difference in the magnitude
between the desired and measured vector.
X 1 error = (lxlI -
Ix*1)
(2.1)
The alignment performance can be evaluated as the maximum error or as an average
of all the errors between pairs of points that are designed to be within a certain distance of
each other.
Areal coverage, A,, describes how much of the scaffold surface area can be used to
hold components such as battery electrode contacts and cells. This value is calculated as a
ratio between the total surface are of the lattice, Atotat, and the surface area of the lattice
covered in components Acomponents. The calculation for the ratio is given in Equation (2.2).
AC
-
Acomponent
Atotal
_
Acomponent
Ahinge + Aext + Aalign + Acomponent
(2.2)
Any fraction of the lattice area that cannot be covered in components reduces the
areal coverage of the lattice and the component density in the final 3D structure. This
fraction includes Ahinges , the area of the hinges, Aex , the area of the lattice that contacts
external machinery and Aaiign , the area that contains features on the panel whose primary
purpose is to align the panels.
27
The panel strain is the deformation of the panel. The panel is assumed to be thin
because thin panels leads to higher component density in the final structure. The
assumption of thin plates means that strain
Cafi
at a point on the surface of the panels can be
measured as function of the thickness and curvature of the panel at that point. This function
is given by equation (2.3) which is the 2D in-plane strain tensor for a bending plate, using
the Kirchoff-Love plate theory. The thickness, t, is twice the distance between the neutral
plane of the panel and the surface of the panel.
pane.
K12
Ku
and K22 are the curvatures of the bending
describes how the slope of one of the in-plane directions changes with the other
orthogonal in-plane direction.
t
Ecq?=
2
Kafl
t K1 1
2 K2 1
K1 2
(2.3)
K 221
Panel strain leads to strain in the components on the panel which are rigidly attached
to the panel. Component strain can lead to mechanical failure and misalignment. In
biological applications, mechanical strain imposed on the cells can change the function of
the cells [27].
28
2.2 Periodic Lattice Constraints
Periodic lattices are constrained to enable folding of all the units in one motion and
prevent buckling and irregular folding of hinges. Periodic lattices are structures that are
formed by repeating a single folding unit in one or more orthogonal directions. Two
examples are the Miura Ori and Accordion lattice arrangements shown in Figure 2.2. The
repeating unit is outlined in red.
z
YL
Figure 2.2 (Figure 1.1 reproduced here for convenience) Accordion (left) and Miura Ori (right)
are two examples of periodic lattices.
The Miura Ori lattice has a single degree of freedom mechanism if modeled as a
lattice with rigid panels and hinges with no stiffness [28]. In this rigid model, the number
of units in the Miura Ori lattice does not change the number of degrees of freedom (DOF).
A Miura Ori structure can be folded by controlling its seven degrees of freedom: six rigid
body DOF and one mechanism DOF.
29
In contrast, an Accordion lattice has an extra DOF for every additional hinge after
the first unit if modeled as a lattice with rigid panels and hinges with no stiffness. However,
stiffness at the hinges transform the Accordion into a highly compliant elastic structure.
This allows it to be controlled by its outer edges and folded.
Both structures can be folded when pressed on the outermost edges along the X-axis
as oriented in Figure 2.2. The X-axis is also the direction that the units are repeated in for
both lattices and thus adding more units does not change the direction of actuation.
2.2.1 Buckling in Under-constrained Elastic Mechanisms
Each possible shape that the structure can assume when deformed is associated with
a different amount of strain energy. The structure chooses to occupy the state with the
lowest energy. During elastic deformation, strain energy within the structure increases.
Buckling is a phenomena that occurs when the structure has reached a point during
deformation where its current shape is no longer energetically preferable and the structure
changes to a shape with lower energy.
Figure 2.3 is an image of a buckled Mirua Ori lattice. The lattice was pressed at the
actuation points labelled in the figure until the lattice buckled in the Z direction. This is
similar to Euler buckling where a beam is axially compressed until it suddenly buckles
outward in a direction normal to the longitudinal axis. Constraining the beam in the
direction that it wants to buckle forces the beam to take on shapes that would have
otherwise been energetically unfavorable [29].
30
Figure 2.3 Buckled Miura Ori lattice
Likewise, a wall that is normal to the Z direction of the lattice can be used to restrict
the displacement of the lattice in the Z direction. This allows the lattice to keep the desired
planar shape seen in Figure 2.2 and continue to fold until completion. Figure 2.4 is a
schematic of the lattice with upper and lower walls to prevent buckling.
e
Actuation Point
e
Hinge
Panel
Figure 2.4 Upper and lower Z walls used during folding prevent large displacements in the Z
direction that result from buckling.
31
2.2.2 Folding Uniformity in Underconstrained Lattices
When force is applied to points on the outer edges of the Miura Ori and Accordion
lattices, the force is not distributed evenly to all hinges due to panel compliance. The panel
compliance reduces how efficiently force at the actuation points is transferred to hinges
furthest away from the actuation points. This results in incomplete folding of the hinges
furthest from the actuation points even though the hinges nearest to the actuation points are
almost completely folded. (See Figure 2.5). The use of externally actuating walls that make
line contacts instead of point contacts results in more uniform folding behavior. These
walls are arranged on the side as seen in see Figure 2.6.
less folded
y from actuation point
n point
Figure 2.5 Miura Ori lattice being pressed by points at the center of the lattice. The hinges close
to the actuation points are much closer to folding completion that than those furthest from the
actuation points.
32
Figure 2.6 Side walls used to fold lattice. The walls enable even folding through lattice.
2.3 Material Selection
The lattice performance is determined by the ratio of the bending stiffness between
the panel and hinge. This conclusion was determined by the results of the fabrication and
folding of the Accordion polypropylene lattice shown in Figure 2.7. Strain in the hinges
from the folding process resulted in panel-panel gaps of 3.05% +/- 0.8% of the panel length.
This is a 26% variation in the panel-panel gap. Lattices with higher stiffness ratios display
behavior that more closely resemble lattice models with rigid panels and thus no panel
strain. Such models have uniform panel-panel gaps since the panels have no strain.
33
Gap = 0.5842mm
Gap = 0.9852mm
Figure 2.7 Polypropylene scaffold with passive hinges.
The bending stiffness of a cantilever beam is given in Equation (2.4) as a function
of the beam length L, area moment of inertia I and elastic modulus E. This ratio can be
separated into the geometric component L3/I and the material component E.
Stiffness
=
L3
3EI
L3
1
(2.4)
(31) E
The ratio of the panel and hinge bending stiffness is given in Equation (2.5)
Panel Stiffness
Hinge Stiffness
Lpanei
Iinge
Ehinge
Lhtinge
*3Ipanel
Epanel
34
(2.5)
The material component of the stiffness ratio is the ratio of the elastic moduli of the
panel and hinge. As a result, optimization of the lattice is determined partially by the range
of the elastic moduli available for the scaffold fabrication.
Other parameters that will affect material choice are:
"
Sensitivity of cells to by-products of scaffold degradation [30]
" Effect of mechanical strain on cell function [31]
" Range of fabrication thicknesses
2.4 Strategies for Mitigating Actuation Side Wall Errors
The simplest wall design is one in which one side wall is fixed and the other side
wall moves relative to the fixed wall. Figure 2.8 is a schematic of the lattice showing the
constraints of the lattice, line contact with the side walls and constraints of the upper and
lower walls.
35
0
---
X
Hinge
Panel
Figure 2.8 Schematic of lattice with external walls restricting displacement in Z. Side walls (not
shown here) make a line contact with the lattice. The line contact runs parallel to the Y axis.
The moving side walls can have six total displacement errors relative to each other:
three displacement errors in X, Y and Z and three angular errors about the X, Y and Z axis
The orientations of these directions are as shown in the schematic Figure 2.8. The Y,Z
displacement errors and the X,Y twist errors are mitigated if contact between the walls and
lattice are assumed to have the following conditions:
" Contact between side walls and lattice is a line contact
" A single corner of lattice is fixed so that the lattice edges 'float' on Y-Z faces
and X-Y faces of the external walls.
These assumptions result in four of the wall errors having no impact on the lattice
folding behavior. A summary of these errors is given in Table 2.2
36
Table 2.2: Mitigation of four of six side wall errors
Error Type
Mitigation strategy
Displacement Y
Lattice Wall contact slides across Y-Z face
Displacement Z
Lattice Wall contact slides across Y-Z face
Twist X
Lattice Wall contact slides across Y-Z face
Twist Y
Lattice makes a line contact with wall
The displacement X error is in the direction of actuation. An ideal kinematic model
of the folding process of the lattice will predict the progress of the lattice folding as a
function of the wall-wall distance and can therefore also model the displacement X error.
Thus, displacement X error only results in the lattice appearing as 'over-' or 'under-folded'.
This model cannot account for the twist Z error shown in Figure 2.9. This behavior will be
studied further in the following chapters.
z4
Wall Actuation
WaN Angular Error
Figure 2.9 Impact of wall angular error about z axis.
Errors can also come from the upper and lower walls being displaced. Under ideal
wall and lattice geometric and material parameters, the lattice should not touch these walls.
37
The lattice does buckle in simulations and experiments. Buckling occurs when the structure
has reached an unstable energy state. Any deviations to the structure will cause the structure
to change shape into a more stable one. These deviations are unavoidable in experiments.
In simulation studies, discretization of the model also results in deviations. The errors of
concern are the distance between the upper and lower walls and their parallelism with each
other. For the purposes of limiting the scope of this thesis, the upper and lower walls were
assumed to be ideal but the analysis of these errors should be included in future work.
2.5 Chapter Summary
Design considerations for periodic lattices as assembly scaffolds are alignment
accuracy, areal coverage and strain. They describe how well the lattice can align
components on the panels, how densely components can be packed in the final structure
and how much strain the components are subjected to as a result of folding. The
performance of the lattice in a specific application is measured by how well the lattice
meets the requirements for these considerations.
Periodic lattices are constructed from a single geometric unit which is repeated in
one or two orthogonal directions across a plane. The actuation direction does not change
when the actuation direction is parallel to the direction that the units are repeated in. Hinge
stiffness and panel compliance in the lattice result in buckling and uneven folding in
periodic lattices respectively. Walls are used to limit the displacement of the lattice when
38
it buckles. Uniform folding is achieved when actuating walls that form line contacts with
the lattice are used instead of actuation points to fold the lattice.
Only the geometric errors from the side walls are considered. Four of the six
geometric errors associated with the side walls are mitigated through the use of line contact
between the lattice and the side walls and by allowing the sides of the walls to move freely
across the face of the side walls. Only a single corner of the lattice is fully constrained in
space. A fifth error results in the lattice being under or over folded. The sixth error, an
angular twist of the side walls, needs to be studied further and is modelled in chapter 3
39
CHAPTER
3
MODELING OF ACCORDION
LATTICE
The accordion lattice was modeled. This lattice type was chosen for its simplicity
and use in current research into tissue scaffolds. This chapter describes the assumptions,
lattice geometric parameters and parameter limits used in the model. A Buckingham Pi
analysis was used to study the twist Z-axis error. At the end of the chapter is an overview
of finite element analysis study setup used for a simulation study to quantify the
Buckingham Pi results.
3.1 Geometric Parameters for model and analysis
The geometric parameters of the Accordion lattice unit are the thickness t, width w,
lengths of the panel and hinge L and Lh respectively and the fold angle y. Figure 3.1 is a
schematic showing the geometric parameters of the accordion unit. Figure 3.2 is an image
of a folded lattice twisting due to the angular wall error (p. The geometric parameters of
the lattice are the angular error g9 , the distance between the external side walls after folding
Xf and the maximum lattice Y-displacement Ayrnax. A summary of the geometric parameters
is given in Table 3.1.
~L
t
Figure 3.1 Geometric Parameters of Accordion unit: width w, panel length L, hinge length Lh,
thickness t and starting fold angle Pi
Y
tin4 X
max
(P0
1
I
I
Xf
Figure 3.2 Geometric parameters of lattice
42
I
I
Table 3.1 List of geometric and material parameters
Parameter
Units
Description
mm
Final Distance between external
side walls
Aymax
mm
Max Y-displacement
w
mm
Width of Panel and Hinge
t
mm
Panel and hinge thickness
Lp
mm
Panel Length
Ep
N/m 2
Shear Modulus of Panel
Lh
mm
Hinge Length
Eh
N/m 2
Shear Modulus of Hinge
(unit less)
Poisson Ratio
y
Radians
Fold Angle
pO
Radians
Wall Angular Error
n
Accordion units
Number of units
3.2 Geometric Limits and Model Assumptions
The model makes the following assumptions
"
Materials are assumed to be linear elastic
*
Panels and hinges are thin
"
Constraint Walls are rigid
*
Zero friction
The assumptions as well as the range and/or limits of parameter values are discussed
further in sections 3.2.1 to 3.2.5 followed by a summary in section 3.2.6
43
3.2.1 Elastic Modulus Range
The model is assumed to be made of linear elastic materials. The range for the elastic
moduli of the lattice materials used in the simulation study were decided after examining
the elastic moduli and Poisson ratios of common biocompatible scaffold materials given in
Table 3.2.
Table 3.2 Elastic moduli of traditional scaffold materials
Material
Elastic Modulus
Polyglycolic acid (PGA)
10 GPa [32]
Polylactic Acid (PLA)
8.3-18.6 GPa [32]
Polyglycerol sebecate (PGS)
0.05 - 1.5 MPa [30]
Polyphenelene sulphide (PPS)
0.05 - 13 MPa [30]
The range of elastic moduli spans at least six orders of magnitude. Within the same
material type, the range can be as high as ~2.5 orders of magnitude, e.g. PPS. The range
for the elastic moduli in the analysis was thus chosen to be two orders of magnitude.
The Poisson's ratio was chosen as 0.3 because this is a common value for metal and
metal alloys and plastics. Many rigid thermoplastics have a Poisson's ratio of 0.2-0.4 [33].
PLA and PPS from Table 3.2 have Poisson's ratios of 0.36 [34] and 0.38 [35] respectively.
3.2.2 Number of Lattice Units in Model
The number of Accordion lattice units in the model is six. Six units is the minimum
number of lattice units necessary such that the center of the lattice is sufficiently far away
from the side walls for edge effects to be neglected. This is an adaption of the St. Venant's
44
principle, and the distance required for the point of measurement to be sufficiently far is
typically 3-5 characteristic lengths. The characteristic length of the Accordion is
approximated as one half of an Accordion unit. Thus the required number of units is given
by equation (3.1).
# of Units = 2 * (5 * 0.5 Unit) + center Unit = 6 Units
(3.1)
Five halves of the accordion unit per side results in a total of five units needed to
isolate the center unit in the lattice from edge effects. Thus the model contains six
Accordion units.
3.2.3 Thin Panels and Hinges
The panel is assumed to be thin since thinner panels yield higher component density
The model was thus modelled as thin to capture this behavior.
t
--
1
(3.2)
W
t
(3.3)
+2*
3.2.4 Stiff Actuation Walls
All external walls are assumed to be rigid. This was achieved in the FEA model
through the use of constraints, high elastic moduli compared to that of the panels, hinges
and geometry. Figure 3.3 is an image of the lattice with external walls. Thin walls above
45
and below the lattice restrict displacement in the Z-axis direction. Actuation direction is
along the X-axis.
z
=X
Figure 3.3 Final model setup with external walls.
The upper and lower walls are constrained to only move in the Z-axis direction
without any bending. Thus the walls' dominant deformation mode is compression. The
walls' thicknesses are 25% of the panel thickness. The elastic modulus is at least one order
of magnitude greater than that of the lattice. Thus, the resulting Z-axis compression
stiffness of the walls, S,, is at least forty times greater than that of the panels.
The side walls are constrained so that they cannot bend. The force reaction from the
lattice is an X-axis compression force. Figure 3.4 is a close up of the side walls with lengths
Lsj and Ls2 and thicknesses tsi and ts2.
46
z
Y
FiN
L S1
Its2
Figure 3.4 Close up of external side walls
The thickness of the side walls, tsj and ts2, are factors 2.5 and 1.5 larger than the
thickness of the panels. The lengths of the side walls, Lsi and Ls2, are at least two orders of
magnitude smaller than the length of the flat lattice. The elastic modulus of the side walls
are at least one order of magnitude greater than that of the lattice panels and hinges. Thus,
the X-axis compressive stiffnesses of the side walls are at least three orders of magnitude
greater than that of the flat lattice.
47
3.2.5 Initial and Final Fold Angle Range
The fold angle of the accordion units is yi before folding the lattice. The fold angle
of the accordion units is yf after folding the lattice. In the model, the range of starting fold
angle yi was chosen as 90-135 degrees (pi/2 to 3*pi/4). The final fold angle yf range was
chosen as 45 - 90 degrees (~pi/4 to pi/2). The justification for these ranges is that yi starts
at a value where small actuation displacements result in a relatively large change in the
hinge angle. The final fold angle yf ends at the angle where small actuation displacements
result in relatively small change in the fold angle.
Figure 3.5 is a schematic of half of an assembly unit: a rigid panel is connected to
ground via a torsional spring of stiffness K. The dashed arc is the path of the panel as it is
folded 90 degrees. This corresponds to the lattice starting with a yi of 180 degrees and
ending at 0 degrees. The segment contained by the arc is divided into four segments of
angle 22.5 degrees each.
48
L
e
d
0
AyA
"f
B
Z
AxA
C
D
D
Figure 3.5 Schematic of rigid panel with torsional spring of stiffness K at hinge.
Figure 3.5 contains the variables AX, AYn and d, that specify the displacement of
the panel end in the X- and Y-axis and the segment arc length respectively of region n. The
length of the panel-hinge assembly is unit 1. The arc length for all four segments is the
same since the angle of the segments, 6 is the same. Equations (3.4) - (3.6) describe how
to calculate XA, XB and d as functions of 0.
xA =
L(1 - cos(6))
XB =
L(sin(0)
d = L6
49
(3.4)
(3.5)
(3.6)
The energy stored in the torsional spring EK when it is deflected through angle 0 is
given by equation (3.7) The value d can thus be shown to be a function of the change in
energy in the torsional spring.
1
EK= -K0
2K
2
-> d = L
2 EK
(37)
K
The dimensionless ratio d/Ax thus gives a measure of how much energy is being put
into the system per unit Ax during actuation At the boundary between region A and D, this
value is ~ 5. At the boundary between region C and D, this value is ~1.
Figure 3.6 shows a schematic of a whole assembly unit. yi starts at 135 degrees and
ends at 90 degrees, spanning region B. The final fold angle yf starts at 90 degrees and ends
at 45 degrees, the spanning region C
K
L
y= 135*0
y= 90*
y= 45*
B
Figure 3.6 Schematic of rigid body model of assembly unit
50
Xi is the distance between the ends of the two panels at a given yfin Figure 3.6. The
value for L in the simulation study is 57mm from which Xi is calculated as shown in
Equation (3.8). The final wall-to-wall distance Xf is six times X because there are six units
in the assembly. The range of values for Xf is calculated to be 483.7mm to 261.8mm or
97.6% to 52.8% of the unfolded lattice length. This range corresponds to a yf range of 90
to 45 degrees.
2 *L
(sin ( )
(3.8)
The schematic in Figure 3.6 does not account for part thickness. The largest value
of Xf for the simulation study was chosen as 454mm which is the value measured in the
pre-actuated simulation assembly with yi of 90 degrees. The smallest value of Xf was
changed to 254 mm in order to divide the span of Xf into increments of 50mm and simplify
running the study, thereby reducing the chance for human error. The resultant percentage
change in the values of yf is at 3.1% to 7.6%. See Table 3.3 for the calculations and values.
51
Table 3.3: Percentage difference between schematic and simulation part values for X.
X
% difference
(mm)
Angle
(degrees)
Angle
(radians)
Schematic
261
45
0.7854
0.7854 - 0.7609
Simulation Part File
254
43.60
0.7609
0.7854
Schematic
483
90
1.5708
1.5708 - 1.4516
Simulation Part File
454
83.17
1.4516
1.5708
Source of Value
=
3.1%
7.6%
3.2.6 Summary of Parameter Values used in Analysis
The exact values and ranges used for the model and FEA simulation study are
summarized in Table 3.4. All variables with units of length were non-dimenisonalized to
the unfolded lattice length 495.4mm in Table 3.5.
Table 3.4: Parameter limits for FEA simulation study
Parameter Name
Description
Value
Units
Eh
Hinge Elastic Modulus
1
GPa
Ep
Panel Elastic Modulus
Ew
Wall Elastic Modulus
1000
GPa
y
Starting Fold Angle
Final Side Wall -Wall
distance
1.57 - 2.36 (90 - 135)
Radians (Degrees)
454-254
mm
Final Top-Bottom Wall
Distance
50
mm
Oe
Wall Twist
0.1 (5.7)
Radians (Degrees)
w
Width (Panel and Hinge)
50
mm
t
Thickness (Panel and
Hinge)
4
mm
Lp
Panel Length
25
mm
Lh
Hinge Length
16
mm
1
52
-
100
GPa
Table 3.5: Non-dimensionalized parameters limits from Table 3.4.
Values
Units
Values
Normalized to
Panel Length
454-254
mm
0.916 - 0.512
Final Top-Bottom
Wall Distance
Width (Panel and
Hinge)
Thickness (Panel and
Hinge)
50
mm
0.10
50
mm
0.10
4
mm
0.008
LP*
Panel Length
25
mm
0.05
Lh *
Hinge Length
16
mm
0.032
Parameter Name
Description
Wall distance
Xv*
*
*
-
Final Side Wall
3.3 Buckingham Pi Analysis
Twisting in of the lattice in Figure 2.9 is only possible in a lattice where the panels
have some finite compliance, allowing them to twist. In the rigid model of the accordion
unit in Figure 3.6, only displacements in the X- and Z-axis directions are permitted. Thus,
the lattice twist is dependent on the panel and hinge torsional stiffnesses. Long thin
structures more easily twist than short compact structures due to smaller torsional
constants. Thus the lattice twist also depends on the initial fold angle yi. The magnitude
will also depend on the magnitude of the angular wall error q9.
