Frequency Response Cyclic Stress Prediction in a Bolted Joint
by
Brian Petrarca
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
December 2008
i
CONTENTS
Frequency Response Cyclic Stress Prediction in a Bolted Joint ........................................ i
LIST OF TABLES ............................................................................................................ iii
LIST OF FIGURES .......................................................................................................... iv
Nomenclature .................................................................................................................... vi
ACKNOWLEDGMENT ................................................................................................ viii
ABSTRACT ..................................................................................................................... ix
1. Introduction.................................................................................................................. 1
2. Analysis of Single Bolted Bracket ............................................................................... 3
2.1
Complex 3-D Solid Model: ................................................................................ 4
2.2
Simplistic Shell Model: ...................................................................................... 8
2.3
Analysis Results ............................................................................................... 10
3. Analysis of Commercial Typical Hardware .............................................................. 21
4. Practical Methods for Improved Results ................................................................... 28
4.1
Spring Method .................................................................................................. 30
5. Conclusion ................................................................................................................. 35
References........................................................................................................................ 37
Appendix.......................................................................................................................... 38
ii
LIST OF TABLES
Table 1: Single Bolt Conditions Considered ..................................................................... 3
Table 2: Analysis Material Properties .............................................................................. 4
Table 3: Mesh Density Statistics ..................................................................................... 19
Table 4: Material Properties Production Bracket ............................................................ 21
iii
LIST OF FIGURES
Figure 1: Bracket Geometric Configuration ...................................................................... 3
Figure 2: Model Description ............................................................................................. 5
Figure 3: Displacement Boundary Conditions ................................................................. 5
Figure 4: Load Description ............................................................................................... 6
Figure 5: Path Description ................................................................................................ 7
Figure 6: Shell Model ....................................................................................................... 9
Figure 7: R-ratio for 0.125”- 1.00” Overhang ................................................................. 11
Figure 8: Bracket Nomenclature ...................................................................................... 12
Figure 9: Bracket Without Overhang .............................................................................. 13
Figure 10: Alternating Stress vs. Location 0.062” – No overhang ................................. 14
Figure 11: Alternating Stress vs. Location 0.125” – No overhang .................................. 14
Figure 12: Alternating Stress vs. Location 0.062” – 0.5” Overhang ............................... 15
Figure 13: Alternating Stress vs. Location 0.062” – 1.00” Overhang ............................. 16
Figure 14: Alternating Stress vs. Location 0.125” – 1.00” Overhang ............................. 17
Figure 15: Alternating Stress vs. Location 0.125” – 0.5” Overhang ............................... 18
Figure 16: Mesh Density Effect, Shell Model ................................................................. 19
Figure 17: Mesh Density Effect, Solid Model ................................................................. 20
Figure 18. Commercial Bracket ....................................................................................... 21
Figure 19: FE Mesh of shell model ................................................................................. 22
Figure 20: FE mesh of solid model with contact ............................................................. 22
Figure 21: Shell model Von Misses Stress ...................................................................... 23
Figure 22: Alternating Stress Solid Model ...................................................................... 24
Figure 23: Alternating Stress Shell Model Top Surface .................................................. 25
Figure 24: Alternating Stress Shell Model Bottom Surface ............................................ 25
Figure 25: Alternating Stress Solid Model Top View ..................................................... 26
Figure 26: Alternating Stress Solid Model Top View ..................................................... 27
Figure 27: Alternating Stress Solid Model Bottom View ............................................... 27