The torsion constants, shear moduli and stiffness ratios of the lattice were calculated
from the geometric parameters in Table 3.4 and used for the Buckingham Pi Analysis. They
are presented in Table 3.6.
53
Table 3.6 Derived variables for Buckingham Pi analysis
Parameter
Units
Jp
mn4
j = 0.333wt 3
Jh
m4
A
Gp
N/m2
G =
E
S2(1 + v)
Panel Shear Modulus
Gh
N/M 2
Gh = 2(
2(1 + v)
Hinge Shear Modulus
SP
N-rn
Sh
N-m
Derivation
= 0.333Wt3
Description
Panel Torsion Constant
Hinge Torsion
Constant
L
J
Gh
Lh
Panel Stiffness
Hinge Stiffness
The lattice twist response Oe is calculated by equation (3.9).
Oe = atan(
max)
Xf
(3.9)
A Buckingham Pi analysis was used to determine the relationship between
Qe
and
the variables in Table 3.6. The dependent and independent variables are described below:
Dependent Variable: 0e
Independent Variables: Sp, Sh, Qpo, )i
The result of the analysis is shown in equation (3.10) which summarizes the final
Buckingham Pi Variables, their derivations and their descriptions
e = f(q40p Sr*,y*)
54
(3.10)
Table 3.7 Non-dimensionalized Buckingham Pi variables
Non-Dimensionalized Variable
Derivation
Description
Lattice Twist Angle
Wall Angular Error
19*
r*
yi
Initial fold angle
Sr*
S
Sh
Panel-Hinge Stiffness Ratio
3.4 FEA Setup
A finite element analysis study was used to quantify equation (3.10). The study was
run using the non-linear simulation package in Solidworks. Figure 3.7 is an image of the
model used in the FEA study (Reproduced here from Figure 3.3) On the left side of the
lattice is the artifice that will apply an angular error (p, on the lattice. On the right of the
lattice is the artifice that displaces the edge of the lattice in the X-axis direction by amount
Ax.
55
xv*
Ax
A
Figure 3.7 (Reproduced here from Figure 3.3 for convenience) Lattice in FEA study
In the study, the angular wall error po* is applied prior Ax because the error is applied
to the lattice by the side walls before actuation. The lower wall is held stationary while the
upper wall is raised during the application of Ax in order to allow the lattice to fold without
jamming between the upper and lower walls. The non-dimenionalized final distance X*
between the upper and lower wall in the study was 10% of the unfolded lattice length. The
timing of the simulation steps in the FEA study is described in Table 3.8.
Table 3.8: Actuation steps in simulation study
Time
Action
(seconds)
0-0.1
p,* applied
Ax Applied. q,* held
0.1-1
constant. Upper wall
raised X,.
56
Visual depiction
3.4.1 Contact Set up
The panels, hinges and side wall artifices were bonded to each other. During folding,
the lattice displaces in the Z-axis direction such that the hinges touch the external walls
above and below the lattice. Thus, contact conditions were set up between the hinges and
the external walls so that these parts could not penetrate each other. Figure 3.8 shows the
lattice with the hinge face highlighted and the face of the external wall above the lattice
highlighted for the 'no penetration' condition. Faces of adjacent panels may also touch
each other during folding. Thus, contact conditions were also set up between the faces of
adjacent lattice panels in order to prevent the lattice from penetrating itself during folding.
Figure 3.9 shows faces of adjacent lattice panels highlighted in the right image with the 'no
penetration' condition. Figure 3.10 is an image of the lattice model near folding completion
with no angular error. Contact between adjacent panels and the upper-lower walls are
circled.
Figure 3.8 No Penetration condition applied to faces of hinges and external walls
57
Figure 3.9 No Penetration condition applied to adjacent faces of lattice
Figure 3.10 Effect of' no penetration' condition.
3.4.2 Mesh Element Size in Model
The constraint walls were meshed using a standard mesh with size 15mm with
tolerance of 0.6mm. 15mm is 3.5 times the thickness of the panels. Mesh Control was
applied to all the faces of the lattice as depicted in Figure 3.11:
0 Lattice sides (parallel to X-Z Plane as described in Figure 3.7)
58
"
Lattice upper-lower faces (normal to X-Z Plane as described in Figure 3.7)
" Hinge Faces (normal to X-Z Plane as described in Figure 3.7)
Table 3.9 summarizes final element sizes.
Figure 3.11 Mesh control applied to highlighted faces. These areas are the lattice side (left),
lattice upper-lower face (center) and lattice hinges (right)
Table 3.9: Mesh control for the lattice faces.
thi
esto
Parameter
Value
Lattice Side
2 mm
0.5
Lattice upper-lower flat
faces
3 mm
0.75
Lattice Hinge
2 mm
0.5
Constraint Wall faces
15 mm
3.5
=4anel
3.4.3 Convergence Analysis
These mesh control values were chosen after a set of convergence analysis tests.
The tests looked at the effect of mesh refinement in three areas:
*
lattice side
*
lattice upper-lower face
59
.
lattice hinge face
The simulations used in the convergence analysis used the actuation steps outlined
in Table 3.8. Aymax was measured as the element sizes changed. Table 3.10 summarizes the
range of values tested in the convergence analysis. The results of the analysis are shown in
Figure 3.12, Figure 3.13 and Figure 3.14. Refining the mesh showed convergence.
For the upper-lower faces, a 3 mm mesh was chosen. A 33% decrease in element
size showed 0.2% change in Aymax. For the lattice side, the largest element size tested was
2mm ensuring that there were at least two elements across the lattice side. A 50% decrease
in element size resulted in 0.09% change in Aymax. For the lattice hinge, the chosen element
size was 2mm. A 25% and 37.5% decrease in element size resulted in 0.46% and 0.52%
change in Aymax respectively.
Table 3.10 Element sizes used in convergence analysis
Parameter
Tested Values
Units
Lattice Side
[0.8, 1, 2]
mm
Lattice upper-lower flat faces
[2, 2.5, 3, 5, 7.5]
mm
Lattice Hinges
[1.25, 1.5, 1.75, 2]
mm
60
Convergence analysis result for lattice upperlower faces
100.4
100.2
100.0
99.8
E
E
99.6
99.4
99.2
99.0
40,000
60,000
100,000
80,000
120,000
160,000
140,000
Element Count
Figure 3.12 Convergence analysis for the lattice upper-lower flat faces.
Convergence analysis result for lattice side faces
100.4
,a
100.2
100.0
E
99.8
E 99.6
99.4
99.2
99.0
40,000
60,000
80,000
100,000
Element Count
Figure 3.13 Convergence analysis for the lattice side faces
61
120,000
140,000
Convergence analysis result for lattice hinge faces
100.4
100.2
100
E
99.8
E
99.6
99.4
99.2
99
40,000
-
-
---
60,000
80,000
100,000
120,000
140,000
Element Count
Figure 3.14 Convergence analysis for the lattice hinge faces
3.5 Chapter Summary
Chapter 3 describes a model of an Accordion unit. The model uses six accordion
units in order to isolate the center of the lattice from edge effects. The model assumes linear
elastic behavior in thin panels and hinges. A Buckingham Pi analysis was used to determine
that the lattice twist error Oe* depends on angular wall error (p, ratio of the panel and hinge
torsional stiffnesses Sr* and initial fold angle yi*. The normalized range for the wall-to-wall
distances X* was calculated to be 0.91 to 0.51 or 91% to 51% of the unfolded lattice length.
The model assumes no friction and rigid external walls. The FEA setup used to quantify
the Buckingham Pi analysis results was described. The results of the FEA study is
presented and discussed in chapter 4.
62
CHAPTER
4
DISCUSSION OF RESULTS
This chapter presents the results from the FEA simulation study described in chapter 3.
Section 4.1 discusses how the error magnitude is modified by yi* and Sr*, the initial fold
angle and stiffness ratio respectively. Section 4.2 shows how the symmetry of the lattice
twist is modified by yi* and Sr*.
The FEA study varied the following parameters
*
Final wall-wall distance of side walls X*
"
Stiffness ratio Sr*
" Initial fold angle y*
The measured data is the initial locations and displacements of the nodes on the
edges of the lattice sides. Figure 4.1 shows a section of the lattice in the study. The initial
locations and displacements of the highlighted nodes on the edge of the lattice sides are
processed in matlab to produce the lattice twist error Oe* and a value for twist symmetry for
each Sr* , yi* and X;* combination.
Figure 4.1 Nodes used for data measurement highlighted.
4.1 Variation in Twist Magnitude Oe* with Stiffness Ratio Sr*
and Initial Fold Angle y*
The maximum displacement along the Y-axis, Aymax, was measured and used to
calculated lattice twist error Oe* using equation (3.9). Oe* was plotted against Sr* and yi* in
Figure 4.2. Each surface represents the same final wall-wall distance X*.
64
Magnitude of lattice twist error 0, as function of Y and Sr
Each surface is for difference value of Xf
605040-
asingk,
30o2010-
09
0
12
80
140
Sr
90
130
y (Degrees)
Figure 4.2 (Figure 1.4 reproduced here for convenience) Twist response Oe* of lattice for varying
stiffness ratio S,* and starting fold angle 7*.
This plot shows two types of behaviors:
*
0e* increases with decreasing X*, decreasing Sr* and increasing y*.
* The surfaces are parallel to each other, that is, X* scales the magnitude of the
twist response but the twist response is dominated by Sr* and yi*. The trends
of a single surface in the plot can be applied to the other surfaces.
The surface X/
=
0.51 corresponds to the highest values of Qe*. Figure 4.3 plots the
twist magnitude Oe* versus the Sr* for X; = 0.51 of the unfolded lattice length. Each line is
for a lattice with different values yi*.
65
60t
Magnitude of lattice twist error 1?
---- -'T
as function of -y and S for X= 0.51
Asymptote at ~55 degrees
=90
5=
97.5
= 105
= 112.5
40
S40
Cn
= 120
$>I\=
a> 30.
135
Change in Curvature ~8 degrees
20
_
Asymptote at -3 degrees
-
10
0 L-
L-
I
0
10
20
- -
i
30
40
----
50
60
70
Sr
Figure 4.3 Single Surface plotted as Twist magnitude vs stiffness ratio.
Figure 4.3 shows the following behaviors:
1) All plots change curvature at
-
8 degrees, or 13% at the maximum value of Oe*
of 60 degrees.
2) At low values of Sr*, Oe* for all plots approaches -55 degrees. The exception is
the plot corresponding to y* of 135 degrees which is not approaching an
asymptote in Figure 4.3.
3) At high values of Sr*, the
Oe*
for all plots approaches an asymptote value of -3
degrees.
4.2 Asymmetry of Lattice Deformation
66
The deformed shape of the lattice is not symmetric about a Y-Z plane located at the
midpoint of the lattice. Figure 4.4 is an image of an actuated lattice with an asymmetric
twist. The midpoint of X* is circled. An arrow points to the location of Aymax.
X, mi1d po1int
Figure 4.4 Asymmetry of twist response lattice deformation during folding.
The asymmetry seen in Figure 4.4 is because of the difference between the angles
that the side walls make with the actuation path. Figure 4.5 a schematic of the side walls
and actuation path. Angle /li and #2 are the angles between the side walls, depicted as grey
rectangles, and the actuation path, depicted as a dashed line.
Xf
Y
Figure 4.5 Schematic showing the angle between the side walls (gray) and the actuation path
(dashed line).
67
The angular wall error (po* is calculated fromf/3 in equation (4.1).
/2
form is a right
angle
(4.1)
Po = A1 - 2
The schematic in Figure 4.5 has four boundary conditions: two Y-axis location
conditions and two X-Y slope conditions. The boundary conditions in Figure 4.5 were used
to solve for a
4 th
degree polynomial whose solution is given by equation (4.2).
x3
y
e(
2x 2
-
+ x)
(4.2)
Equation (4.2) is plotted against the final X-axis and Y-axis location data of lattices
with yi* of 105 degrees and X* of 0.51. The results are presented in Figure 4.6. The
following observations are made:
" As Sr* decreases, the apex of the curve formed by the lattice data approaches
the point of symmetry at 0.5
" As Sr*, the apex of the curve of the lattice data approaches the apex of the
analytical solution.
68
1200
Normalized position of lattice nodes along X- and Y-axis. X= 0.714.
S
0.9~
= 64
rSr= 13
0.8
!- Analytical Solution
0.7
tion
Apex I
of a ytical
ion at 0.33
S
0 O.6 f
0
Apex location
of data for Sr= 3.
at -0.45
0.4
03
0.2
0.1
0
0.1
0.2
0.7
0.6
0.5
0.4
0.3
Lattice node X-axis position normalized to Xf
0.8
0.9
1
Figure 4.6 Graph showing displacement along lattice face for different values of Sr*.
Each set of location data of the lattice corresponds to a particular combination of yi*,
X* and Sr* and is fitted to a
4 th
degree polynomial using a least squares fit. The purpose of
fitting the data to the polynomial is to smooth out the irregulaties in the curve seen in Figure
4.6. The degree of the polynomial was chosen as four because the lattice had four boundary
conditions like the schematic in Figure 4.5. The data is normalized to X/* and Aymax prior to
fitting. The quality of the fit is calculated using equation (4.3) , the formula for coefficient
.
of determination R2
R2
1
YdataYfit
ZYdata -
69
Ydata
(4.3)
The R 2 value for all the datasets are greater than 0.9. The X-axis values of the
datasets are normalized and centered so that the midpoint of X;* is located at 0. The
symmetry value a is the distance from the midpoint at 0 to the location of the apex of each
curve, normalized to Xf. The value a was calculated for each data set and plotted versus X;*
and Sr* . The results are grouped accordion to yi*, and presented in Figure 4.7, Figure 4.8,
Figure 4.9 and Figure 4.10.
S=90"
0.5:
Xf =0.916
0.4
-
-X
0512-
-X
=0.816
0.3
---
0.2
--- X =0.613
0. 1
-
= 0715
0
-0.2
-0.3
-0.4
-0.5
0
10
40
30
20
S
Figure 4.7 Symmetry results for all lattice datasets with
70
(
= 90 degrees.
50
60
, = 105
05
X =0.916
0.4
-
0.3
X- =0.816
--- X =0.715
=0.613
0.2
j---X
0.1
[..--X =0.512
-0 3
0 4--------
-0.3:
-0.41
-0.5
0
10
20
40
30
50
60
S
Figure 4.8 Symmetry results for all lattice datasets with 7* = 105 degrees.
Y = 120'
0.5
X =0.916i
0.4
--- X =0.816
0.3
x =0.715
0.2
--- X = 0.613
---
=0
.
0.1
0
-0. 1
---------------
-0.2
-0.3
-0.4~
-0.5
0
10
20
30
40
50
S
Figure 4.9 Symmetry results for all lattice datasets with 7* = 120 degrees.
71
60
12
=135"
0.5
-
--
tXt =0.916
0.41
X= 0 816
0.3
--- X =0715
0.2
--- x
0 .613
--- X
05121
0.1
0.
-
X
-0.2
-0.3
-0.5
- -
-
0
10
20
-
-0.4
40
30
50
60
S
Figure 4.10 Symmetry results for all lattice datasets with 7i*= 135 degrees.
Figure 4.7, Figure 4.8, Figure 4.9 and Figure 4.10 indicate the trend presented by
Figure 4.6: that symmetry decreases as Sr* increases. The graphs also show that at yi* of 90
and 110 degrees, there is convergence towards a single value of a at the extreme values of
Sr* = 0.64 and 64. In the graphs corresponding to yi*
120 and 135 degrees, the data has a
wider spread. The average values and deviation from the average of a for each value of Sr*
in the graphs are summarized in Table 4.1.
72
*
Table 4.1 a averaged across S,* for each value of 7
a averaged across Sr
Sr
-*
(degrees)
Standard deviation
90
90''6
0.
90
0.070463
105
64
0.12952
0.018421
105
0.6
0.01356
0.009844
«2
120
120
135
64
-0.11071
0.052187
135
0.6
-0.01545
0.021688
The observations were made regarding the information in Table 4.1:
" The average value for a was one order of magnitude less for a two order of
magnitude decrease in Sr* for all yi*.
" The deviation increased by at least a factor of 2 for a two order of magnitude
increase in Sr* for all yj*.
* At
y*
= 90 degrees, the curve corresponding to X;* = 0.93 was relatively flat. The
average value of a is 0.17304 with a standard deviation of 0.0007 across all values
of Sr* for
*i = 90 degrees. This may be because in this lattice, yP*= /. This meant
that the strain energy from folding EK was 0. This indicates that a is inversely
proportional to EK.
73
4.3 Chapter Summary
The twist response Oe* of the lattice to angular wall error 9o * was measured as the
stiffness ratio Sr* and initial fold angle yi* was modified. The magnitude Oe*increased as Sr*
increased and yi*
The symmetry of the shape of the lattice about the X* midpoint was also
measured. A
degree polynomial analytical solution to the shape of the lattice is
4 th
presented. The analytical solution was plotted against the final X-axis and Y-axis data of
lattices to show that as Sr* increased, the data approached that of the analytical solution. As
Sr* decreased, the data became more symmetric. The symmetry of the lattice is quantified
as the value a, the distance along the actuation direction between the Ay.ax point and the
midpoint of X/, normalized to X*. A value of 0 means that the shape is symmetric. a was
averaged across all values of X* for the maximum and minimum value Sr* for each value
of yi*. The average value of a decreased by one order of magnitude when S* decreased by
two orders of magnitude. The variation of a increased by a factor of 2 when Si* increased
by two orders of magnitude. The results also showed that the magnitude of a depended on
the difference between the initial and final fold angle, Ay.
74
CHAPTER
5
CONCLUSION
5.1 Introduction
The panels of periodic lattices become misaligned when an angular twist error is
applied to the constrained lattice edges. The purpose of this research was to understand
how design parameters in periodic lattices change the shape of the lattice distortion in
response to this angular error. The import to engineers is that they may use this knowledge
to deterministically design and optimize the performance of periodic lattices used as
assembly scaffolds and augment pre-existing 2D manufacturing techniques to create 3D
heterogeneous structures such as human organs for transplant patients and micro-batteries.
The impact is that these lattices are envisioned to enable the production of human organs
for transplant, saving 23,000 lives per year. The micro battery industry is estimated to be
worth a $1.5bn industry by 2017.
The research lays the groundwork for how to constrain these devices, how to actuate
them with walls external to the lattice and how to modify the design parameters in order to
reduce the sensitivity of the lattice to geometric errors from these walls. Current research
does not address how stiffness ratios interact with the strain energy added during folding
to increase and distort the lattice response to the errors of the lattice constraints.
5.2 Summary
Periodic lattices consist of a single folded unit that is repeated along one or two
orthogonal directions. Two examples are the Miura Ori lattice and the Accordion lattice.
The actuation direction for these two lattices runs parallel to the direction that the lattice
unit is repeated in. Thus, adding more units will not change the actuation direction and a
single actuating step can fold all the lattice units simultaneously.
Stiff hinges lead to buckling within the lattice. Walls above and below the lattice
limit the buckling displacement. Panel compliance results in uneven folding completion
when the lattices are folded through point contacts on the edge. This is because panel
compliance decreases how efficiently force is transmitted from the actuation points to
hinges furthest away. Folding completion was made uniform was changing these point
contacts into line contacts through the use of externally actuating walls.
Larger stiffness ratios between the panels and hinges lead to behavior that more
closely resemble the rigid body models of these lattices. The ratio has geometrical and
elastic components. A survey of possible materials to be used for scaffolds in the
76
application of tissue fabrication showed that elastic moduli of scaffold materials can span
several orders of magnitude. Furthermore, the elastic moduli of many of these polymers
are tuneable. Polyphenelene sulphide polymers, a polymer used in tissue scaffolds, can
have elastic moduli spanning over two orders of magnitude.
The walls constraining the lattice can have six errors relative to each other.
However, allowing the lattice to move freely on the face of the walls isolates three errors
from the lattice. The assumption of a line contact between the actuating walls and the lattice
isolates the lattice from another. Of the remaining two, one is in the direction of the
actuating wall and thus only results in the lattice appearing over or under folded. The last
is an angular error that causes the lattice panels to twist, resulting in lattice misalignment
The sensitivity of the lattice twist response to this angular wall error was modelled
and analyzed. An Accordion with six units was chosen to be studied in order to isolate the
center of the accordion from edge effects. A Buckingham pi analysis of the lattice twist
response Oe* to the angular wall error was calculated to be dependent on the initial fold
angle yi* , the angular wall error p,* and the ratio of torsional stiffnesses of the panel and
hinge S,*. A finite element analysis was used to quantify the Buckingham pi equation.
The first step in the simulation was to apply the angular wall error. The second step
was to actuate the wall to different lattice lengths X* in order to attempt to fold the lattice.
Then the lattice was folded as it would be if used as an assembly scaffold. Convergence
analysis of the element sizes of showed the maximum displacement of the lattice due to
twist, Aymax, converging with finer meshes.
77
I
The simulation study measured Aymax as yi*, Sr* and Xf* were varied. The lattice twist
response Oe* is calculated as the ratio of Aymax and X* .Results from the simulation study
analysis showed that as yi* increased and as Sr*, that is, as the lattice began folding from a
less folded state, the magnitude of the twist response Oe* of the lattice increased. The twist
error was also not symmetric about the midpoint of X*. The data was fitted to a
4 th
degree
polynomical with residuals greater than 0.9. The results showed that symmetry increased
with decreasing values of S,*. It also showed that the symmetry depends on the difference
change in fold angle Ay.
5.3 Future Work
Future work needs to be done to confirm the FEA results with experimental
scaffolds. The analysis needs to be repeated with the Miura Ori pattern: both in FEA and
with experimental results. These experimental results require that an imaging apparatus be
built to measure the magnitude and shape of the lattice after it is actuated. This analysis
assumed that the upper and lower external walls that constrained the buckling displacement
were ideal. The impact of these errors must also be further studied. The relationship
between a, Oe* and the panel alignment error magnitude and distribution within the lattice
needs to be quantified.
78
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80
Appendix
A
Data Processing MATLAB Code
This appendix contains the MATLAB code used to do the following:
*
Import text files that contain the location and displacement results of the
finite element analysis
" Process the data from the text files to get magnitude and X-axis and Y-axis
location of twist response Oe*.
*
Produce plots in chapter 4
The function mainXloc.m is the function for producing the plots in Figure 4.7,
Figure 4.8, Figure 4.9 and Figure 4.10 for asymmetry a. The function mainTwistMag.m is
the function for producing the plots in Figure 4.2 and Figure 4.3 of twist response
magnitude Oe*. LatticeNodePlot.m produces the plots in Figure 4.6.
function() = mainTwistMag()
%Main function for generating plots of
twist
response magnitude
%% Add folders of text files
to path
addpath('July 20 - Final Data')
addpath('July 31 - Final Data 2')
addpath('Aug 2 - 50mm Data')
%%
Import the data from the text files
%-[FoldAngle,
YMax90
YMax105
YMax120
YMax135
Ratio,
XDisp,
Node# YDisp XLoc YLoc
ZLoc]
YDispDataAng90;
=
YDispDataAnglO5;
YDispDataAng120;
YDispDataAng135;
=
=
=
%% Arrange
data
in
grid
for
plotting
surface
plots
[m,n] = size(YMax9O);
c = 5;
XOData = zeros(24,n);
X50Data = zeros(24,n);
X10OData
=
zeros(24,n);
X150Data = zeros(24,n);
X200Data = zeros(24,n);
XOData(1:6,:)
= YMax90(1:c:end,:);
XQData(7:12,:) = YMaxl05(1:c:end,:);
XQData(13:18,:) = YMax120(1:c:end,:);
XQData(19:24,:) = YMax135(1:c:end,:);
X50Data(1:6,:)
=
YMax90(2:c:end,:);
X5QData(7:12,:) = YMaxl05(2:c:end,:);
X5OData(13:18,:)
= YMaxl20(2:c:end,:);
X50Data(19:24,:)
= YMax135(2:c:end,:);
X10OData(1:6,:) = YMax90(3:c:end,:);
X10OData(7:12,:)
= YMaxl05(3:c:end,:);
X10OData(13:18,:) = YMax120(3:c:end,:);
X10OData(19:24,:) = YMax135(3:c:end,:);
X15OData(1:6,:) = YMax90(4:c:end,:);
X15OData(7:12,:)
= YMaxl05(4:c:end,:);
X15OData(13:18,:) = YMaxl20(4:c:end,:);
X15OData(19:24,:) = YMaxl35(4:c:end,:);
X200Data(1:6,:) = YMax90(5:c:end,:);
X200Data(7:12,:)
= YMaxl05(5:c:end,:);
X200Data(13:18,:) = YMax120(5:c:end,:);
X200Data(19:24,:) = YMax135(5:c:end,:);
LRatio = 16/25; % factor for Convert elasic Ratio to stiffness Ratio
%% Calculate twist response pheta_e.
Plot Surface plots
[X,Y,Z]=SurfGenADist(XOData);
Z = atand(Z./(454*0.5)); %Calculate Twist
mesh (X, Y*LRatio, Z)
hold on
[X,Y,Z]=SurfGenADist(X5OData);
Z = atand(Z./(404*0.5)); %Calculate Twist
mesh(X,Y*LRatioZ)
[X,Y,Z]=SurfGenADist(X1OOData);
Z = atand(Z./(354*0.5)); %Calculate Twist
mesh(X,Y*LRatioZ)
[X,Y,Z]=SurfGenADist(X150Data);
Z = atand(Z./(304*0.5)); %Calculate Twist
mesh(X,Y*LRatioZ)
[X,Y,Z]=SurfGenADist(X200Data);
Z = atand(Z./(254*0.5)); %Calculate Twist
mesh(X,Y*LRatioZ)
(Degrees)','FontSize
ylabel('{Sr}^*',
24
'
xlabel('\gamma_i
)
hold off
shading interp
'FontSize', 24)
zlabel('\thetae (Degrees)', 'FontSiz ', 24)
title({'Magnitude of lattice twist er or \thetae as function of
{Sr}^* .'
...
'Each surface is for difference value of Xf'})
\gamma-i
and
set(gca, 'FontSize',20)
This
section is to
read additional data for the 200mm plot and create
200mm plot
%Format for matlab data is as follows
YDisp XLoc YLoc ZLoc]
YMax97_5 = YDispDataAng97_5;
YMax112_
= YDispDataAng112_5;
AdData
=
->
[Fold Angle,
Ratio,
AdData200mm;
%% Uncomment this section to get data for Xf
psize = 15;
Z = X200Data(1:6,5);
Z = atand(Z./(254*0.5));
plot(X20Data(1:6,2)*LRatio,Z,'k.-
= 254mm
viarkerSize',psize)
hold on
Z = YMax97_5( :,5);
Z = atand(Z./ (254*0.5));
plot(YMax97_5 (:,2)*LRatio,Z, 'b.-', 'MarkerSize',psize)
Z = X200Data( 7:12,5);
Z = atand(Z./ (254*0.5));
plot(X200Data (7:12,2)*LRatio ,Z,'g.-','MarkerSize',psize)
Z = YMax112_5 (:,5);
Z = atand(Z./ (254*0.5));
plot(YMax112_5 (:,2)*LRatio,Z ,'r.-','MarkerSize',psize)
Z = X200Data(13:18,5);
Z = atand(Z./(254*0.5));
plot(X200Data(13:18,2)*LRati o,Z,'m.-','MarkerSize',psize)
Z = X200Data(19:24,5);
Z = atand(Z./(254*0.5));
plot(X200Data(19:24,2)*LRati O, Z, 'c.-','MarkerSize',psize)
XDisp,
Node#
the
xlabel({Sr}^*', 'FontSize', 24)
ylabel('\theta e (Degrees)', 'FontSize', 24)
title('Magnitude of lattice twist error \thetae as function of
{Sr)^* for Xf
= 0.51')
legend('\gamma_i
=
\gammai and
90A{\circ},'\gammai = 97.5^{\circ}),'\gamma i
105A{\circ}',...
'\gamma-i = 112.5^{\circ}', '\gamma-i =
135A{\circ}','FontSize',24);
set(gca,
'FontSize',20)
hold off
120^{\circ}', '\gammai =
=
......
..
..
function() = mainXLoc()
%Main function for calculating symmetry of datatsets
to path
%-% Add folders of text files
addpath('July 20 - Final Data')
addpath('July 31 - Final Data 2')
addpath('Aug 2 - 50mm Data')
%% Import, process text files
for asymmetry values
clC
Ang900ut = (XLocAng90);
Ang90YmaxLoc = Ang900ut(:,1:6)-0.5;
Ang90Res = Ang900ut(:,7:12);
AnglQ50ut = (XLocAnglO5);
Ang105YmaxLoc = Ang105Out(:,1:6)-0.5;
Ang105Res = AnglO5Out(:,7:12);
Ang1200ut = (XLocAngl20);
Angl20YmaxLoc = Angl200ut(:,1:6)-0.5;
Ang120Res = Angl200ut(:,7:12);
Ang1350ut = (XLocAng135);
Ang135YmaxLoc = Ang1350ut(:,1:6)-0.5;
Ang135Res = Angl350ut(:,7:12);
%% Plot asymmetry values
SRatio = [100 50 20 10 5 1] *16/25;
psize = 3;
figure
plot(SRatio, Ang90YmaxLoc(l,:)
hold on
,'x',
plot(SRatio,
plot(SRatio,
plot(SRatio,
plot(SRatio,
hold off
,'r-.','LineWidth',psize)
Ang90YmaxLoc(2,:)
Ang90YmaxLoc(3,:)
Ang90YmaxLoc(4,:)
Ang90YmaxLoc(5,:)
title('{\gamma_i}A*
'LineWidth',psize)
,'k-.','LineWidth',psize)
,'b-.',
'LineWidth',psize)
,'g-.','LineWidth',psize)
= 90A{\circ}1,
'FontSize',
20)
'FontSize', 24)
ylabel('\alpha',
xlabel('{S_r}^*', 'FontSize', 20)
axis([0 65 -0.5 0.5])
legend({Xf}^* = 0.916','{X_f}A* = 0.816','{X_f}A*= 0.715,'{Xf}*
0.613','{X_f}^* = 0.512','FontSize',20);
% v = get(h,'title');
% set(v, 'string',
'X_f', 'FontSize',20);
set(gca,'FontSize',20)
figure
plot(SRatio, Ang105YmaxLoc(1,:)
hold on
plot(SRatio, Angl05YmaxLoc(2,:)
,'x', 'LineWidth',psize)
,'r-.',
'LineWidth',psize)
=
plot(SRatio,
plot(SRatio,
plot(SRatio,
Angl05YmaxLoc(3,:)
Angl05YmaxLoc(4,:)
Angl05YmaxLoc(5,:)
'k-., 'LineWidth',psize)
b-.', 'LineWidth',psize)
g-.,
'LineWidth',psize)
,
,
,
hold off
title('{\gammai}^* =
105A{\circ}',
'FontSize',
20)
ylabel
\alpha',
'FontSize', 24)
'FontSize', 20)
{Sr}^*'
axis ([0 65 -0.5 0.5])
legend '{X-f}^* =0.916','{Xf}^* = 0.816','{Xf}^*= 0.715','{Xf}^*
0.613 ', {X f}^* = 0.512','FontSize',20);
% v = get(h,'title');
xlabel
% set(v,'string','Xf','FontSize',20);
set(gca, 'FontSize',20)
figure
plot(SRatio,
Angl20YmaxLoc(l,:)
'x','LineWidth',psize)
Angl20YmaxLoc(2,:)
Angl20YmaxLoc(3,:)
Angl20YmaxLoc(4,:)
Angl20YmaxLoc(5,:)
'r-.','LineWidth',psize)
'k-.','LineWidth',psize)
'b-.', 'LineWidth',psize)
'g-.','LineWidth',psize)
hold on
plot(SRatio,
plot(SRatio,
plot(SRatio,
plot(SRatio,
hold off
title('{\gammai}A* = 120A{\circ}',
'FontSize', 20)
'FontSize', 24)
ylabel('\alpha',
xlabel('{S_rl*', 'FontSize', 20)
axis([0 65 -0.5 0.5])
legend('{X_f}^* = 0.916','{X-f}^* = 0.81 6','{X_f}^*=
0.613','{X_f}^* = 0.512','FontSize',20);
0.715','{X_f}'* =
set(gca, 'FontSize',20)
figure
plot(SRatio,
Angl35YmaxLoc(l,:)
,'x','LineWidth',psize)
Angl35YmaxLoc(2,:)
Angl35YmaxLoc(3,:)
Angl35YmaxLoc(4,:)
Angl35YmaxLoc(5,:)
'r-.', 'LineWidth',psize)
hold on
plot(SRatio,
plot(SRatio,
plot(SRatio,
plot(SRatio,
hold off
title('{\gammai}^* = 135^{\circ}
ylabel('\alpha',
'FontSize', 20)
xlabel('{S-r}^*',
'FontSize', 20)
'k-.','LineWidth',psize)
'b-.', 'LineWidth',psize)
,'g-.', 'LineWidth',psize)
',
axis([0 65 -0.5 0.5])
legend('{X_f}A* = 0.916','{Xf}A* =
0.613','{Xf}A* = 0.512','FontSiz
set(gca, 'FontSize',20)
'FontSize', 20)
0.816','{Xf}^*= 0.715',{Xf}^*
= LatticeNodePlot()
function()
A135R100T100X =
'8_11_2015 Disp and Twist 135 Deg 100 Ratio X Disp 100-
0_1.txt';
A135R100T100Y =
18_11_2015 Disp and Twist 135 Deg 100 Ratio Y Disp 100-
0_1.txt';
A135R10OT200X =
0_1.txt';
A135R100T200Y =
'8_11_2015 Disp and Twist 135 Deg 100 Ratio X Disp 200'8_11_2015 Disp and Twist 135 Deg 100 Ratio Y Disp 200-
0_1.txt';
A135R5OT100X =
'8_11_2015 Disp and Twist 135 Deg 50 Ratio X
Disp 100-
0_1.txt';
A135R5OT100Y =
0_1.txt';
A135R50T200X =
'8_11_2015 Disp and Twist 135 Deg 50 Ratio Y Disp 100'7_20_2015 Disp and Twist 135 Deg 50 Ratio X Disp 200-
0_1.txt';
A135R50T200Y =
'7_20_2015 Disp and Twist 135 Deg 50 Ratio Y Disp 200-
0_1.txt';
A135R2OT100X =
'7_20_2015 Disp and Twist 135 Deg 20 Ratio X Disp 100-
0_1.txt';
A135R2OT100Y =
'7_20_2015 Disp and Twist 135 Deg 20 Ratio Y Disp 100-
0_1.txt';
A135R20T200X =
'7_20_2015 Disp and Twist 135 Deg 20 Ratio X Disp 200-
0_1.txt';
A135R20T200Y =
'7_20_2015 Disp and Twist 135 Deg 20 Ratio Y Disp 200-
0_1.txt';
A135R5T100X
A135R5T100Y
A135R5T200X
A135R5T200Y
A135R1T100X =
A135R1T1OQY =
A135R1T200X =
A135R1T200Y =
'7_20_2015
'7_20_2015
'7_20_2015
'7_20_2015
Disp
Disp
Disp
Disp
and
and
and
and
Twist
Twist
Twist
Twist
135
135
135
135
Deg
Deg
Deg
Deg
5 Ratio X Disp 100-0_1.txt';
5 Ratio Y Disp 100-0_1.txt';
'7_20_2015
'7_20_2015
'8_11_2015
'8_11_2015
Disp
Disp
Disp
Disp
and
and
and
and
Twist
Twist
Twist
Twist
135
135
135
135
Deg
Deg
Deg
Deg
1
1
1
1
5 Ratio X Disp 200-0_1.txt';
5 Ratio Y Disp 200-0_1.txt';
Ratio X Disp 100-0_1.txt';
Ratio Y Disp 100-0
1.txt';
Ratio X Disp 200-0 1.txt';
Ratio Y Disp 200-0_1.txt';
%The following two datasets should have the same node
DataTestY = sldwrksTxtImp(A135R100T200Y,9);%[node# YDisp XLoc
DataTestX = sldwrksTxtImp(A135R100T200X, 8) ;%[node# XDisp XLoc
YDispLocR100 = YatXLoc(DataTestX,DataTestY);
YLoc
YLoc
ZLoc]
ZLoc]
= sldwrksTxtImp (A135R20T200Y, 10) ;% [node# YDisp XLoc
YLoc
ZLoc]
DataTestY
DataTestX = sldwrksTxtImp(A135R20T200X,9);%
YDispLocR20
[node#
XDisp XLoc YLoc ZLoc]
= YatXLoc (DataTestX, DataTestY);
DataTestY = sldwrksTxtImp(A135R1T200Y,9);%[node#
DataTestX = sldwrksTxtImp(A135R1T200X,8);%[node#
YDispLocR5 = YatXLoc (DataTestX, DataTestY);
plot(YDispLocR100(:,1)/330,
hold on
YDisp XLoc YLoc
XDisp XLoc YLoc
YDispLocR100(:,2),'b.')
ZLoc]
ZLoc]
plot(YDispLocR20(:,1)/330, YDispLocR20(:,2),'g.')
plot(YDispLocR5(:,1)/330, YDispLocR5(:,2),'c.')
%solveTwistTheory(330,0.1)
hold off
axis([O 1 0 1])
legend('Stiffness Ratio:
40','Stiffness Ratio: 4 ','Stiffness Ratio:
2', 'Theoretical Equation')
xlabel('Lattice
Node Position
ylabel('Y
Displacement due
to
along Actuation Direction
(Normalized) ')
Angular Error (Normalized)
')
function[XMLoc, rsq] = findYMaxLocFit(XData,YData)
%This function reads tyhe XData and YData arrays
%-1) Zero X location and add displacement to find final X location
%2) Find Y max data for one side of lattice
%3) Normalize X location and Y displacement
%'4) Fit data to polynomial
%5) Find residual
%6) Output location of center and residual
%6% Zero X location and add displacement to find final X location
BaseX = min(XData(:,3));
XData(:,3) = XData(:,3)- BaseX;
FinXLocAll = XData(:,3) +(XData(:,2));
%% Find Y max data for one side of lattice
R25Index = YData(:,4)==-25;
YData(R25Index,:) = [];
[m,n] = size(YData);
FinXLoc = zeros(1,m);
for k = 1:m
index = YData(k,l);
XIndex = find(XData(:,l) == index);
if isempty(XIndex) == 1
FinXLoc(k) = 0;
YData(k,l) = 0;
else
FinXLoc(k) = FinXLocAll(XIndex);
end
end
ZIndex = YData(:,l)
YData(ZIndex,:)
FinXLoc(ZIndex)
=
==
0;
[1;
=
YMax = MaxYDispLoc(YData);
YMax = YMax(1,2);
%% Normalize X location and Y displacement
XMaxDisp = max(FinXLoc) - 20; %Find length of lattice (location of node at
point that lattice touches wall)
XNorm = FinXLoc./XMaxDisp;%Normalize to lattice length
YNorm = YData(:,2)./YMax; %Normalize Y displacement
WallIndex = XNorm > 1;%find side wall nodes
XNorm(WallIndex) = []; %remove wall nodes
YNorm(WallIndex) = [;
%% Fit data to polynomial
p = polyfit(XNorm',YNorm,4);
%Find true max point form fitted
YFit = polyval(p,XNorm);
maxYFit = max(YFit);
MaxIndex =
find(YFit == maxYFit);
MaxIndex = MaxIndex(l);
YMLoc = YFit(MaxIndex);
points
%%'6
Find Residual
yresid = YNorm'
-
YFit;
SSresid
=
sum(yresid.^2);
SStotal
=
(length(YNorm)-1)
* var(YNorm);
%% Output location of YMax and residual
XMLoc = XNorm(MaxIndex);
rsq = 1 - SSresid/SStotal;
function
[dataout]
= sldwrksTxtImp(fname,num)
%sldwrksTxtImp imports a solidworks generated text
%1) Find start of data
%2) Extract first 5 columns
%3) Convert read data to array
%Input: fname. name of file
%num: unused
%% Find start
file:
of data
#
fid = fopen(fname); %Import Text file
s = textscan(fid, '%s %*[^\n]'); %look only at first column -> node
ind = find(strcmp(s{l}, 'Node')); %find index of for column label ('node').
%% Extract numbers
from
.txt file
fid = fopen(fname);%need to reopen the file name or else textscan returns
empty
DataCells = textscan(fid,'%f %f %f %f %f
%* [^\n]'I,'delimiter'
fclose('all');
,'\t'
,'HeaderLines'
, (ind+2))
%% Get X,Y,Z location of node with max Y
arrary
node
disp
XLoc
YLoc
=
=
=
=
ZLoc
= cell2mat(DataCells(5));
cell2mat(DataCells(l));
cell2mat(DataCells(2));
cell2mat(DataCells(3));
cell2mat(DataCells(4));
dataout =
[node disp XLoc YLoc ZLoc];
location and magnitude.
Convert to
function
[YOut]
= XLocAng90()
A90R100TOX = '7_20_2015 Disp and Twist 90 Deg 100 Ratio X
A90R100TOY = '7_20_2015 Disp and Twist 90 Deg 100 Ratio Y
A90R100T5QX = '8_2_2015 Disp and Twist 90 Deg 100 Ratio X
A90R100T50Y = '8_2_2015 Disp and Twist 90 Deg 100 Ratio Y
A90R100T100X = '7_20_2015 Disp and Twist 90 Deg 100 Ratio
Disp 0-0_1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-
0_1.txt';
A90R100T100Y =
'7_20 2015 Disp and Twist 90 Deg 100 Ratio Y Disp 100-
0_1.txt';
A9OR100T15QX =
'8_11_2015 Disp and Twist 90 Deg 100 Ratio X Disp 150-
0_1.txt';
A90R100T150Y =
'8112015 Disp and Twist 90 Deg 100 Ratio Y Disp 150-
0_1.txt';
A90R100T200X =
'7_20_2015 Disp and Twist 90 Deg 100 Ratio X Disp 200-
0_1.txt';
A90R100T200Y =
'7_20 2015 Disp and Twist 90 Deg 100 Ratio Y Disp 200-
0_1.txt';
A90R50TOX =
'8_11_2015 Disp and Twist 90 Deg 50 Ratio X Disp 0-0_l.txt';
A90R50TOY = '8_11_2015 Disp and Twist 90 Deg 50 Ratio Y
A90R5QT50X = '8_2_2015 Disp and Twist 90 Deg 50 Ratio X
A90R5QT50Y = '8_2_2015 Disp and Twist 90 Deg 50 Ratio Y
A90R5OT100X = '8_11_2015 Disp and Twist 9 0 Deg 50 Ratio
A90R5OT100Y = '8_11_2015 Disp and Twist 9 0 Deg 50 Ratio
A90R5OT15OX = '8_11_2015 Disp and Twist 9 0 Deg 50 Ratio
A90R50T150Y = '8_11_2015 Disp and Twist 9 0 Deg 50 Ratio
A90R5OT200X = '8_11_2015 Disp and Twist 9 0 Deg 50 Ratio
A90R5OT200Y = '8_11_2015 Disp and Twist 9 0 Deg 50 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-0_1.txt';
Y Disp 100-0_1.txt';
X
Y
X
Y
Disp
Disp
Disp
Disp
150-0 1.txt';
150-0_1.txt';
200-0_1.txt';
200-0_1.txt';
A90R20TOX =
'8_11_2015 Disp and Twist 90 Deg 20 Ratio X Disp 0-0 1.txt';
A90R20TOY =
'8_11_2015 Disp and Twist 90 Deg 20 Ratio Y Disp 0-0_1.txt';
A90R2OT50X = '8_11_2015 Disp and Twist 90 Deg 20 Ratio X Disp 50-0_1.txt';
A90R2QT50Y = '8_11_2015 Disp and Twist 90 Deg 20 Ratio Y Disp 50-0_1.txt';
A90R2OT100X = '8_11_2015 Disp and Twist 90 Deg 20 Ratio X Disp 100-
0_1v2.txt';
A90R2OT100Y =
'8_11_2015 Disp and Twist 90 Deg 20 Ratio Y Disp 100-
0_1v2.txt';
A90R20T150X
A90R20T150Y
A90R2OT200X
A90R2OT200Y
=
=
=
=
'8_11_2015 Disp and Twist 90 Deg 20 Ratio X Disp 150-0_1.txt';
'8_11_2015 Disp and Twist 90 Deg 20 Ratio Y Disp 150-0_1.txt';
'8_11_2015 Disp and Twist 90 Deg 20 Ratio X Disp 200-0_1.txt';
'8_11_2015 Disp and Twist 90 Deg 20 Ratio Y Disp 200-0_1.txt';
A90R10TOX = '8_11_2015 Disp and Twist 90 Deg 10
A90R10TOY = '8_11_2015 Disp and Twist 90 Deg 10
A90R1OT50X = '8_2_2015 Disp and Twist 90 Deg 10
A90R10T50Y = '8_2_2015 Disp and Twist 90 Deg 10
A90R1OT100X = '7_20_2015 Disp and Twist 90 Deg
A90R1OT100Y = '7_20_2015 Disp and Twist 90 Deg
A90RlT15QX = '7 20 2015 Disp and Twist 90 Deg
A90R10T150Y = '7_20_2015 Disp and Twist 90 Deg
A90R1OT200X = '7_20_2015 Disp and Twist 90 Deg
A90R1OT200Y = '7_20_2015 Disp and Twist 90 Deg
A90R5TOX =
A90R5TOY =
Ratio X Disp 0-0_1.txt';
Ratio Y Disp 0-0_1.txt';
Ratio X Disp 50-0_1.txt';
Ratio Y Disp 50-0_1.txt';
10 Ratio X Disp 100-0_l.txt';
10 Ratio Y Disp 100-0_l.txt';
10 Ratio X Disp 150-0 1.txt';
10 Ratio Y Disp 150-0_1.txt';
10 Ratio X Disp 200-0_1.txt';
10 Ratio Y Disp 200-0_1.txt';
'8 11_2015 Disp and Twist 90 Deg 5 Ratio X
'8 11_2015 Disp and Twist 90 Deg 5 Ratio Y
Disp 0-0_1.txt';
Disp 0-0_1.txt';
A90R5T50X =
A90R5T50Y =
'8 2 2015
'8 2 2015
Disp and Twist
Disp and Twist
90 Deg 5 Ratio X Disp 50-0_1.txt';
90 Deg 5 Ratio Y Disp 50-0_1.txt';
A90R5T100X =
A90R5T100Y =
A90R5T15OX =
'7_20_2015 Disp and Twist 90 Deg 5 Ratio X Disp 100-0_1.txt';
'7 20_2015 Disp and Twist 90 Deg 5 Ratio Y Disp 100-0_1.txt';
'7 20_2015 Disp and Twist 90 Deg 5 Ratio X Disp 150-0_1.txt';
A90R5T150Y =
A90R5T200X =
A90R5T200Y =
'7 20_2015
A90R1TOX =
A90R1TOY =
'7_20_2015 Disp and Twist
'7_20_2015 Disp and Twist
A90R1T5OX =
A90R1T50Y =
A90R1T100X
A90R1T100Y
A90R1T15OX
A90R1T15OY
A90R1T200X
A90R1T200Y
Disp and Twist
=
=
=
=
=
=
90 Deg 5 Ratio Y Disp
150-0_1.txt';
'7 20 2015 Disp and Twist 90 Deg 5 Ratio X Disp 200-0 1.txt';
'7_20_2015 Disp and Twist 90 Deg 5 Ratio Y Disp 200-0_1.txt';
90 Deg 1 Ratio X
90 Deg 1 Ratio Y
'8_2_2015 Disp and Twist 90 Deg 1 Ratio X
'8 2 2015 Disp and Twist 90 Deg 1 Ratio Y
'7_20_2015 Disp and Twist 90 Deg 1 Ratio
'7 20_2015 Disp and Twist 90 Deg 1 Ratio
'7 20_2015 Disp and Twist 90 Deg 1 Ratio
'7 20_2015 Disp and Twist 90 Deg 1 Ratio
'8 11_2015 Disp and Twist 90 Deg 1 Ratio
'8_11_2015 Disp and Twist 90 Deg 1 Ratio
Disp 0-0_1.txt';
Disp 0-0_1.txt';
Disp 50-0 1.txt';
Disp 50-0_1.txt';
X Disp 100-0_1.txt';
Y Disp 100-0_1.txt';
X Disp 150-0_1.txt';
Y Disp 150-0_1.txt';
X Disp 200-0_1.txt';
Y Disp 200-0_1.txt';
%Each pair of datasets share the same subset of nodes
R100TOY = sldwrksTxtImp(A9OR100TOY,9);%[node# YDisp XLoc YLoc ZLocl
R100TOX = sldwrksTxtImp(A9OR100TOX,9);%[node# XDisp XLoc YLoc ZLocl
R100T5OY = sldwrksTxtImp(A9OR100T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R100T50X = sldwrksTxtImp(A9OR100T50X,9);%[node# XDisp XLoc YLoc ZLoc]
R10OT100Y = sldwrksTxtImp(A9QR100T100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R100T100X = sldwrksTxtImp(A9OR100T100X,9);% [node# XDisp XLoc YLoc ZLoc]
R100T150Y = sldwrksTxtImp(A9OR100T15QY,9);%[node# YDisp XLoc YLoc ZLoc]
R100T15OX = sldwrksTxtImp(A9OR100T15OX,9);%[node# XDisp XLoc YLoc ZLoc]
R100T200Y = sldwrksTxtImp(A9OR100T200Y,9);%[node# YDisp XLoc YLoc ZLoc]
R100T200X = sldwrksTxtImp(A9OR100T200X,9);% [node# XDisp XLoc YLoc ZLocl
R50TOY = sldwrksTxtImp(A9OR50TOY,9);%[node# YDisp XLoc YLoc ZLoc]
R50TOX = sldwrksTxtImp(A9OR50TOX,9);%[node# XDisp XLoc YLoc ZLoc]
R50T5OY = sldwrksTxtImp(A9OR5OT50Y,9);%[node# YDisp XLoc YLoc ZLocl
R5QT50X = sldwrksTxtImp(A9OR5OT50X,9);%[node# XDisp XLoc YLoc ZLocl
R50T100Y = sldwrksTxtImp(A9OR5OT100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R50T100X = sldwrksTxtImp(A9R5OT100X,9);%[node# XDisp XLoc YLoc ZLocl
R5OT150Y = sldwrksTxtImp(A9OR5OT15OY,9);%[node# YDisp XLoc YLoc ZLocl
R50T150X = sldwrksTxtImp(A90R5OT150X,9);%[node# XDisp XLoc YLoc ZLoc]
R50T200Y = sldwrksTxtImp(A9OR5OT200Y,9);%[node# YDisp XLoc YLoc ZLocl
R50T200X = sldwrksTxtImp(A9OR5OT200X,9);%[node# XDisp XLoc YLoc ZLocl
R20TOY = sldwrksTxtImp(A9OR20TOY,9);%[node# YDisp XLoc YLoc ZLocl
R20TOX = sldwrksTxtImp(A9OR20TOX,9);%[node# XDisp XLoc YLoc ZLoc]
R20T50Y = sldwrksTxtImp(A9OR2OT50Y,9);%[node# YDisp XLoc YLoc ZLocl
R20T50X = sldwrksTxtImp(A9OR2OT50X,9);%[node# XDisp XLoc YLoc ZLocl
R20T100Y = sldwrksTxtImp(A9QR2OT100Y,9);%[node# YDisp XLoc YLoc ZLocl
R20T100X = sldwrksTxtImp(A9OR2OT1OOX,9);%[node# XDisp XLoc YLoc ZLocl
R20T150Y = sldwrksTxtImp(A9OR2OT15OY,9);%[node# YDisp XLoc YLoc ZLocl
R20T150X = sldwrksTxtImp(A9OR2OT15OX,9);%[node# XDisp XLoc YLoc ZLocl
R20T200Y = sldwrksTxtImp(A9OR2OT200Y,9);%[node# YDisp XLoc YLoc ZLocl
R20T200X = sldwrksTxtImp(A9OR2OT200X,9);%[node# XDisp XLoc YLoc ZLocl
R10TOY = sldwrksTxtImp(A9OR1OTOY,9);%[node# YDisp XLoc YLoc ZLoc]
sldwrksTxtImp(A90R1OTOX,9);%[node# XDisp XLoc YLoc ZLoc]
R10T5OY = sldwrksTxtImp(A90R1OT50Y,9);%[node# YDisp XLoc YLoc ZLocl
R1OT50X = sldwrksTxtImp(A90R1OT50X,9);%[node# XDisp XLoc YLoc ZLocl
RlOT100Y = sldwrksTxtImp(A9OR1OT100Y,9);%[node# YDisp XLoc YLoc ZLoc]
RlOT100X = sldwrksTxtImp(A9QR1OT100X,9);%[node# XDisp XLoc YLoc ZLoc]
R1OT150Y = sldwrksTxtImp(A9OR1OT15OY,9);%[node# YDisp XLoc YLoc ZLoc]
R1OT150X = sldwrksTxtImp(A9OR1OT15OX,9);%[node# XDisp XLoc YLoc ZLocl
R1OT200Y = sldwrksTxtImp(A9OR1OT200Y,9);%[node# YDisp XLoc YLoc ZLocl
R1OT200X = sldwrksTxtImp(A9OR1OT20X,9);%[node# XDisp XLoc YLoc ZLoc]
R10TOX =
R5TOY = sldwrksTxtImp(A90R5TOY,9);%[node# YDisp XLoc YLoc ZLoc]
R5TOX = sldwrksTxtImp(A90R5TOX,9);%[node# XDisp XLoc YLoc ZLoc]
R5T50Y = sldwrksTxtImp(A9OR5T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5T5OX = sldwrksTxtImp(A90R5T50X,9);%[node# XDisp XLoc YLoc ZLoc]
R5T100Y = sldwrksTxtImp(A9OR5T100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5T100X = sldwrksTxtImp(A9OR5T100X,9);%[node# XDisp XLoc YLoc ZLoc]
R5T150Y = sldwrksTxtImp(A90R5T150Y,9);%[node# YDisp XLoc YLoc ZLocl
R5T15OX = sldwrksTxtImp(A9OR5T15OX,9);%[node# XDisp XLoc YLoc ZLocl
R5T200Y = sldwrksTxtImp(A9OR5T200Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5T200X = sldwrksTxtImp(A9OR5T20OX,9);%[node# XDisp XLoc YLoc ZLoc]
RiTOY = sldwrksTxtImp(A9OR1TOY,9);%[node# YDisp XLoc YLoc ZLoc]
RITOX = sldwrksTxtImp(A9OR1TOX,9);%[node# XDisp XLoc YLoc ZLoc]
R1T50Y = sldwrksTxtImp(A9OR1T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R1T5OX = sldwrksTxtImp(A9OR1T50X,9);%[node# XDisp XLoc YLoc ZLoc]
RiT1OY = sldwrksTxtImp(A9OR1T100Y,9);%[node# YDisp XLoc YLoc ZLoc]
RiT1OX = sldwrksTxtImp(A9OR1T1OOX,9);%[node# XDisp XLoc YLoc ZLoc]
R1T150Y = sldwrksTxtImp(A9QR1T15OY,9);%[node# YDisp XLoc YLoc ZLoc]
R1T150X = sldwrksTxtImp(A9OR1T15X,9);%[node# XDisp XLoc YLoc ZLoc]
R1T200Y = sldwrksTxtImp(A9OR1T200Y,9);%[node# YDisp XLoc YLoc ZLoc]
R1T200X = sldwrksTxtImp(A9OR1T200X,9);%[node# XDisp XLoc YLoc ZLoc]
[YMaxR100TO,ResR100TO] = findYMaxLocFit(R100TOX,R100TOY);
[YMaxR100T50, ResR100T50]= findYMaxLocFit(R100T50X,R100T50Y);
[YMaxR100T100, ResR100T100]= findYMaxLocFit(R100T100X,R100T100Y)
[YMaxR100T150, ResR100T150]= findYMaxLocFit(R100T150X,R100T150Y);
[YMaxR100T200, ResR100T200]= findYMaxLocFit(R100T200X,R100T200Y);
[YMaxR50TO, ResR50TO] = findYMaxLocFit(R50TOX,R5OTOY);
[YMaxR5QT5Q, ResR5QT50] = findYMaxLocFit(R50T50X,R5QT50Y);
[YMaxR50T100, ResR50T100] = findYMaxLocFit(R50T100X,R5OT100Y);
[YMaxR50T15Q, ResR50T150] = findYMaxLocFit(R50T15OX,R5OT15OY);
[YMaxR50T200, ResR50T200] = findYMaxLocFit(R50T200X,R5OT200Y);
[YMaxR20TO, ResR20TO] = findYMaxLocFit(R20TOX,R2OTOY);
[YMaxR20T5O, ResR20T50] = findYMaxLocFit(R20T50X,R2OT50Y);
[YMaxR20T100, ResR20T100] = findYMaxLocFit(R20T100X,R2QT100Y);
[YMaxR20T15Q, ResR20T150] = findYMaxLocFit(R20T15OX,R2QT15OY);
[YMaxR20T200, ResR20T200] = findYMaxLocFit(R20T200X,R2OT200Y);
[YMaxR1OTO,
ResRiOTO]
= findYMaxLocFit (R1QTOX,R1OTOY);
[YMaxR1OT50, ResR1OT5O] = findYMaxLocFit (R1OT5QX,R1QT50Y);
[YMaxR1OT100, ResRiOT100] = findYMaxLocFit(R1QT100X,R1QT100Y);
[YMaxRIQT150, ResR1OT150] = findYMaxLocFit(R1OT150X,R1QT150Y);
[YMaxR1QT200,
ResR1OT200]
= findYMaxLocFit(R1OT200X,R1OT200Y);
[YMaxR5TO, ResR5TO] = findYMaxLocFit(R5TOX,R5TOY);
[YMaxR5T5O, ResR5T50] = findYMaxLocFit(R5T50X,R5T50Y);
[YMaxR5T100, ResR5T100] = findYMaxLocFit (R5T100X,R5T100Y);
[YMaxR5T15O, ResR5T150] = findYMaxLocFit(R5T15OX,R5T15Y);
[YMaxR5T200, ResR5T200] = findYMaxLocFit(R5T200X,R5T200Y);
[YMaxR1TO, ResRiTO] = findYMaxLocFit(R1TOX,R1TOY);
[YMaxR1T50, ResR1T50] = findYMaxLocFit(R1T50X,R1T50Y);
[YMaxR1T100, ResRiT1O] = findYMaxLocFit(R1T100X,R1T100Y);
[YMaxR1T150, ResR1T15O] = findYMaxLocFit(R1T15OX,R1T15OY);
[YMaxR1T200, ResR1T200] = findYMaxLocFit (R1T200X,R1T200Y);
YMaxLocTO
[YMaxR100TO
=
YMaxR50TO
YMaxR20TO
YMaxR1QTO
YMaxR5TO
YMaxR5OT50
YMaxR20T50
YMaxR1OT50
YMaxR5T50
YMaxR1TO];
YMaxLocT5O =
[YMaxR100T50
YMaxR1T50];
YMaxLocTlOO =
[YMaxR100T100
YMaxR5T100
YMaxR1T100];
YMaxLocTl50 =
[YMaxR100T150
YMaxR5OT100 YMaxR20T100 YMaxR1OT100
YMaxR5OT15Q YMaxR20T15O YMaxR1OT150
YMaxR5T15O
YMaxR1T15O];
YMaxLocT200 =
[YMaxR100T200
YMaxR50T200 YMaxR20T200 YMaxR1QT200
YMaxR1T200];
= [YMaxLocTO; YMaxLocT50; YMaxLocTlOO; YMaxLocTl50; YMaxLocT200];
YMaxR5T200
YMaxLocAll
ResLocTO
=
[ResR100TO
ResR50TO
ResR20TO
ResR1OTO
ResR5TO
[ResR100T50
ResR5OT50
ResR20T50
ResR1OT50
ResR5T50
[ResR100T100
ResR50T1OO ResR20T100 ResRiOT100 ResR5T100
ResR1TO];
ResLocT50
ResR1T50];
ResLocT10
=
=
ResRiT1O];
ResLocT150 =
[ResR100T150
ResR50T150 ResR20T150 ResR1OT150 ResR5T150
ResR1T150];
ResLocT200 =
[ResR100T200
ResR50T200 ResR20T200 ResR1OT200 ResR5T200
ResR1T200];
ResAll = [ResLocTO; ResLocT5O; ResLocT100; ResLocT150; ResLocT200];
YOut =
[YMaxLocAll ResAll];
function
[YOut]
= XLocAngl05()
A105R100TOX = '8_11_2015 Disp and Twist 105 Deg 100 Ratio X Disp 0-0_1.txt';
A105R100TOY = '8_11_2015 Disp and Twist 105 Deg 100 Ratio Y Disp 0-0_1.txt';
A105R100T5OX = '8_11_2015 Disp and Twist 105 Deg 100 Ratio X Disp 500_1.txt';
A105R100T50Y = '8_11_2015 Disp and Twist 105 Deg 100 Ratio Y Disp 50-
O_1.txt';
AlOSR10OT10OX =
'8_11_2015 Disp and Twist 105 Deg 100 Ratio X Disp 100-
0_1.txt';
A105R100T100Y =
'7_20_2015 Disp and Twist 105 Deg 100 Ratio Y Disp 100-
0_1.txt';
A1O5R1OOT15OX =
'8_11_2015 Disp and Twist 105 Deg 100 Ratio X Disp 150-
0_1.txt';
A105R100T150Y =
'7_20_2015 Disp and Twist 105 Deg 100 Ratio Y Disp 150-
0_1.txt';
A105R100T200X =
'8_11_2015 Disp and Twist 105 Deg 100 Ratio X Disp 200-
0_1.txt';
A105R100T200Y =
'8_11_2015 Disp and Twist 105 Deg 100 Ratio Y Disp 200-
0_1.txt';
'8_11_2015 Disp and Twist 105 Deg 50 Ratio X Disp 0-0_1.txt';
A105R50TOY = '8_11_2015 Disp and Twist 105 Deg 50 Ratio Y Disp 0-0_1.txt';
A105R50T50X = '8 11 2015 Disp and Twist 105 Deg 50 Ratio X Disp 50-0 1.txt';
A105R5OT50Y = '8_2_2015 Disp and Twist 105 Deg 50 Ratio Y Disp 50-0_1.txt';
A105R50T100X = '7_20_2015 Disp and Twist 105 Deg 50 Ratio X Disp 100A15R50TOX =
0_1.txt';
A105R50T100Y =
'7_20_2015 Disp and Twist 105 Deg 50 Ratio Y Disp 100-
0_1.txt';
A105R50T150X =
'7_20_2015 Disp and Twist 105 Deg 50 Ratio X Disp 150-
0_1.txt';
A105R50T150Y =
'7_20_2015 Disp and Twist
105 Deg 50 Ratio Y Disp 150-
'7_20_2015 Disp and Twist
105 Deg 50 Ratio X Disp 200-
0_1.txt';
A105R5OT200X =
0_1.txt';
A105R50T200Y =
0_1.txt';
'7_20_2015 Disp and Twist 105 Deg 50 Ratio Y Disp 200-
A105R20TOX = '8 11 2015 Disp and Twist 105 Deg 20 Ratio X
A105R20TOY = '7_20_2015 Disp and Twist 105 Deg 20 Ratio Y
A105R20T50X = '8_2_2015 Disp and Twist 105 Deg 20 Ratio X
A105R20T50Y = '8_2_2015 Disp and Twist 105 Deg 20 Ratio Y
A105R20T100X = '7_20_2015 Disp and Twist 105 Deg 20 Ratio
Disp 0-0 1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-
0_1.txt';
A105R20T100Y =
'7_20_2015 Disp and Twist 105 Deg 20 Ratio Y Disp 100-
0_1.txt';
A105R20T150X =
'7_20_2015 Disp and Twist
105 Deg 20 Ratio X Disp 150-
0_1.txt';
A105R20T150Y =
0_1.txt';
A105R20T200X =
'7_20_2015 Disp and Twist 105 Deg 20 Ratio Y Disp 150'7_20_2015 Disp and Twist 105 Deg 20 Ratio X Disp 200-
0_1.txt';
A1O5R2OT200Y =
'7_20_2015 Disp and Twist 105 Deg 20 Ratio Y Disp 200-
0_1.txt';
A105R10TOX =
'8_11_2015 Disp and Twist 105 Deg 10 Ratio X Disp 0-0_1.txt';
'8 11_2015 Disp and Twist 105 Deg 10
'8 2_2015 Disp and Twist 105 Deg 10
= '8 2_2015 Disp and Twist 105 Deg 10
A105R1QT100X = '7_20_2015 Disp and Twist 105 Deg
A105R10TOY =
A105R1OT50X
A105R10T50Y
=
Disp 0-0_1.txt';
Ratio X Disp 50-0_1.txt';
Ratio Y Disp 50-0_1.txt';
Ratio Y
10 Ratio X
Disp 100-
0_1.txt';
A105R1OT100Y =
'7_20_2015 Disp and Twist 105 Deg 10 Ratio Y Disp 100-
0_1.txt';
A105R10T150X =
'7_20_2015 Disp and Twist 105 Deg 10 Ratio X Disp 150-
0_1.txt';
A105R10T150Y =
'7_20_2015 Disp and Twist 105 Deg 10 Ratio Y Disp 150-
0_1.txt';
A105R1OT200X =
'7_20_2015 Disp and Twist 105
Deg 10
Ratio X
Disp 200-
'7_20_2015 Disp and Twist 105
Deg 10
Ratio Y
Disp 200-
0_1.txt';
A105R1QT200Y =
0_1.txt';
A105R5TOX = '8 11 2015 Disp and Twist 105 Deg 5
A105R5TOY = '8_11_2015 Disp and Twist 105 Deg 5
A105R5T50X = '8_2_2015 Disp and Twist 105 Deg 5
A105R5T50Y = '8 2 2015 Disp and Twist 105 Deg 5
A105R5T100X = '7 20_2015 Disp and Twist 105 Deg
A105R5T100Y = '7 20_2015 Disp and Twist 105 Deg
A105R5T15OX = '7 20_2015 Disp and Twist 105 Deg
A105R5T150Y = '7 20_2015 Disp and Twist 105 Deg
A105R5T200X = '7 20_2015 Disp and Twist 105 Deg
A105R5T200Y = '7_20_2015 Disp and Twist 105 Deg
Ratio X
Ratio Y
Ratio X
Ratio Y
5 Ratio
5 Ratio
5 Ratio
5 Ratio
5 Ratio
5 Ratio
Disp 0-0_1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0 1.txt';
X Disp 100-0_1.txt';
Y Disp 100-0_1.txt';
X Disp 150-0_1.txt';
Y Disp 150-0 1.txt';
X Disp 200-0_1.txt';
Y Disp 200-0_1.txt';
A105R1TOX = '8 11 2015 Disp and Twist 105 Deg 1
A105R1TOY = '8 11 2015 Disp and Twist 105 Deg 1
A105R1T50X = '8_2_2015 Disp and Twist 105 Deg 1
A105R1T50Y = '8 2 2015 Disp and Twist 105 Deg 1
A105R1T100X = '7 20_2015 Disp and Twist 105 Deg
A105RiTlOQY = '7 20_2015 Disp and Twist 105 Deg
A105R1T15OX = '8 11_2015 Disp and Twist 105 Deg
A105R1T15OY = '8 11_2015 Disp and Twist 105 Deg
A105R1T200X = '7 20_2015 Disp and Twist 105 Deg
A105R1T200Y = '7_20_2015 Disp and Twist 105 Deg
Ratio X
Ratio Y
Ratio X
Ratio Y
1 Ratio
1 Ratio
1 Ratio
1 Ratio
1 Ratio
1 Ratio
Disp 0-0_1.txt';
Disp 0-0 1.txt';
Disp 50-0_1.txt';
Disp 50-0 1.txt';
X Disp 100-0_1.txt';
Y Disp 100-0_1.txt';
X Disp 150-0_1.txt';
Y Disp 150-0_1.txt';
X Disp 200-0_1.txt';
Y Disp 200-0_1.txt';
0.%%
%Each pair of datasets share the same subset of nodes
R100TOY = sldwrksTxtImp(A1O5R100TOY,9);%[node# YDisp XLoc YLoc ZLoc]
R100TOX = sldwrksTxtImp(A1O5R1QOTOX,9);%[node# XDisp XLoc YLoc ZLoc]
R100T50Y = sldwrksTxtImp(A1O5R100T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R100T50X = sldwrksTxtImp(A1Q5R100T50X,9);%[node# XDisp XLoc YLoc ZLocl
R10OT100Y = sldwrksTxtImp(A1Q5R100T100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R10OT10OX = sldwrksTxtImp(A1O5R100T100X,9);%[node# XDisp XLoc YLoc ZLocl
R100T150Y =
R100T15OX =
R100T200Y =
R100T200X =
sldwrksTxtImp(A1O5R100T15Y,9);%[node# YDisp XLoc YLoc ZLocl
sldwrksTxtImp(A1Q5R100T15OX,9);%[node# XDisp XLoc YLoc ZLoc]
sldwrksTxtImp(A1Q5R100T200Y,9);%[node# YDisp XLoc YLoc ZLoc]
sldwrksTxtImp(A1O5R1OQT20OX,9);%[node# XDisp XLoc YLoc ZLoc]
R50TOY = sldwrksTxtImp(A1O5R50TOY,9);%[node# YDisp XLoc YLoc ZLoc]
R50TOX = sldwrksTxtImp(A1O5R50TOX,9);%[node# XDisp XLoc YLoc ZLoc]
R5OT50Y = sldwrksTxtImp(A1Q5R5OT50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5OT50X = sldwrksTxtImp(A1Q5R5OT50X,9);%[node# XDisp XLoc YLoc ZLoc]
R50T100Y = sldwrksTxtImp(A1Q5R5QT100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R50T100X
R50T150Y
R50T150X
R50T200Y
RSOT200X
=
=
=
=
=
sldwrksTxtImp(A105R5OT100X, 9) ;%[node#
sldwrksTxtImp(A1O5R5QT15OY,9);%[node#
sldwrksTxtImp(A1O5R5QT15OX,9);%[node#
sldwrksTxtImp(A1O5R5OT200Y,9);%[node#
sldwrksTxtImp(A1Q5R5OT200X,9);%[node#
XDisp
YDisp
XDisp
YDisp
XDisp
XLoc
XLoc
XLoc
XLoc
XLoc
YLoc
YLoc
YLoc
YLoc
YLoc
ZLoc]
ZLoc]
ZLocl
ZLocl
ZLoc]
R20TOY = sldwrksTxtImp(A1O5R20TOY,9);%[node# YDisp XLoc YLoc ZLocl
R20TOX = sldwrksTxtImp(A1O5R20TOX,9);%[node# XDisp XLoc YLoc ZLoc]
R20T50Y = sldwrksTxtImp(A105R20T50Y,9);%[node# YDisp XLoc YLoc ZLocl
R20T50X = sldwrksTxtImp(A105R20T5OX,9);%[node# XDisp XLoc YLoc ZLocl
R20T100Y = sldwrksTxtImp(A1O5R2OT100Y,9);%[node# YDisp XLoc YLoc ZLocl
R20T100X = sldwrksTxtImp(A1Q5R2OT100X,9);%[node# XDisp XLoc YLoc ZLocl
R20T150Y = sldwrksTxtImp(A1O5R2OT15OY,9);%[node# YDisp XLoc YLoc ZLocl
R20T150X = sldwrksTxtImp(A1O5R20T150X,9);%[node# XDisp XLoc YLoc ZLoc]
R20T200Y = sldwrksTxtImp(A1O5R2OT200Y,9);%[node# YDisp XLoc YLoc ZLocl
R20T200X = sldwrksTxtImp(A1O5R2OT200X,9);%[node# XDisp XLoc YLoc ZLoc]
R10TOY = sldwrksTxtImp(AO5ROTOY,9);%[node# YDisp XLoc YLoc ZLoc]
R10TOX = sldwrksTxtImp(A1O5R1OTOX,9);%[node# XDisp XLoc YLoc ZLoc]
R1OT50Y = sldwrksTxtImp(A105R10T50Y,9);%[node# YDisp XLoc YLoc ZLocl
R1OT50X = sldwrksTxtImp(A105R1OT50X,9);%[node# XDisp XLoc YLoc ZLocl
RlOT100Y = sldwrksTxtImp(A1Q5R1OT100Y,9);%[node# YDisp XLoc YLoc ZLoc]
RIOT10OX = sldwrksTxtImp(A1O5R1OT100X,9) ;% [node# XDisp XLoc YLoc ZLoc]
R1OT150Y = sldwrksTxtImp(A1O5R1OT15OY,9);%[node# YDisp XLoc YLoc ZLocl
RlT150X = sldwrksTxtImp(A1O5R1OT15X,9);%[node# XDisp XLoc YLoc ZLocl
RlT200Y = sldwrksTxtImp(AO5R1QT200Y,9);%-I[node# YDisp XLoc YLoc ZLoc]
R1OT200X = sldwrksTxtImp(AO5ROT20X,9);%[node# XDisp XLoc YLoc ZLocl
R5TOY = sldwrksTxtImp(A105R5TOY,9);%[node# YDisp XLoc YLoc ZLocl
R5TOX = sldwrksTxtImp(A105R5TOX,9);%[node# XDisp XLoc YLoc ZLocl
R5T50Y = sldwrksTxtImp(A105R5T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5T50X = sldwrksTxtImp(A105R5T50X,9);%[node# XDisp XLoc YLoc ZLoc]
R5T100Y = sldwrksTxtImp(A1Q5R5T100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5T100X = sldwrksTxtImp(A1O5R5T100X,9);%[node# XDisp XLoc YLoc ZLoc]
R5T150Y =
R5T150X =
R5T200Y =
R5T200X =
sldwrksTxtImp(A1O5R5T15OY,9);%[node# YDisp XLoc YLoc ZLocl
sldwrksTxtImp(A1O5R5T150X,9);%[node# XDisp XLoc YLoc ZLocl
sldwrksTxtImp(A1O5R5T200Y,9);%[node# YDisp XLoc YLoc ZLoc]
sldwrksTxtImp(A1O5R5T200X,9);%[node# XDisp XLoc YLoc ZLoc]
RiTOY = sldwrksTxtImp(A1O5R1TOY,9);%[node# YDisp XLoc YLoc ZLoc]
RiTOX = sldwrksTxtImp(A1O5R1TOX,9);%[node# XDisp XLoc YLoc ZLocl
R1T50Y = sldwrksTxtImp(A105R1T50Y,9);%[node# YDisp XLoc YLoc ZLocl
R1T50X = sldwrksTxtImp(A105R1T50X,9);%[node# XDisp XLoc YLoc ZLoc]
R1TlOY = sldwrksTxtImp(A1Q5R1T100Y,9);%[node# YDisp XLoc YLoc ZLocl
RiTlOOX = sldwrksTxtImp(A1O5R1T100X,9);%[node# XDisp XLoc YLoc ZLocl
R1T150Y = sldwrksTxtImp(A1O5R1T15OY,9);%[node# YDisp XLoc YLoc ZLocl
R1T150X = sldwrksTxtImp(A1O5R1T15OX,9);%[node# XDisp XLoc YLoc ZLocl
R1T200Y = sldwrksTxtImp(A1Q5R1T200Y,9);%[node# YDisp XLoc YLoc ZLocl
R1T200X = sldwrksTxtImp(AO5RT20X,9);%[node# XDisp XLoc YLoc ZLoc]
[YMaxR100TO,ResR100TO] = findYMaxLocFit (R100TOX,R100TOY);
[YMaxR100T50, ResR100T50] = findYMaxLocFit (R100T50X,R100T50Y)
[YMaxR100T100, ResR0OT100] = findYMaxLocFit (R100T100X,R100T100Y)
[YMaxR100T150, ResR100T150]= findYMaxLocFit(R100T150X,R100T150Y)
[YMaxR100T200, ResR100T200]= findYMaxLocFit(R100T200X,R100T200Y)
[YMaxR50TO, ResR50TO] = findYMaxLocFit(R50TOX,R50TOY);
[YMaxR50T50, ResR50T50] = findYMaxLocFit(R50T50X,R5OT50Y);
[YMaxR50T100, ResR50T100] = findYMaxLocFit(R5OT100X,R5QT100Y);
[YMaxR50T15O, ResR5OT15O] = findYMaxLocFit(R5QT15OX,R5OT15OY);
[YMaxR50T200, ResR50T200] = findYMaxLocFit (R50T200X,R50T200Y);
[YMaxR20TO, ResR20TQ] = findYMaxLocFit(R20TOX,R20TOY);
[YMaxR20T50, ResR20T50] = findYMaxLocFit (R20T50X,R20T50Y);
[YMaxR20T100,
[YMaxR20T15O,
[YMaxR20T200,
ResR20T100]
ResR20T150]
ResR20T200]
= findYMaxLocFit(R20T100X,R2OT100Y);
= findYMaxLocFit(R20T15OX,R2OT15OY);
= findYMaxLocFit(R20T200X,R2QT200Y);
[YMaxR1OTO, ResRiOTO] = findYMaxLocFit(R1OTOX,R10TOY);
[YMaxR1OT50, ResR1OT50] = findYMaxLocFit(R1OT50X,R1OT50Y);
[YMaxR1OT100, ResR1OT100] = findYMaxLocFit(R1OT100X,R1QT100Y);
[YMaxR1OT150, ResR1OT150] = findYMaxLocFit(R1OT150X,R1OT150Y);
[YMaxR1OT200,
ResR1OT200]
= findYMaxLocFit(R1OT200X,R1QT200Y);
[YMaxR5TO, ResR5TO] = findYMaxLocFit(R5TOX,R5TOY);
[YMaxR5T50, ResR5T50] = findYMaxLocFit(R5T50X,R5T50Y);
[YMaxR5T100, ResR5T100] = findYMaxLocFit(R5T100X,R5T100Y);
[YMaxR5T15O, ResR5T15O] = findYMaxLocFit(R5T15OX,R5T15OY);
[YMaxR5T200, ResR5T200] = findYMaxLocFit(R5T200X,R5T200Y);
[YMaxR1TO,
= findYMaxLocFit(R1TOX,R1TOY);
= findYMaxLocFit(R1T50X,R1T50Y);
ResRiT1O] = findYMaxLocFit(R1T100X,R1T100Y);
ResR1T15OI = findYMaxLocFit(R1T150X,R1T15OY);
ResR1T200] = findYMaxLocFit(R1T200X,R1T200Y);
ResRiTO]
[YMaxR1T50, ResR1T50]
[YMaxR1T100,
[YMaxR1T150,
[YMaxR1T200,
YMaxLocTO
=
[YMaxR100TO
YMaxR50TO
YMaxR20TO
YMaxR1QTO
YMaxR5TO
YMaxR1TO];
YMaxLocT50
[YMaxR100T50
YMaxR50T50 YMaxR20T50
YMaxR1OT50 YMaxR5T50
YMaxR1T50];
YMaxLocTlOO =
[YMaxR100T100
YMaxR50T100 YMaxR20T100 YMaxR1OT100
YMaxR5T100
YMaxR1T100];
[YMaxR100T150
YMaxR5OT150 YMaxR20T15O YMaxR1OT150
YMaxLocTl50 =
YMaxR1T15];
YMaxR5T150
YMaxLocT200 =
[YMaxR100T200
YMaxR50T200 YMaxR20T200 YMaxR1OT200
YMaxR5T200
YMaxR1T200];
YMaxLocAll = [YMaxLocTO; YMaxLocT50; YMaxLocTlOO; YMaxLocTl5O; YMaxLocT200];
ResLocTO =
[ResR1OTO
ResR50TO
ResR20TO
ResR1OTO
ResR5TO
ResRiTO];
ResR5T50
[ResR100T50
ResR50T50
ResR20T50 ResR1OT50
ResLocT50 =
ResR1T50];
[ResR100T100
ResR50T100 ResR20T100 ResRiOT100 ResR5T100
ResLocT10
=
ResRiT1O];
[ResR100T150
ResR50T15O ResR20T150 ResR1OT150 ResR5T15O
ResLocT150 =
ResR1T15O];
ResLocT200 =
[ResR100T200
ResR50T200 ResR20T200 ResR1OT200 ResR5T200
ResR1T200];
ResAll = [ResLocTO; ResLocT50; ResLocT100; ResLocT150; ResLocT200];
YOut =
[YMaxLocAll ResAll];
function
= XLocAngl20()
[YOut]
'8_11_2015 Disp and Twist 120 Deg 100 Ratio X Disp 0-0_1.txt';
A120R100TOX =
A120R100TOY = '8_11_2015 Disp and Twist 120 Deg 100 Ratio Y Disp 0-0_1.txt';
A120R100T50X = '8_11_2015 Disp and Twist 120 Deg 100 Ratio X Disp 50-
0_1.txt';
A120R100T50Y =
'8_11_2015 Disp and Twist 120 Deg 100 Ratio Y Disp 50-
0_1.txt';
A120R100T100X =
'8 11 2015 Disp and Twist 120 Deg 100 Ratio X Disp 100-
0_1.txt';
A120R100T100Y =
'8_11_2015 Disp and Twist 120 Deg 100 Ratio Y Disp 100-
0_1.txt';
A120R100T15OX =
'8_11_2015 Disp and Twist 120 Deg 100 Ratio X Disp 150-
0_1.txt';
A120R100T150Y =
'8_11_2015 Disp and Twist 120 Deg 100 Ratio Y Disp 150-
0_1.txt';
A120R100T200X =
'7_20_2015 Disp and Twist 120 Deg 100 Ratio X Disp 200-
0_1.txt';
A120R100T200Y =
'7_20_2015 Disp and Twist 120 Deg 100 Ratio Y Disp 200-
0_1.txt';
A120R50TOX = '8_11_2015 Disp and Twist 120 Deg 50 Ratio X
A120R50TOY = '8_11_2015 Disp and Twist 120 Deg 50 Ratio Y
A120R50T50X = '8 2 2015 Disp and Twist 120 Deg 50 Ratio X
A120R5OT50Y = '8_2_2015 Disp and Twist 120 Deg 50 Ratio Y
A120R5OT100X = '8_11_2015 Disp and Twist 120 Deg 50 Ratio
Disp 0-0_1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-
0_1.txt';
A120R5OT100Y =
'8_11_2015 Disp and Twist 120 Deg 50 Ratio Y Disp 100-
0_1.txt';
A120R50T150X =
'8_11_2015 Disp and Twist 120 Deg 50 Ratio X Disp 150-
0_1.txt';
A120R50T150Y =
'8_11_2015 Disp and Twist 120 Deg 50 Ratio Y Disp 150-
0_1.txt';
A120R50T200X =
'7_20_2015 Disp and Twist 120 Deg 50 Ratio X Disp 200-
0_1.txt';
A120R50T200Y =
'7_20_2015 Disp and Twist 120 Deg 50 Ratio Y Disp 200-
0_1.txt';
A120R20TOX = '8 11 2015 Disp and Twist 120 Deg 20 Ratio X
A120R20TOY = '8_11_2015 Disp and Twist 120 Deg 20 Ratio Y
A120R2OT50X = '8_2_2015 Disp and Twist 120 Deg 20 Ratio X
A120R2OT50Y = '8_2_2015 Disp and Twist 120 Deg 20 Ratio Y
A120R2OT100X = '7_20_2015 Disp and Twist 120 Deg 20 Ratio
Disp 0-0 1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-
0_1.txt';
A120R2QT100Y =
'7_20 2015 Disp and Twist 120 Deg 20 Ratio Y
Disp 100-
0_1.txt';
A120R2OT15OX =
'7_20 2015 Disp and Twist
120 Deg 20 Ratio X Disp
150-
0_1.txt';
A120R2OT15OY =
'7_20_2015 Disp and Twist 120 Deg 20 Ratio Y
Disp 150-
'7_20_2015 Disp and Twist 120 Deg 20 Ratio X
Disp 200-
'7_20_2015 Disp and Twist 120 Deg 20 Ratio Y
Disp 200-
0_1.txt';
A120R20T200X =
0_1.txt';
A120R2OT200Y =
0_1.txt';
A120R10TOX =
'8_11_2015 Disp and Twist 120 Deg 10 Ratio X Disp 0-0_1.txt';
A120R10TOY = '8 11 2015
A120R1OT50X = '8 2 2015
Disp and Twist 120 Deg 10 Ratio Y
Disp and Twist 120 Deg 10 Ratio X
A120R10T50Y = '8 2 2015 Disp and Twist 120 Deg 10 Ratio Y
A120R1OT100X = '7_20_2015 Disp and Twist 120 Deg 10 Ratio
0_1.txt';
A120R1OT100Y = '7_20_2015 Disp and Twist 120 Deg 10 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100Y Disp 100-
0_1.txt';
A120R1OT15OX =
'7_20_2015 Disp and Twist 120 Deg 10 Ratio X Disp 150-
0_1.txt';
A120R1OT150Y =
0_1.txt';
A120RlT200X =
'7_20_2015 Disp and Twist 120 Deg 10 Ratio Y Disp 150'7_20_2015 Disp and Twist 120 Deg 10 Ratio X Disp 200-
0_1.txt';
A120R1OT200Y =
'7_20_2015 Disp and Twist 120 Deg 10 Ratio Y Disp 200-
0_1.txt';
A120R5TOX = '8 11 2015 Disp and Twist 120 Deg 5
A120R5TOY = '8 11 2015 Disp and Twist 120 Deg 5
A120R5T50X = '8_2_2015 Disp and Twist 120 Deg 5
A120R5T50Y = '8 2 2015 Disp and Twist 120 Deg 5
A120R5T100X = '7 20_2015 Disp and Twist 120 Deg
A120R5T100Y = '7 20_2015 Disp and Twist 120 Deg
A120R5T15OX = '7 20_2015 Disp and Twist 120 Deg
A120RST150Y = '7 20 2015 Disp and Twist 120 Deg
A120R5T200X = '7 20_2015 Disp and Twist 120 Deg
A120R5T200Y = '7_20_2015 Disp and Twist 120 Deg
Ratio X
Ratio Y
Ratio X
Ratio Y
5 Ratio
5 Ratio
5 Ratio
5 Ratio
A120R1TOX =
A120R1TOY =
A120R1T5OX =
A120R1T50Y =
A120R1T100X
A120R1T100Y
A120R1T15OX
A120R1T15OY
A120R1T200X
A120R1T200Y
Ratio X
Ratio Y
Ratio X
Ratio Y
1 Ratio
1 Ratio
1 Ratio
1 Ratio
1 Ratio
1 Ratio
'8 11 2015 Disp and Twist 120 Deg 1
'8 11 2015 Disp and Twist 120 Deg 1
'8_2_2015 Disp and Twist 120 Deg 1
'8 2 2015 Disp and Twist 120 Deg 1
= '7 20_2015 Disp and Twist 120 Deg
= '7 20_2015 Disp and Twist 120 Deg
= '7 20_2015 Disp and Twist 120 Deg
= '7 20_2015 Disp and Twist 120 Deg
= '7 20_2015 Disp and Twist 120 Deg
= '7_20_2015 Disp and Twist 120 Deg
Disp 0-0 1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-0_1.txt';
Y Disp 100-0_1.txt';
X Disp 150-0_1.txt';
Y Disp 150-0 1.txt';
5 Ratio X Disp 200-0_1.txt';
5 Ratio Y Disp 200-0_1.txt';
Disp 0-0_1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-0_1.txt';
Y Disp 100-0_1.txt';
X Disp 150-0_1.txt';
Y Disp 150-0_1.txt';
X Disp 200-0_1.txt';
Y Disp 200-0_1.txt';
0.%%
%Each pair of datasets share the same subset of nodes
R100TOY = sldwrksTxtImp(A12OR100TOY,9);%[node# YDisp XLoc YLoc ZLoc]
R100TOX = sldwrksTxtImp(A12OR100TOX,9);%[node# XDisp XLoc YLoc ZLocl
R100T50Y = sldwrksTxtImp(A12OR100T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R100T50X = sldwrksTxtImp(A12OR1OOT50X,9);%[node# XDisp XLoc YLoc ZLoc]
R10OT100Y = sldwrksTxtImp(A12QR100T100Y,9);%[node# YDisp XLoc YLoc ZLocl
R100T100X = sldwrksTxtImp(A12OR100T100X,9);%[node# XDisp XLoc YLoc ZLocl
R100T150Y = sldwrksTxtImp(A12OR100T15Y,9);%[node# YDisp XLoc YLoc ZLocl
R100T15OX = sldwrksTxtImp(A12OR100T15X,9);%[node# XDisp XLoc YLoc ZLocl
R100T200Y = sldwrksTxtImp(A12OR100T200Y,9);%[node# YDisp XLoc YLoc ZLocl
R100T200X = sldwrksTxtImp(A12OR100T200X,9);%[node# XDisp XLoc YLoc ZLocl
R50TOY = sldwrksTxtImp(A12OR50TOY,9);%[node# YDisp XLoc YLoc ZLocl
R50TOX = sldwrksTxtImp(A12OR50TOX,9);%[node# XDisp XLoc YLoc ZLocl
R50T50Y = sldwrksTxtImp(A12OR5OT50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R50T50X = sldwrksTxtImp(A12QR5OT50X,9);%[node# XDisp XLoc YLoc ZLoc]
R50T100Y = sldwrksTxtImp(A12QR5QT100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R50T100X =
R50T150Y =
R50T150X =
R50T200Y =
sldwrksTxtImp(A120R50T1OOX,9);%[node#
sldwrksTxtImp(A120R50T150Y,9);%[node#
sldwrksTxtImp(A12OR5OT15OX,9);%[node#
sldwrksTxtImp(A120R5T200Y,9);%[node#
R50T200X = sldwrksTxtImp(A120R50T200X,9);%[node#
XDisp
YDisp
XDisp
YDisp
XDisp
XLoc
XLoc
XLoc
XLoc
XLoc
YLoc
YLoc
YLoc
YLoc
YLoc
ZLoc]
ZLoc]
ZLocl
ZLoc]
ZLoc]
R20TOY = sldwrksTxtImp(A120R20TOY,10);%[node# YDisp XLoc YLoc ZLoc]
R20TOX = sldwrksTxtImp(A12OR20TOX,9);%[node# XDisp XLoc YLoc ZLoc]
R20T50Y = sldwrksTxtImp(A120R20T50Y,10);%[node# YDisp XLoc YLoc ZLoc
R20T50X = sldwrksTxtImp(A120R20T50X,9);%[node# XDisp XLoc YLoc ZLoc]
R20T100Y = sldwrksTxtImp(A12OR2OT100Y,10);%[node# YDisp XLoc YLoc ZLocl
R20T100X = sldwrksTxtImp(A12OR2OT100X,9);%[node# XDisp XLoc YLoc ZLocl
R20T150Y = sldwrksTxtImp(A120R20T150Y,10);%[node# YDisp XLoc YLoc ZLoc]
R20T150X = sldwrksTxtImp(A120R20T150X,9);%[node# XDisp XLoc YLoc ZLoc]
R20T200Y = sldwrksTxtImp(A120R20T200Y,10);%[node# YDisp XLoc YLoc ZLocl
R20T200X = sldwrksTxtImp(A12OR2OT200X,9);%[node# XDisp XLoc YLoc ZLoc]
R10TOY = sldwrksTxtImp(A12OR1OTOY,10);%[node# YDisp XLoc YLoc ZLoc]'
R10TOX = sldwrksTxtImp(A120R1OTOX,10);%[node# XDisp XLoc YLoc ZLocl
R10T50Y = sldwrksTxtImp(A120R10T50Y, 10) ;%[node# YDisp XLoc YLoc ZLoc]
R1OT50X = sldwrksTxtImp(A12OR1OT50X,10);%[node# XDisp XLoc YLoc ZLoc]
RIOT100Y = sldwrksTxtImp(A12OR1OT100Y,10);%[node# YDisp XLoc YLoc ZLocl
RlOT100X = sldwrksTxtImp(A120R10T100X,10);% [node# XDisp XLoc YLoc ZLoc]
R10T150Y = sldwrksTxtImp(A12OR10T15OY,10);%[node# YDisp XLoc YLoc ZLoc]
R1OT150X = sldwrksTxtImp(A120R10T150X,10);%[node# XDisp XLoc YLoc ZLoc]
R1OT200Y = sldwrksTxtImp(A120R10T200Y,10);%[node# YDisp XLoc YLoc ZLocl
RlT200X = sldwrksTxtImp(A120R10T200X,10);%[node# XDisp XLoc YLoc ZLoc]
R5TOY = sldwrksTxtImp(A120R5TOY,9);%[node# YDisp XLoc YLoc ZLoc]
R5TOX = sldwrksTxtImp(A12OR5TOX,9);%[node# XDisp XLoc YLoc ZLocl
R5T50Y = sldwrksTxtImp(A120R5T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5T50X = sldwrksTxtImp(A120R5T50X,9);%[node# XDisp XLoc YLoc ZLoc]
R5T100Y = sldwrksTxtImp(A12OR5T100Y,9);%[node# YDisp XLoc YLoc ZLocl
R5T100X = sldwrksTxtImp(A12OR5T100X,9);%[node# XDisp XLoc YLoc ZLoc]
R5T150Y = sldwrksTxtImp(A12OR5T15OY,9);%[node# YDisp XLoc YLoc ZLoc]
R5T15OX = sldwrksTxtImp(A12OR5T15OX,9);%[node# XDisp XLoc YLoc ZLoc]
R5T200Y = sldwrksTxtImp(A12OR5T200Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5T200X = sldwrksTxtImp(A120R5T200X,9);%[node# XDisp XLoc YLoc ZLocl
RiTOY = sldwrksTxtImp(A12OR1TOY,10);%[node# YDisp XLoc YLoc ZLoc]
RiTOX = sldwrksTxtImp(A12OR1TOX,10);%[node# XDisp XLoc YLoc ZLoc]
R1T50Y = sldwrksTxtImp(A120R1T50Y,10);%[node# YDisp XLoc YLoc ZLoc]
R1T50X = sldwrksTxtImp(A120R1T50X,10);%[node# XDisp XLoc YLoc ZLoc]
RiTlOQY = sldwrksTxtImp(A12OR1T100Y,10);%[node# YDisp XLoc YLoc ZLoc]
RiTlOOX = sldwrksTxtImp(A12OR1T100X,10);%[node# XDisp XLoc YLoc ZLoc]
R1T150Y = sldwrksTxtImp(A12OR1T150Y,10);%[node# YDisp XLoc YLoc ZLoc]
R1T150X = sldwrksTxtImp(A120R1T150X,10);%[node# XDisp XLoc YLoc ZLocl
R1T200Y = sldwrksTxtImp(A120R1T200Y,10);%[node# YDisp XLoc YLoc ZLocl
R1T200X = sldwrksTxtImp(A12OR1T200X,10);%[node# XDisp XLoc YLoc ZLocl
[YMaxR100TO,ResR100TO] = findYMaxLocFit(R100TOX,R100TOY);
[YMaxR100T50, ResR100T50]= findYMaxLocFit(R100T50X,R100T50Y);
[YMaxR100T100, ResR100T100]= findYMaxLocFit(R100T100X,R100T100Y);
[YMaxR100T150, ResR100T150]= findYMaxLocFit(R100T150X,R100T150Y);
[YMaxR100T200, ResR100T200I= findYMaxLocFit(R100T200X,R100T200Y);
[YMaxR50TO, ResR50TO] = findYMaxLocFit(R50TOX,R50TOY);
[YMaxR50T50, ResR50T50] = findYMaxLocFit(R50T50X,R5OT50Y);
[YMaxR50T100, ResRSQT100] = findYMaxLocFit(R50T100X,R5OT100Y);
[YMaxR50T15, ResR50T150] = findYMaxLocFit(R50T15OX,R5OT15OY);
[YMaxR50T200, ResR50T200] = findYMaxLocFit(R50T200X,R5OT200Y);
[YMaxR20TO, ResR20TO] = findYMaxLocFit(R20TOX,R20TOY);
[YMaxR20T50, ResR20T50] = findYMaxLocFit(R20T50X,R2OT50Y);
[YMaxR20T100, ResR20T100] = findYMaxLocFit(R20T100X,R2OT100Y);
[YMaxR20T15O,
= findYMaxLocFit(R20T15OX,R2OT15OY);
= findYMaxLocFit(R20T200X,R2OT200Y);
ResR20T150]
[YMaxR20T200, ResR20T200]
[YMaxR1OTO, ResRiOTO] = findYMaxLocFit(R1OTOX,R10TOY);
[YMaxR1OT50, ResR1OT50] = findYMaxLocFit(R1QT50X,R1OT50Y);
[YMaxR1OT100, ResR1OT100] = findYMaxLocFit(R1OT100X,R1OT100Y);
[YMaxR1OT150, ResR1OT150] = findYMaxLocFit(R1OT150X,R1OT150Y);
[YMaxR1OT200,
= findYMaxLocFit(R1OT200X,R1OT200Y);
ResR1OT200]
[YMaxR5TO, ResR5T] = findYMaxLocFit(R5TOX,R5TOY);
[YMaxR5T50, ResR5T50] = findYMaxLocFit(R5T50X,R5T50Y);
[YMaxR5T1OO, ResR5T100] = findYMaxLocFit(R5T100X,R5T100Y);
[YMaxR5T15O, ResR5T150] = findYMaxLocFit(R5T15OX,R5T15OY);
[YMaxR5T200, ResR5T200] = findYMaxLocFit(R5T200X,R5T200Y);
[YMaxR1TO, ResRlTO]
= findYMaxLocFit(R1TOX,R1TOY);
ResR1T50] = findYMaxLocFit(R1T50X,R1T50Y);
[YMaxR1T100, ResRiT1O] = findYMaxLocFit(R1T100X,R1T100Y);
[YMaxR1T150, ResR1T150] = findYMaxLocFit(R1T150X,R1T15QY);
[YMaxR1T200, ResR1T200] = findYMaxLocFit(R1T200X,R1T200Y);
[YMaxR1T50,
YMaxLocTO =
[YMaxR100TO
YMaxR1TO];
YMaxLocT50 =
[YMaxR100T50
YMaxR1T50];
YMaxLocTlOO =
[YMaxR100T100
YMaxR5T100
YMaxR1T100];
YMaxLocTl50 =
[YMaxR100T150
YMaxR5T15O
YMaxR1T150];
YMaxLocT200 =
[YMaxR100T200
YMaxR5T200
YMaxR1T200];
YMaxLocAll
=
ResLocTO =
ResRlTO];
ResLocT50 =
ResR1T50];
ResLocT10
=
ResRiT1O];
ResLocT150 =
[YMaxLocTO;
YMaxR50TO
YMaxR20TO
YMaxR1OTO
YMaxR5TO
YMaxR50T50
YMaxR20T50
YMaxR1OT50
YMaxR5T50
YMaxR50T100 YMaxR20T100 YMaxR1OT100
YMaxR50T15O YMaxR20T15O YMaxR1OT150
YMaxR50T200 YMaxR20T200 YMaxR1QT200
YMaxLocT50;
YMaxLocTlOO;
YMaxLocTl50;
YMaxLocT200];
[ResR1OTO
ResR50TO
ResR20TO
ResRiOTO
ResR 5TO
[ResR100T50
ResR5OT50
ResR20T50
ResR1OT50
ResR 5T50
[ResR1OT100
ResR5OT100 ResR20T100 ResRiOT100 ResR 5T100
[ResR100T150
ResR50T150 ResR20T150 ResR1OT150 ResR 5T150
[ResR100T200
ResR5OT200 ResR20T200 ResR1OT200 ResR 5T200
ResR1T15Q];
ResLocT200 =
ResR1T200];
ResAll
=
YOut =
[YMaxLocAll ResAll];
[ResLocTO;
ResLocT50;
ResLocT100;
ResLocT150;
ResLocT200];
function
[YOut]
=
XLocAngl35()
A135R100TOX =
A135R100TOY =
'8_11_2015 Disp and Twist 135 Deg 100 Ratio X Disp 0-0_1.txt';
'8_11_2015 Disp and Twist 135 Deg 100 Ratio Y Disp 0-0_1.txt';
A135R100T50X = '8_11_2015 Disp and Twist 135 Deg 100 Ratio X Disp 50-
0_1.txt';
A135R100T50Y =
'8_11_2015 Disp and Twist 135 Deg 100 Ratio Y Disp 50-
0_1.txt';
A135R100T100X =
'8_11_2015 Disp and Twist 135 Deg 100 Ratio X Disp
100-
'8_11_2015
Disp and Twist
135 Deg 100
Ratio Y Disp
100-
'8_11_2015
Disp and Twist
135 Deg 100
Ratio X Disp
150-
'8_11_2015
Disp and Twist 135 Deg 100 Ratio Y Disp
150-
'8_11_2015
Disp and Twist
1;5 Deg 100
Ratio X Disp 200-
'8_11_2015
Disp and Twist
135 Deg 100
Ratio Y Disp 200-
0_1.txt';
A135R100T100Y =
0_1.txt';
A135R100T150X =
0_1.txt';
A135R100T150Y =
0_1.txt';
A135R100T200X =
0_1.txt';
A135R100T200Y =
0_1.txt';
A135R50TOX = '8 11 2015 Disp and Twist 135 Deg 50 Ratio X
A135R50TOY = '8_11_2015 Disp and Twist 135 Deg 50 Ratio Y
A135R50T50X = '8_2_2015 Disp and Twist 135 Deg 50 Ratio X
A135R50T50Y = '8_2_2015 Disp and Twist 135 Deg 50 Ratio Y
A135R5QT100X = '8_11_2015 Disp and Twist 135 Deg 50 Ratio
Disp 0-0 1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-
0_1.txt';
A135R50T100Y =
0_1.txt';
A135R50T150X =
Ratio Y Disp
100-
'7_20_2015
Disp and Twist 135 Deg 50 Ratio X Disp
150-
'7_20_2015
Disp and Twist
150-
'8_11_2015 Disp and Twist 135 Deg 50
0_1.txt';
A135R50T150Y =
0_1.txt';
A135R50T200X =
0_1.txt';
A135R50T200Y =
'7_20_2015 Disp and Twist
135 Deg 50 Ratio Y Disp
135 Deg 50 Ratio X Disp 200-
'7_20_2015 Disp and Twist 135 Deg 50 Ratio Y Disp 200-
0_1.txt';
A135R20TOX = '8 11 2015 Disp and Twist 135 Deg 20 Ratio X
A135R20TOY = '8_11_2015 Disp and Twist 135 Deg 20 Ratio Y
A135R20T50X = '8_2_2015 Disp and Twist 135 Deg 20 Ratio X
A135R20T50Y = '8_2_2015 Disp and Twist 135 Deg 20 Ratio Y
A135R2OT100X = '7_20_2015 Disp and Twist 135 Deg 20 Ratio
Disp 0-0 1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-
0_1.txt';
A135R2OT100Y =
0_1.txt';
A135R20T150X =
0_1.txt';
A135R20T150Y =
'7_20_2015 Disp and Twist
135 Deg 20 Ratio Y Disp
100-
'7_20 2015 Disp and Twist 135 Deg 20 Ratio X Disp
150-
'7_20 2015 Disp and Twist 135 Deg 20 Ratio Y Disp
150-
0_1.txt';
A135R20T200X =
'7_20_2015
Disp and Twist 135 Deg 20 Ratio X Disp 200-
'7_20_2015
Disp and Twist 135 Deg 20 Ratio Y Disp 200-
0_1.txt';
A135R20T200Y =
0_1.txt';
A135R10TOX =
'8_11_2015
Disp and Twist
135 Deg 10
Ratio X Disp
0-0_1.txt';
A135R10TOY = '8 11_2015 Disp and Twist 135 Deg 10 Ratio Y
A135R1OT50X = '8 2_2015 Disp and Twist 135 Deg 10 Ratio X
A135R10T50Y
'8 2_2015 Disp and Twist 135 Deg 10 Ratio Y
A135R1OT100X = '7_20_2015 Disp and Twist 135 Deg 10 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-
0_1.txt';
=
'7_20_2015 Disp and Twist 135 Deg 10 Ratio Y Disp
100-
A135R10T150X =
'7_20_2015 Disp and Twist 135 Deg 10 Ratio X Disp
150-
'7_20_2015 Disp and Twist 135 Deg 10 Ratio Y Disp
150-
A135R10T100Y
0_1.txt';
0_1.txt';
A135R10T150Y
=
0_1.txt';
A135R1QT200X =
0_1.txt';
A135R1OT200Y =
'7_20_2015 Disp and Twist 135 Deg 10 Ratio X Disp 200'7_20_2015 Disp and Twist 135 Deg 10 Ratio Y Disp 200-
0_1.txt';
A135R5TOX = '8 11 2015 Disp and Twist 135 Deg 5
A135R5TOY = '8 11 2015 Disp and Twist 135 Deg 5
A135R5T50X = '8 2_2015 Disp and Twist 135 Deg 5
A135R5T50Y = '8 2 2015 Disp and Twist 135 Deg 5
A135R5T100X = '7 20_2015 Disp and Twist 135 Deg
A135R5T100Y = '7 20_2015 Disp and Twist 135 Deg
A135R5T150X = '7 20 2015 Disp and Twist 135 Deg
A135R5T150Y = '7 20_2015 Disp and Twist 135 Deg
A135R5T200X = '7 20_2015 Disp and Twist 135 Deg
A135R5T200Y = '7_20_2015 Disp and Twist 135 Deg
Ratio X
Ratio Y
Ratio X
Ratio Y
5 Ratio
5 Ratio
5 Ratio
5 Ratio
5 Ratio
5 Ratio
A135R1TOX = '8 11 2015 Disp and Twist 135 Deg 1
A135R1TOY = '8 11 2015 Disp and Twist 135 Deg 1
A135R1T50X = '8 2 2015 Disp and Twist 135 Deg 1
A135R1T50Y = '8 2 2015 Disp and Twist 135 Deg 1
A135R1T100X = '7 20_2015 Disp and Twist 135 Deg
A135R1T100Y = '7 20_2015 Disp and Twist 135 Deg
A135R1T15OX = '7 20_2015 Disp and Twist 135 Deg
A135R1T15OY = '7 20_2015 Disp and Twist 135 Deg
A135R1T200X = '8_11_2015 Disp and Twist 135 Deg
A135R1T200Y = '8_11_2015 Disp and Twist 135 Deg
Ratio X Disp 0-0_1.txt';
Ratio Y Disp 0-0_1.txt';
Ratio X Disp 50-0_1.txt';
Ratio Y Disp 50-0_1.txt';
Disp 0-0_1.txt';
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Disp 50-0_1.txt';
X Disp 100-0_1.txt';
Y Disp 100-0_1.txt';
X Disp 150-0 l.txt';
Y Disp 150-0_1.txt';
X Disp 200-0 1.txt';
Y Disp 200-0_l.txt';
1 Ratio X Disp 100-0_1.txt';
1
1
1
1
Ratio
Ratio
Ratio
Ratio
Y
X
Y
X
Disp 100-0_1.txt';
Disp 150-0_1.txt';
Disp 150-0_1.txt';
Disp 200-0_1.txt';
1 Ratio Y Disp 200-0_1.txt';
0%%
%Each pair of datasets share the same subset of nodes
R100TOY = sldwrksTxtImp(A135R100TOY,9);%[node# YDisp XLoc YLoc ZLoc]
R100TOX = sldwrksTxtImp(A135R1OOTOX,9);%[node# XDisp XLoc YLoc ZLocl
R100T50Y = sldwrksTxtImp(A135R100T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
R100T50X = sldwrksTxtImp(A135R1OOT50X,9);%[node# XDisp XLoc YLoc ZLoc]
R100T100Y = sldwrksTxtImp(A135R100T100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R10OT10OX = sldwrksTxtImp(A135R100T100X,9);%[node# XDisp XLoc YLoc ZLoc]
R100T150Y = sldwrksTxtImp(A135R100T15OY,9);%[node# YDisp XLoc YLoc ZLocl
R100T15OX = sldwrksTxtImp(A135R100T15OX,9);%[node# XDisp XLoc YLoc ZLocl
R100T200Y = sldwrksTxtImp(A135R100T200Y,9);%[node# YDisp XLoc YLoc ZLoc]
R100T200X = sldwrksTxtImp(A135R100T200X,9);% [node# XDisp XLoc YLoc ZLocl
R50TOY =
R50TOX =
R50T50Y =
R50T50X =
sldwrksTxtImp(A135R50TOY,9);%[node# YDisp XLoc YLoc ZLocl
sldwrksTxtImp(A135R50TOX,9);%[node# XDisp XLoc YLoc ZLoc]
sldwrksTxtImp(A135R50T50Y,9);%[node# YDisp XLoc YLoc ZLocl
sldwrksTxtImp(A135R50T50X,9);%[node# XDisp XLoc YLoc ZLocl
R50T100Y
= sldwrksTxtImp(A135R50T100Y,9);%[node#
YDisp XLoc
YLoc
ZLocl
R5OT100X
R50T150Y
R50T150X
R50T200Y
R50T200X
= sldwrksTxtImp(A135R5OT100X,9);%[node#
= sldwrksTxtImp(A135R50T150Y,9);%[node#
= sldwrksTxtImp(A135R50T150X,9);%[node#
= sldwrksTxtImp(A135R50T200Y,9);%[node#
= sldwrksTxtImp(A135R50T200X,9);%[node#
XDisp
YDisp
XDisp
YDisp
XDisp
XLoc
XLoc
XLoc
XLoc
XLoc
YLoc
YLoc
YLoc
YLoc
YLoc
ZLocl
ZLocl
ZLoc]
ZLocl
ZLoc]
R20TOY = sldwrksTxtImp(A135R20TOY,10);%[node# YDisp XLoc YLoc ZLoc]
R20TOX = sldwrksTxtImp(A135R20TOX,9);%[node# XDisp XLoc YLoc ZLoc]
R20T50Y = sldwrksTxtImp(A135R20T50Y,10);%[node# YDisp XLoc YLoc ZLoc]
R20T50X = sldwrksTxtImp(A135R20T50X,9);%[node# XDisp XLoc YLoc ZLoc]
R20T100Y = sldwrksTxtImp(A35R20T00Y,10);%[node# YDisp XLoc YLoc ZLoc]
R20T100X = sldwrksTxtImp(A135R20T100X,9);%[node# XDisp XLoc YLoc ZLocl
R20T150Y = sldwrksTxtImp(A135R20T150Y,10);%[node# YDisp XLoc YLoc ZLoc]
R20T150X = sldwrksTxtImp(A135R20T150X,9);%[node# XDisp XLoc YLoc ZLocl
R20T200Y = sldwrksTxtImp(A135R20T200Y,10);%[node# YDisp XLoc YLoc ZLocl
R20T200X = sldwrksTxtImp(A35R20T20X,9);%[node# XDisp XLoc YLoc ZLoc]
R10TOY = sldwrksTxtImp(A35ROTOY,10);%[node# YDisp XLoc YLoc ZLoc]
R10TOX = sldwrksTxtImp(A135R1QTOX,10);%[node# XDisp XLoc YLoc ZLocl
R10TSOY = sldwrksTxtImp(A135R1OT5OY,10);%[node# YDisp XLoc YLoc ZLocl
R1OT50X = sldwrksTxtImp(A135R10T50X,10);%[node# XDisp XLoc YLoc ZLoc]
RlOT100Y = sldwrksTxtImp(A135R1OT100Y,10);%[node# YDisp XLoc YLoc ZLocl
RlOT100X = sldwrksTxtImp(A135R1OT100X,10);%[node# XDisp XLoc YLoc ZLocl
R1OT150Y = sldwrksTxtImp(A135R10T150Y,10);%[node# YDisp XLoc YLoc ZLoc]
RlT150X = sldwrksTxtImp(A135R10T150X,10);%[node# XDisp XLoc YLoc ZLoc]
R1OT200Y = sldwrksTxtImp(A135R1OT200Y,10);%[node# YDisp XLoc YLoc ZLoc]
RlT200X = sldwrksTxtImp(A135R10T200X,10);%[node# XDisp XLoc YLoc ZLoc]
sldwrksTxtImp(A135R5TOY,9);%[node# YDisp XLoc YLoc ZLoc]
sldwrksTxtImp(A135R5TOX,9);%[node# XDisp XLoc YLoc ZLocl
= sldwrksTxtImp(A135R5T50Y,9);%[node# YDisp XLoc YLoc ZLoc]
= sldwrksTxtImp(A135R5T50X,9);%[node# XDisp XLoc YLoc ZLocl
R5T100Y = sldwrksTxtImp(A135RST100Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5T100X = sldwrksTxtImp(A135R5T100X,9);%[node# XDisp XLoc YLoc ZLoc]
R5T150Y = sldwrksTxtImp(A135R5T150Y,9);%[node# YDisp XLoc YLoc ZLocl
R5T15OX = sldwrksTxtImp(A135R5T150X,9);%[node# XDisp XLoc YLoc ZLoc]
R5T200Y = sldwrksTxtImp(A135R5T200Y,9);%[node# YDisp XLoc YLoc ZLoc]
R5TOY =
R5TOX =
R5T50Y
R5T50X
R5T200X = sldwrksTxtImp(A135R5T200X,9);%[node#
XDisp XLoc YLoc ZLoc]
R1TOY = sldwrksTxtImp(A135R1TOY,10);%[node# YDisp XLoc YLoc ZLoc]
RITOX = sldwrksTxtImp(A135R1TOX,10);%[node# XDisp XLoc YLoc ZLocI
R1T5OY = sldwrksTxtImp(A135R1T50Y,10);%[node# YDisp XLoc YLoc ZLocl
R1T50X = sldwrksTxtImp(A135R1T50X,10);%[node# XDisp XLoc YLoc ZLoc]
RlTlOQY = sldwrksTxtImp(A135R1T1O0Y,10);%[node# YDisp XLoc YLoc ZLoc]
RiTlOOX = sldwrksTxtImp(A135R1T100X,10);%[node# XDisp XLoc YLoc ZLocl
R1T150Y = sldwrksTxtImp(A135R1T15OY,10);%[node# YDisp XLoc YLoc ZLoc]
R1T150X =
R1T200Y =
sldwrksTxtImp(A135R1T15OX,10);%[node# XDisp XLoc YLoc ZLoc]
sldwrksTxtImp(A135R1T200Y,10);%[node# YDisp XLoc YLoc ZLoc]
R1T200X = sldwrksTxtImp(A135R1T200X,10);%[node# XDisp XLoc YLoc ZLocl
[YMaxR100TO,ResR100TO] = findYMaxLocFit(R100TOX,R100TOY);
[YMaxR100T50, ResR100T50]= findYMaxLocFit(R100T50X,R100T50Y);
[YMaxR100T100, ResR100T100]= findYMaxLocFit(R100T100X,R100T100Y);
[YMaxR100T150, ResR100T150]= findYMaxLocFit(R100T150X,R100T150Y);
[YMaxR100T200, ResR100T200]= findYMaxLocFit(R100T200X,R100T200Y);
[YMaxR5OTO, ResR50TO] = findYMaxLocFit(R50TOX,R50TOY);
[YMaxR50T50, ResRSOT50] = findYMaxLocFit(R50T50X,R5OT50Y);
[YMaxR5OT100, ResR5OT100] = findYMaxLocFit(R5OT100X,R5OT100Y);
[YMaxR5QT150,
ResR50T150]
[YMaxR50T200, ResR50T2001
=
findYMaxLocFit(R50T15OX,R5QT15OY);
= findYMaxLocFit(R5OT200X,R5OT200Y);
[YMaxR20TO, ResR20TO] = findYMaxLocFit(R20TOX,R20TOY);
[YMaxR20T50, ResR20T50] = findYMaxLocFit(R20T50X,R2OT50Y);
[YMaxR20T100, ResR20T100] = findYMaxLocFit(R20T100X,R2OT100Y);
[YMaxR20T15O, ResR20T150] = findYMaxLocFit(R20T15OX,R2OT15QY);
[YMaxR20T200,
ResR20T200]
=
findYMaxLocFit(R20T200X,R2OT200Y);
[YMaxR1OTO, ResRiOTO] = findYMaxLocFit(R1OTOX,R10TOY);
[YMaxR1QT50, ResR1OT50] = findYMaxLocFit(R1QT50X,R1OT50Y);
[YMaxR1OT100, ResRiOT100] = findYMaxLocFit(R1OT100X,R1OT100Y);
[YMaxR1OT150, ResR1OT150] = findYMaxLocFit(R1OT150X,R1OT150Y);
[YMaxR1QT200, ResR1OT200] = findYMaxLocFit(R1OT200X,R1OT200Y);
ResR5TO] = findYMaxLocFit(R5TOX,R5TOY);
[YMaxR5T50, ResR5T50] = findYMaxLocFit(R5T50X,R5T50Y);
[YMaxR5T100, ResR5T100] = findYMaxLocFit(R5T100X,R5T100Y);
[YMaxR5T150, ResR5T150] = findYMaxLocFit(R5T15OX,R5T15OY);
[YMaxR5T200, ResR5T200] = findYMaxLocFit(R5T200X,R5T200Y);
[YMaxR5TO,
[YMaxR1TO, ResRiTO] = findYMaxLocFit(RiTOX,RiTOY);
[YMaxR1T50, ResR1T50] = findYMaxLocFit(R1T50X,R1T50Y);
[YMaxR1T100, ResRTlOOI] = findYMaxLocFit(R1T100X,R1T100Y);
[YMaxR1T150, ResR1T150] = findYMaxLocFit(R1T150X,R1T15QY);
[YMaxR1T200, ResR1T200] = findYMaxLocFit(R1T200X,R1T200Y);
YMaxLocTO
=
[YMaxR100TO
YMaxR50TO
YMaxR20TO
YMaxR1OTO
YMaxR5TO
[YMaxR100T5O
YMaxR5OT50
YMaxR20T50
YMaxR1QT50
YMaxR5T50
[YMaxR100T100
YMaxRSOTTOO YMaxR20T100 YMaxR1OT100
YMaxR1TO];
YMaxLocT50 =
YMaxR1T50];
YMaxLocTlOO =
YMaxR1T100];
[YMaxR100T150
YMaxLocTl5O =
YMaxR5T100
YMaxR5OT15O YMaxR20T15O YMaxR1QT150
YMaxR5T150 YMaxR1T15O];
YMaxR5OT200 YMaxR20T200 YMaxR1OT200
[YMaxR100T200
YMaxLocT200 =
YMaxR1T200];
YMaxR5T200
YMaxLocAll = [YMaxLocTO; YMaxLocT50; YMaxLocTlOO; YMaxLocTl50; YMaxLocT200];
ResLocTO
[ResR100TO
ResR50TO
ResR20TO
ResRiOTO
ResR5TO
[ResR1OOT50
ResR50T50
ResR20T50
ResR1QT50
ResR5T50
=
[ResR100T100
ResR5OT100 ResR20T100 ResR1OT100 ResR5T100
=
[ResR100T150
ResR50T150 ResR20T150 ResR1QT150 ResR5T150
=
ResRiTO];
ResLocT50
=
ResR1T50];
ResLocT10
ResR1T100];
ResLocT150
ResR1T150];
ResR50T200 ResR20T200 ResR1OT200 ResR5T200
[ResR100T200
ResLocT200 =
ResR1T200];
ResAll = [ResLocTO; ResLocT50; ResLocT100; ResLocT150; ResLocT200];
YOut =
[YMaxLocAll
ResAll];
function [YMaxOut] = YDispDataAng90();
%this function does the follwing:
%1) Save name of files. Each file is the Y displacement data for
ratio,
%stiffness
displacement
%2) Use sldwrksTxtImp.m
%3)
a given
fold angle
and initial
to read each file
Use MaxYDispLoc.m to get maximum Y displacement value for each file
values
%3) Export all
%Each row in YMaxOut:
YMaxOut
called
in an array
[Fold Angle, Ratio, XDisp, Node# YDisp XLoc YLoc
ZLoc].
XDisp is the disp
wall (0,100,150 and 200mm)
%of the side
%Column is in order of stiffness Ratio
%% Save Names of files
7 20 2015 Disp and Twist 90 Deg 100 Ratio Y Disp 0-0_1.txt';
'8 2_2015 Disp and Twist 90 Deg 100 Ratio Y Disp 50-0_1.txt';
R10OT100Y = '7_20_2015 Disp and Twist 90 Deg 100 Ratio Y Disp 100-0_1.txt';
R100TOY =
R100T50Y =
R100T150Y =
R100T200Y =
'7_20_2015 Disp and Twist 90 Deg 100 Ratio Y Disp 150-0_1.txt';
'7_20_2015 Disp and Twist 90 Deg 100 Ratio Y Disp 200-0_1.txt';
'7 20_2015 Disp and Twist 90 Deg 50 Ratio Y Disp 0-0_1.txt';
'_ 2 2015 Disp and Twist 90 Deg 50 Ratio Y Disp 50-0_1.txt';
R50T100Y = '7 20_2015 Disp and Twist 90 Deg 50 Ratio Y Disp 100-0_1.txt';
R50TOY
R50T50Y
=
=
R50T150Y =
R50T200Y =
'7 20_2015 Disp and Twist 90 Deg 50 Ratio Y Disp 150-0_1.txt';
'7_20_2015 Disp and Twist 90 Deg 50 Ratio Y Disp 200-0_1.txt';
R20TOY = '7 20_2015 Disp and Twist 90 Deg 20 Ratio Y
R20T50Y = '8 2_2015 Disp and Twist 90 Deg 20 Ratio Y
R20T100Y = '7 20 2015 Disp and Twist 90 Deg 20 Ratio
R20T150Y = '7 20_2015 Disp and Twist 90 Deg 20 Ratio
R20T200Y = '7_20_2015 Disp and Twist 90 Deg 20 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0 1.txt';
Y Disp 150-0_1.txt';
R10TOY = '7 20_2015 Disp and Twist 90 Deg 10 Ratio Y
R10T5OY = '8 2_2015 Disp and Twist 90 Deg 10 Ratio Y
RlOT100Y = '7 20_2015 Disp and Twist 90 Deg 10 Ratio
R1OT150Y = '7 20 2015 Disp and Twist 90 Deg 10 Ratio
R1OT200Y = '7_20_2015 Disp and Twist 90 Deg 10 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 200-0_1.txt';
Y Disp 100-0_1.txt';
Y Disp 150-0 l.txt';
Y Disp 200-0_1.txt';
Disp 0-0_l.txt';
Disp 50-0_1.txt';
Y Disp 100-0_1.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
R5TOY = '7 20 2015 Disp and Twist 90 Deg 5
R5T50Y = '8 2 2015 Disp and Twist 90 Deg 5
R5T100Y = '7 20_2015 Disp and Twist 90 Deg
R5T150Y = '7 20_2015 Disp and Twist 90 Deg
R5T200Y = '7_20_2015 Disp and Twist 90 Deg
Ratio Y
Ratio Y
5 Ratio
5 Ratio
5 Ratio
R1TOY = '7 20 2015 Disp and Twist 90 Deg 1
R1T50Y = '8 2 2015 Disp and Twist 90 Deg 1
R1T1OY = '7 20_2015 Disp and Twist 90 Deg
R1T150Y = '7 20_2015 Disp and Twist 90 Deg
RlT200Y = '7 20_2015 Disp and Twist 90 Deg
Ratio Y Disp 0-0_1.txt';
Ratio Y Disp 50-0_1.txt';
1 Ratio Y Disp 100-0_1.txt';
1 Ratio Y Disp 150-0_l.txt';
1 Ratio Y Disp 200-0_1.txt';
%% Read each file and get maximum Y displacement
c = 5;
n = 6*c;
YMax = zeros(n,8);
YMax(:,1) = 90;
YMax(1:c,2) = 100;
%[Fold
Angle,
Ratio,
XDisp,
Node# YDisp XLoc YLoc ZLoc]
YMax(c+1:2*c,2) = 50;
YMax(2*c+1:3*c,2) = 20;
YMax(3*c+1:4*c,2) = 10;
YMax(4*c+l: 5*c, 2) = 5;
YMax(5*c+1:6*c,2) - 1;
ERatio = [0 50 100 150 200];
YMax(:,3) = [ERatio ERatio ERatio ERatio ERatio ERatiol;
YMax(1,4:8)
YMax(2,4:8)
YMax(3,4:8)
YMax(4,4:8)
YMax(5,4:8)
MaxYDispLoc(sldwrksTxtImp(R100TOY,10));
MaxYDispLoc(sldwrksTxtImp(RiOOT50Y,10))
YMax(6, 4 :8)
YMax(7, 4 :8)
YMax(8, 4 :8)
YMax (9, 4 :8)
YMax (10, 4:8)
MaxYDispLoc(sldwrksTxtImp(R5OTOY,10));
)
MaxYDispLoc(sldwrksTxtImp(R100T150Y,10)
MaxYDispLoc(sldwrksTxtImp(R100T200Y,10)
MaxYDispLoc(sldwrksTxtImp(R5OT50Y,10));
MaxYDispLoc(sldwrksTxtImp(R5OT100Y,10))
MaxYDispLoc(sldwrksTxtImp(R5OT150Y,10))
= MaxYDispLoc(sldwrksTxtImp(R5OT200Y,10)
4:8)
4:8)
4:8)
4:8)
4:8)
=
(16, 4:8)
(17, 4:8)
(18, 4:8)
(19, 4:8)
(20, 4:8)
=
YMax(21,4:8)
YMax(22,4:8)
YMax(23,4:8)
YMax(24,4:8)
YMax(25, 4:8)
=
=
=
=
=
MaxYDispLoc(sldwrksTxtImp(R20TOY,10));
MaxYDispLoc(sldwrksTxtImp(R2OT50Y,10))
= MaxYDispLoc(sldwrksTxtImp(R2OT100Y,10)
= MaxYDispLoc(sldwrksTxtImp(R2OT15OY,10)
= MaxYDispLoc(sldwrksTxtImp(R2OT200Y,10)
=
MaxYDispLoc(sldwrksTxtImp(R1OTOY,10));
MaxYDispLoc(sldwrksTxtImp(R1OT5OY,10))
=
MaxYDispLoc(sldwrksTxtImp(R1OT100Y,10)
=
MaxYDispLoc(sldwrksTxtImp(R1OT150Y,10)
MaxYDispLoc(sldwrksTxtImp(R1OT200Y,10)
=
YMax (26,4:8)
YMax(27, 4:8)
YMax(28, 4:8)
YMax(29, 4:8)
YMax(30,4:8)
%% Export array
YMaxOut = YMax;
;
)
YMax
YMax
YMax
YMax
YMax
=
MaxYDispLoc(sldwrksTxtImp(R5TOY,10));
MaxYDispLoc(sldwrksTxtImp(R5T50Y,10));
MaxYDispLoc(sldWrksTxtImp(R5T100Y,10))
MaxYDispLoc(sldwrksTxtImp(R5T15OY,10))
MaxYDispLoc(sldwrksTxtImp(R5T200Y,10))
;
;
;
MaxYDispLoc(sldwrksTxtImp(RiTOY,10));
MaxYDispLoc(sldwrksTxtImp(R1T50Y,10))
MaxYDispLoc(sldwrksTxtImp(RiTlOQY,10)
MaxYDispLoc(sldwrksTxtImp(R1T15OY,10)
;
)
YMax (11,
YMax(12,
YMax(13,
YMax(14,
YMax (15,
;
MaxYDispLoc(sldwrksTxtImp(R100T100Y,10)
MaxYDispLoc(sldwrksTxtImp(R1T200Y,10)
;
;
;
;
;
;
function [YMaxOut] = YDispDataAnglO5O;
%this function does the follwing:
%1) Save name of files. Each file is the Y displacement data for a given
%stiffness ratio, displacement and initial fold angle
%2) Use sldwrksTxtImp.m to read each file
%3) Use MaxYDispLoc.m to get maximum Y displacement value for each file
YMaxOut
values
in an array
called
%3) Export all
%Each row in YMaxOut: [Fold Angle, Ratio, XDisp, Node# YDisp XLoc YLoc ZLoc].
XDisp is the disp
%of the
side
wall (0,100,150 and 200mm)
%Column is in order of stiffness Ratio
%% Save Names of files
R100TOY = '8 11_2015 Disp and Twist 105 Deg 100 Ratio Y
R100T50Y = '8 2 2015 Disp and Twist 105 Deg 100 Ratio Y
R10OT100Y = '7_20_2015 Disp and Twist 105 Deg 100 Ratio
R10OT150Y = '7_20_2015 Disp and Twist 105 Deg 100 Ratio
R100T200Y = '7_20_2015 Disp and Twist 105 Deg 100 Ratio
Disp 0-0_1.txt';
Disp 50-0 1.txt';
Y Disp 100-0_1.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
R50TOY = '8 11_2015 Disp and Twist 105 Deg 50 Ratio Y Disp 0-0_1.txt';
R5OT50Y = '8 2_2015 Disp and Twist 105 Deg 50 Ratio Y Disp 50-0_1.txt';
R50T100Y = '7 20 2015 Disp and Twist 105 Deg 50 Ratio Y Disp 100-0 1.txt';
R50T150Y =
R5QT200Y =
R20TOY =
R20T50Y
'7 20_2015 Disp and Twist 105 Deg 50 Ratio Y Disp 150-0_1.txt';
'7_20_2015 Disp and Twist 105 Deg 50 Ratio Y Disp 200-0_1.txt';
Disp 0-0_1.txt';
'8 2_2015 Disp and Twist 105 Deg 20 Ratio Y Disp 50-0_1.txt';
'8 11_2015 Disp and Twist 105 Deg 20 Ratio Y
=
R20T100Y =
R20T150Y =
R20T200Y =
'7 20_2015 Disp and Twist 105 Deg 20 Ratio Y Disp 100-0_1.txt';
'7 20 2015 Disp and Twist 105 Deg 20 Ratio Y Disp 150-0 1.txt';
'7_20_2015 Disp and Twist 105 Deg 20 Ratio Y Disp 200-0_1.txt';
R10TOY =
'8 11_2015 Disp and Twist 105 Deg 10 Ratio Y
'8 2_2015 Disp and Twist 105 Deg 10 Ratio Y
RlOT100Y = '7 20_2015 Disp and Twist 105 Deg 10 Ratio
R1OT150Y = '7 20_2015 Disp and Twist 105 Deg 10 Ratio
RIT200Y = '7_20_2015 Disp and Twist 105 Deg 10 Ratio
R1OT50Y
R5TOY
=
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0_l.txt';
Y Disp 150-0_l.txt';
Y Disp 200-0_1.txt';
'8 11 2015 Disp and Twist 105 Deg 5
'8 2 2015 Disp and Twist 105 Deg 5
R5T100Y = '7 20_2015 Disp and Twist 105 Deg
R5T15OY = '7 20_2015 Disp and Twist 105 Deg
R5T200Y = '7_20_2015 Disp and Twist 105 Deg
Ratio Y
Ratio Y
5 Ratio
5 Ratio
5 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0_1.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
R1TOY = '8 11 2015 Disp and Twist 105 Deg 1
R1T50Y = '8 2 2015 Disp and Twist 105 Deg 1
R1T10OY = '7 20_2015 Disp and Twist 105 Deg
R1T150Y = '7 20_2015 Disp and Twist 105 Deg
R1T200Y = '7_20_2015 Disp and Twist 105 Deg
Ratio Y
Ratio Y
1 Ratio
1 Ratio
1 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0_1.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
=
R5T50Y =
%% Read each file and get maximum Y displacement
c = 5;
n = 6*c;
YMax = zeros(n,8); %[Fold Angle, Ratio, XDisp, Node# YDisp XLoc YLoc ZLocl
YMax(:,1) = 105;
YMax(l:c,2) = 100;
YMax(c+1:2*c,2) = 50;
YMax(2*c+1:3*c,2) = 20;
YMax(3*c+1:4*c,2) = 10;
YMax(4*c+1:5*c,2) = 5;
YMax(5*c+1:6*c,2) = 1;
ERatio = [0 50 100 150 200];
YMax(:,3) = [ERatio ERatio ERatio ERatio ERatio ERatio];
% path = 'Test Data/';
% strcat(path,R100TOY)
% fname = 'testTable.txt';
o
D = sldwrksTxtImp(R5OT15OY,10);
% Dl = MaxYDispLoc(D);
YMax (1, 4:8)
MaxYDispLoc(sldwrksTxtImp (R1OTOY,10));
YMax (2, 4:8)
MaxYDispLoc(sldwrksTxtImp (R100T50Y,10))
YMax (3, 4:8)
MaxYDispLoc(sldwrksTxtImp (R1OT100Y,10) ;
YMax (4, 4:8)
MaxYDispLoc(sldwrksTxtImp (R100T150Y,10) ;
YMax (5, 4:8)
MaxYDispLoc(sldwrksTxtImp (R100T200Y,10) ;
YMax
YMax
YMax
YMax
YMax
(6, 4:8)
(7, 4:8)
(8, 4:8)
(9, 4:8)
(10 ,4:8)
YMax (11,4: 8)
YMax
YMax
YMax
YMax
(12,4:
(13,4:
(14,4:
(15,4:
8)
8)
8)
8)
MaxYDispLoc(sldwrksTxtImp (R50TOY,10));
MaxYDispLoc(sldwrksTxtImp (R50T5OY,10)) ;
MaxYDispLoc(sldwrksTxt.Imp (R50T100Y,10));
MaxYDispLoc(sldwrksTxtImp (R50T150Y,10));
= MaxYDispLoc(sldwrksTxtImp(R5OT200Y,10));
MaxYDispLoc (sldwrksTxtImp (R20TOY,10));
MaxYDispLoc (sldwrksTxtImp (R20T5OY,10)) ;
;
;
;
YMax (16,4:8)
YMax(17,4:8)
YMax(18,4:8)
YMax(19,4:8)
YMax(20,4:8)
MaxYDispLoc (sldwrksTxtImp(RiOTOY,10));
MaxYDispLoc (sldwrksTxtImp(R1OT50Y,10)) ;
MaxYDispLoc (sldwrksTxtImp(RiOT100Y,10)
MaxYDispLoc (sldwrksTxtImp(RiOT150Y,10)
MaxYDispLoc (sldwrksTxtImp(R1OT200Y,10)
;
;
;
YMax(21,4:8)
YMax(22,4:8)
YMax(23,4:8)
YMax(24,4:8)
YMax(25,4:8)
MaxYDispLoc (sldwrksTxtImp(R5TOY,10));
MaxYDispLoc (sldwrksTxtImp(R5T50Y,10));
MaxYDispLoc (sldwrksTxtImp(R5T100Y,10))
MaxYDispLoc (sldwrksTxtImp(R5T15OY,10))
MaxYDispLoc (sldwrksTxtImp(R5T200Y,10))
YMax(26,4:8)
YMax (27, 4: 8)
YMax (28,4:8)
YMax(29,4:8)
YMax(30,4:8)
MaxYDispLoc (sldwrksTxtImp(RiTOY,10));
%% Export
YMaxOut =
)
)
MaxYDispLoc (sldwrksTxtImp (R20T100Y,10)
MaxYDispLoc (sldwrksTxtImp (R20T150Y,10)
MaxYDispLoc (sldwrksTxtImp (R20T200Y,10)
array
YMax;
MaxYDispLoc (sldwrksTxtImp(R1T50Y,10));
MaxYDispLoc (sldwrksTxtImp(RiTlOQY,10))
MaxYDispLoc (sldwrksTxtImp(RiTi5OY,10))
MaxYDispLoc (sldwrksTxtImp(R1T200Y,10))
function [YMaxOut] = YDispDataAng120(;
%this function does the follwing:
%1)
Save name of files. Each file is the Y
%stiffness ratio,
displacement data for a given
displacement and initial fold angle
%2) Use sldwrksTxtImp.m to read each file
%3) Use MaxYDispLoc.m to get maximum Y displacement value for each file
%-3) Export all
values
in an array
called
YMaxOut
%Each row in YMaxOut: [Fold Angle, Ratio, XDisp, Node# YDisp XLoc YLoc ZLoc].
XDisp is the disp
%of the side wall
(0,100,150 and 200mm)
%Column is in order of stiffness Ratio
%% Save Names of files
R100TOY
=
'8 11 2015 Disp and Twist 120 Deg 100 Ratio Y Disp 0-0_1.txt';
R100T50Y = '8_2_2015 Disp and Twist 120 Deg 100 Ratio Y
R100T100Y = '7_20_2015 Disp and Twist 120 Deg 100 Ratio
R10OT150Y = '7_20_2015 Disp and Twist 120 Deg 100 Ratio
R100T200Y = '7_20_2015 Disp and Twist 120 Deg 100 Ratio
Disp 50-0_1.txt';
Y Disp 100-0_l.txt';
Y Disp 150-0_l.txt';
Y Disp 200-0_1.txt';
R50TOY = '8 11_2015 Disp and Twist 120 Deg 50 Ratio Y
R50T50Y = '8 2 2015 Disp and Twist 120 Deg 50 Ratio Y
R5QT100Y = '7 20_2015 Disp and Twist 120 Deg 50 Ratio
R50T150Y = '7_20_2015 Disp and Twist 120 Deg 50 Ratio
R50T200Y = '7_20_2015 Disp and Twist 120 Deg 50 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
R20TOY = '8 11_2015 Disp and Twist 120 Deg 20 Ratio Y
R20T50Y = '8 2_2015 Disp and Twist 120 Deg 20 Ratio Y
R20T100Y = '7 20 2015 Disp and Twist 120 Deg 20 Ratio
R20T150Y = '7 20_2015 Disp and Twist 120 Deg 20 Ratio
R20T200Y = '7_20_2015 Disp and Twist 120 Deg 20 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0 l.txt';
Y Disp 150-0_l.txt';
Y Disp 200-0_1.txt';
'R10TOY =
'8 11_2015 Disp and Twist
Y Disp 100-0_1.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
120 Deg 10 Ratio Y Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0_l.txt';
Y Disp 150-0 l.txt';
Y Disp 200-0_1.txt';
R1OT50Y = '8 2_2015 Disp and Twist 120 Deg 10 Ratio Y
R1OT100Y = '7 20_2015 Disp and Twist 120 Deg 10 Ratio
R10T150Y = '7 20 2015 Disp and Twist 120 Deg 10 Ratio
RlT200Y = '7_20_2015 Disp and Twist 120 Deg 10 Ratio
R5TOY = '8 11 2015 Disp and Twist 120 Deg 5
R5T50Y = '8 2 2015 Disp and Twist 120 Deg 5
R5T100Y = '7 20_2015 Disp and Twist 120 Deg
R5T150Y = '7 20_2015 Disp and Twist 120 Deg
R5T200Y = '7_20_2015 Disp and Twist 120 Deg
Ratio Y
Ratio Y
5 Ratio
5 Ratio
5 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0_l.txt';
Y Disp 150-0_l.txt';
Y Disp 200-0 1.txt';
R1TOY = '8 11 2015 Disp and Twist 120 Deg 1
RlT50Y = '8 2 2015 Disp and Twist 120 Deg 1
R1T100Y = '7 20_2015 Disp and Twist 120 Deg
R1T150Y = '7 20_2015 Disp and Twist 120 Deg
R1T200Y = '7_20_2015 Disp and Twist 120 Deg
Ratio Y
Ratio Y
1 Ratio
1 Ratio
1 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0 l.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
%% Read each file
and get maximum Y displacement
c = 5;
n = 6*c;
YMax = zeros(n,8); %[Fold Angle, Ratio, XDisp, Node# YDisp XLoc YLoc ZLoc]
YMax(:,1) = 120;
YMax(l:c,2) = 100;
YMax(c+1:2*c,2) = 50;
YMax(2*c+1:3*c,2) = 20;
YMax(3*c+1:4*c,2) = 10;
YMax(4*c+1:5*c,2) = 5;
YMax(5*c+1:6*c,2) = 1;
ERatio = [0 50 100 150 200];
YMax(:,3) = [ERatio ERatio ERatio ERatio ERatio ERatio];
(1,4
(2,4
(3, 4
(4,4
(5,4
:8)
:8)
:8)
:8)
:8)
YMax(6,4:8)
YMax(7,4:8)
YMax(8,4:8)
YMax(9,4:8)
YMax(10,4:8)
MaxYDispLoc (sldwrksTxtImp(R1OTOY,10));
MaxYDispLoc (sldwrksTxtImp(R100T50Y,10)) ;
MaxYDispLoc (sldwrksTxtImp(R1OT100Y,10)
MaxYDispLoc (sldwrksTxtImp(R1OT150Y,10)
MaxYDispLoc (sldwrksTxtImp(R100T200Y,10)
)
YMax
YMax
YMax
YMax
YMax
;
;
;
MaxYDispLoc(sldwrksTxtImp(R5OTOY,10));
MaxYDispLoc(sldwrksTxtImp(R5OT50Y,10));
MaxYDispLoc(sldwrksTxtImp(R5OT100Y,10));
=
MaxYDispLoc(sldwrksTxtImp(R5OT15OY,10));
MaxYDispLoc(sldwrksTxtImp(R5OT200Y,10));
YMax
YMax
YMax
YMax
YMax
(11,4
(12,4
(13,4
(14,4
(15,4
:8)
:8)
:8)
:8)
:8)
MaxYDispLoc (sldwrksTxtImp(R20TOY,10));
YMax
YMax
YMax
YMax
YMax
(16,4 :8)
(17,4 :8)
(18,4 :8)
(19,4 :8)
(20,4 :8)
MaxYDispLoc (sldwrksTxtImp(RiOTOY,10));
MaxYDispLoc (sldwrksTxtImp(R1OT50Y,10))
MaxYDispLoc (sldwrksTxtImp(R1OT100Y,10)
MaxYDispLoc (sldwrksTxtImp(RiOT150Y,10)
MaxYDispLoc (sldwrksTxtImp(R1OT200Y,10)
YMax
YMax
YMax
YMax
YMax
(21,4 :8)
(22,4 :8)
(23,4 :8)
(24,4 :8)
(25,4 :8)
MaxYDispLoc
MaxYDispLoc
MaxYDispLoc
MaxYDispLoc
MaxYDispLoc
YMax
YMax
YMax
YMax
YMax
(26,4 :8)
(27,4 :8)
(28,4 :8)
(29,4 :8)
(30,4 :8)
MaxYDispLoc (sldwrksTxtImp(RiTOY,10));
%% Export array
YMaxOut = YMax;
)
MaxYDispLoc (sldwrksTxtImp(R2OT50Y,10)) ;
MaxYDispLoc (sldwrksTxtImp(R2OT100Y,10)
MaxYDispLoc (sldwrksTxtImp(R2OT15OY,10)
MaxYDispLoc (sldwrksTxtImp(R2OT200Y,10)
(sldwrksTxtImp(R5TOY,10));
(sldwrksTxtImp(R5T50Y,10));
(sldwrksTxtImp(R5T100Y,10))
(sldwrksTxtImp(R5T15OY,10))
(sldwrksTxtImp(R5T200Y,10))
;
;
;
MaxYDispLoc (sldwrksTxtImp(R1T50Y,10));
MaxYDispLoc (sldwrksTxtImp(RiTlOQY,10))
MaxYDispLoc (sldwrksTxtImp(RiTi5OY,10))
;
;
MaxYDispLoc(sldwrksTxtImp(R1T200Y,10));
[YMaxOut]
function
= YDispDataAng135);
%this function does the follwing:
%1) Save name of files. Each file is the Y displacement data for a given
%stiffness ratio, displacement and initial fold angle
%2) Use sldwrksTxtImp.m to read each file
%3) Use MaxYDispLoc.m to get maximum Y displacement value for each file
called
YMaxOut
values
in an array
%3) Export all
%Each row in YMaxOut: [Fold Angle, Ratio, XDisp, Node# YDisp XLoc YLoc ZLoc].
XDisp is the disp
wall (0,100,150 and 200mm)
%of the
side
%Column is in order of stiffness Ratio
%% Save Names of files
R100TOY = '8 11 2015 Disp and Twist 135 Deg 100 Ratio Y
R100T50Y = '8 2_2015 Disp and Twist 135 Deg 100 Ratio Y
R10OT100Y = '7_20 2015 Disp and Twist 135 Deg 100 Ratio
R10OT150Y = '7_20 2015 Disp and Twist 135 Deg 100 Ratio
R100T200Y = '7_20_2015 Disp and Twist 135 Deg 100 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0_l.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
0-0_1.txt';
R50TOY = '8 11_2015 Disp and Twist 135 Deg 50 Ratio Y
R50T50Y = '8 2 2015 Disp and Twist 135 Deg 50 Ratio Y
R50T100Y = '7 20_2015 Disp and Twist 135 Deg 50 Ratio
R50T150Y = '7 20_2015 Disp and Twist 135 Deg 50 Ratio
R50T200Y = '7_20_2015 Disp and Twist 135 Deg 50 Ratio
Disp
Disp
R20TOY = '8 11_2015 Disp and Twist 135 Deg 20 Ratio Y
R20T50Y = '8 2_2015 Disp and Twist 135 Deg 20 Ratio Y
R20T100Y = '7 20 2015 Disp and Twist 135 Deg 20 Ratio
R20T150Y = '7 20_2015 Disp and Twist 135 Deg 20 Ratio
R20T200Y = '7_20_2015 Disp and Twist 135 Deg 20 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0 l.txt';
Y Disp 150-0_l.txt';
Y Disp 200-0_1.txt';
R10TOY =
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0_1.txt';
Y Disp 150-0 1.txt';
Y Disp 200-0_1.txt';
'8 11_2015 Disp and Twist 135 Deg 10 Ratio Y
'8 2_2015 Disp and Twist 135 Deg 10 Ratio Y
RlOT100Y = '7 20_2015 Disp and Twist 135 Deg 10 Ratio
R10T150Y = '7 20 2015 Disp and Twist 135 Deg 10 Ratio
R1OT200Y = '7_20_2015 Disp and Twist 135 Deg 10 Ratio
R1OT50Y
=
50-0_1.txt';
Y Disp 100-0_l.txt';
Y
Y
Disp 150-0_1.txt';
Disp 200-0_1.txt';
'8 11 2015 Disp and Twist 135 Deg 5
'8_2_2015 Disp and Twist 135 Deg 5
R5T100Y = '7 20_2015 Disp and Twist 135 Deg
R5T150Y = '7 20_2015 Disp and Twist 135 Deg
R5T200Y = '7_20_2015 Disp and Twist 135 Deg
Ratio Y
Ratio Y
5 Ratio
5 Ratio
5 Ratio
Disp 0-0_l.txt';
Disp 50-0_1.txt';
Y Disp 100-0_1.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
R1TOY = '8 11 2015 Disp and Twist 135 Deg 1
R1T50Y = '8 2 2015 Disp and Twist 135 Deg 1
R1T1OY = '7 20_2015 Disp and Twist 135 Deg
R1T150Y = '7 20_2015 Disp and Twist 135 Deg
R1T200Y = '7_20_2015 Disp and Twist 135 Deg
Ratio Y
Ratio Y
1 Ratio
1 Ratio
1 Ratio
Disp 0-0_1.txt';
Disp 50-0_1.txt';
Y Disp 100-0_1.txt';
Y Disp 150-0_1.txt';
Y Disp 200-0_1.txt';
R5TOY =
R5T50Y
=
%% Read each file and get maximum Y displacement
c = 5;
n = 6*c;
YMax = zeros(n,8);
YMax(:,1)
= 135;
YMax(1:c,2) = 100;
%[Fold
Angle,
Ratio,
XDisp,
Node# YDisp XLoc YLoc ZLocl
YMax(c+1:2*c,2) = 50;
YMax(2*c+1:3*c,2) = 20;
YMax(3*c+1:4*c,2) = 10;
YMax(4*c+1:5*c,2) = 5;
YMax(5*c+1:6*c,2) = 1;
ERatio = [0 50 100 150 200];
YMax(:,3) = [ERatio ERatio ERatio ERatio ERatio ERatio];
MaxYDispLoc (sldwrksTxtImp(R1OTOY,10));
MaxYDispLoc (sldwrksTxtImp(R100T50Y,10)) ;
MaxYDispLoc (sldwrksTxtImp(RO1OT100Y,10)
YMax(6,4:8)
YMax(7,4:8)
YMax(8,4:8)
YMax(9,4:8)
YMax(10,4:8)
MaxYDispLoc (sldwrksTxtImp(R5OTOY,10));
MaxYDispLoc (sldwrksTxtImp(R50T5OY,10));
MaxYDispLoc (sldwrksTxtImp(R5OT100Y,10)) ;
)
YMax(1,4:8)
YMax(2,4:8)
YMax(3,4:8)
YMax(4,4:8)
YMax(5,4:8)
MaxYDispLoc (sldwrksTxtImp(RO1OT150Y,10)
MaxYDispLoc (sldwrksTxtImp(R100T200Y,10)
MaxYDispLoc (sldwrksTxtImp(R5OT15OY,10)) ;
= MaxYDispLoc(sldwrksTxtImp(R5OT200Y,10));
MaxYDispLoc (sldwrksTxtImp(R20TOY,10));
MaxYDispLoc (sldwrksTxtImp(R2OT50Y,10)) ;
MaxYDispLoc (sldwrksTxtImp(R2OT100Y,10)
YMax (16, 4: 8)
YMax (17,4: 8)
YMax(18, 4: 8)
YMax(19, 4: 8)
YMax (20,4: 8)
MaxYDispLoc (sldwrksTxtImp(RiOTOY,10));
MaxYDispLoc (sldwrksTxtImp(R1OT50Y,10)) ;
MaxYDispLoc (sldwrksTxtImp(R1OT100Y,10)
MaxYDispLoc (sldwrksTxtImp(R1OT150Y,10)
MaxYDispLoc (sldwrksTxtImp(R1OT200Y,10)
YMax(21,4:8)
YMax(22,4:8)
YMax(23,4:8)
YMax(24,4:8)
YMax(25,4:8)
MaxYDispLoc (sldwrksTxtImp(R5TOY,10));
MaxYDispLoc (sldwrksTxtImp(R5T50Y,10))
MaxYDispLoc (sldwrksTxtImp(R5T100Y,10)
MaxYDispLoc (sldwrksTxtImp(R5T15OY,10)
MaxYDispLoc (sldwrksTxtImp(R5T200Y,10)
MaxYDispLoc (sldwrksTxtImp(R2OT15OY,10)
)
MaxYDispLoc (sldwrksTxtImp(R2OT200Y,10)
YMax (26,4 :8)
MaxYDispLoc
YMax (27,4 :8)
MaxYDispLoc
MaxYDispLoc
YMax (28,4 :8)
MaxYDispLoc
YMax (29,4 :8)
MaxYDispLoc
YMax (30,4 :8)
%% Export array
YMaxOut = YMax;
(sldwrksTxtImp(RiTOY,10));
(sldwrksTxtImp(R1T50Y,10)) ;
(sldwrksTxtImp(RiT1OY,10)
)
(11,4:
(12,4:
(13,4:
(14,4:
(15,4:
)
8)
8)
8)
8)
8)
YMax
YMax
YMax
YMax
YMax
;
;
;
(sldwrksTxtImp(RiTi5OY,10)
(sldwrksTxtImp(R1T200Y,10)