Figure 28: Model with springs in contact region ............................................................. 28
Figure 29: Alternating stress vs. position for varying spring stiffness ............................ 29
Figure 30: Alternating Stress; Solid Model vs. Shell Model Constrained ...................... 30
iv
Figure 31: Alternating Stress Comparison; Solid Model vs. Shell with Springs ............ 31
Figure 32: Alternating Stress Solid Model Modified Elastic Modulus ........................... 33
Figure 33: Shell Spring Model, Bracket and Spring Stiffness Relationship ................... 34
v
Nomenclature
k
spring stiffness
Rratio
the ratio of minimum to maximum stress for a load cycle
σ
stress
𝜎𝑚𝑎𝑥 Maximum stress 𝜎𝑉𝑀𝑚𝑒𝑎𝑛 + 𝜎𝑉𝑀𝑎𝑙𝑡
𝜎𝑚𝑖𝑛
Minimum stress 𝜎𝑉𝑀𝑚𝑒𝑎𝑛 − 𝜎𝑉𝑀𝑎𝑙𝑡
𝜎𝑥𝑎𝑙𝑡
Alternating stress in the x direction = 𝜎𝑥𝑝𝑜𝑠 − 𝜎𝑥𝑛𝑒𝑔
𝜎𝑥𝑛𝑒𝑔 Stress in the x direction for a negative application of load, which corresponds to
the solution to load step 3 in the FEA analysis
𝜎𝑥𝑝𝑜𝑠
Stress in the x direction for a positive application of load, which corresponds to
the solution to load step 2 in the FEA analysis
𝜎𝑦𝑎𝑙𝑡
Alternating stress in the y direction = 𝜎𝑦𝑝𝑜𝑠 − 𝜎𝑦𝑛𝑒𝑔
𝜎𝑦𝑛𝑒𝑔 Stress in the y direction for a negative application of load, which corresponds to
the solution to load step 3 in the FEA analysis
𝜎𝑦𝑝𝑜𝑠
Stress in the y direction for a positive application of load, which corresponds to
the solution to load step 2 in the FEA analysis
𝜎𝑧𝑎𝑙𝑡
Alternating stress in the z direction = 𝜎𝑧𝑝𝑜𝑠 − 𝜎𝑧𝑛𝑒𝑔
𝜎𝑧𝑝𝑜𝑠
Stress in the z direction for a positive application of load, which corresponds to
the solution to load step 2 in the FEA analysis
𝜎𝑧𝑛𝑒𝑔 Stress in the z direction for a negative application of load, which corresponds to
the solution to load step 3 in the FEA analysis
𝜎𝑉𝑀𝑎𝑙𝑡 Alternating stress calculated using von Mises
𝜎𝑉𝑀𝑚𝑒𝑎𝑛 Mean stress calculated using von Mises
𝜏𝑥𝑦𝑝𝑜𝑠 Shear stress in x-y plane, which corresponds to the solution to load step 2 in the
FEA analysis
𝜏𝑥𝑦𝑛𝑒𝑔 Shear stress in x-y plane, which corresponds to the solution to load step 3 in the
FEA analysis
𝜏𝑥𝑦𝑎𝑙𝑡 Alternating shear stress in the x-y plane = 𝜏𝑥𝑦𝑝𝑜𝑠 − 𝜏𝑥𝑦𝑛𝑒𝑔
vi
𝜏𝑦𝑧𝑝𝑜𝑠 Shear stress in y-z plane, which corresponds to the solution to load step 2 in the
FEA analysis
𝜏𝑦𝑧𝑛𝑒𝑔 Shear stress in y-z plane, which corresponds to the solution to load step 3 in the
FEA analysis
𝜏𝑦𝑧𝑎𝑙𝑡 Alternating shear stress in the y-z plane = 𝜏𝑦𝑧𝑝𝑜𝑠 − 𝜏𝑦𝑧𝑛𝑒𝑔
𝜏𝑧𝑥𝑝𝑜𝑠 Shear stress in z-x plane, which corresponds to the solution to load step 2 in the
FEA analysis
𝜏𝑧𝑥𝑛𝑒𝑔 Shear stress in z-x plane, which corresponds to the solution to load step 3 in the
FEA analysis
𝜏𝑧𝑥𝑎𝑙𝑡 Alternating shear stress in the z-x plane = 𝜏𝑧𝑥𝑝𝑜𝑠 − 𝜏𝑧𝑥𝑛𝑒𝑔
vii
ACKNOWLEDGMENT
Scott Hjelm, Externals Structures Deputy Manager, for providing the inspiration for this
paper and technical assistance.
viii
ABSTRACT
In Finite Element Analysis software packages, such as ANSYS, the stiffness matrix is
constant for a frequency response analysis. This restriction prevents the inclusion of
contact in the model. The absence of contact leads to unrealistic predictions of the
alternating stress. The alternating stress is higher without the contact because in reality a
fully reversing load will not generate a fully reversing stress in the contact region as it
does when contact is omitted.
A study was conducted to quantify the effect of contact using static models. Two
different static models were created. One contained contact, the other did not. The static
models were solved twice for a load of the same magnitude. The direction of the applied
load was reversed in the second solution. This was done to simulate the effect of
harmonic loading. The difference in stress between the two solutions was used to
calculate the alternating stress. The alternating stress from the model with contact was
then compared to the alternating stress from the model that did not contain contact. It
was found that the results did not mach.
The magnitude and the location of the
maximum alternating stress were different. This is demonstrated for a multitude of parts
were the geometry of the part is varied. In all cases the alternating stress was higher in
the model without contact in the region where there should be contact. Both models had
similar alternating stress in the non contact region of the part.
Methods of modifying the model that did not contain contact to improve correlation to
the contact model were examined. The methods were limited to types that generate a
linear solution so they could be applied to a frequency response analysis.
It was
determined that springs having stiffness normal to the contact plane should be included
in the contact region. The equivalent stiffness of the spring elements should be 10% of
the elastic modulus of the bracket to obtain the best results.
ix
1. Introduction
Modeling techniques used to calculate the alternating stress in the face to face contact
region of a bolted flange due to a frequency response do not capture the non-linear effect
of the contact region.
Finite Element Analysis (FEA) software packages, such as
ANSYS, do not permit any non linear effects in a harmonic model because the stiffness
matrix is constant. In a static model the contact effects can be captured because the
stiffness matrix does update. The stiffness matrix is a fundamental part of FEA and it
defines the geometric and material properties of the model. The effect that a constant
stiffness matrix has on the calculated results will be evaluated.
Since contact cannot be included in a harmonic analysis, the analyst is left with several
options. The typical process used in industry does not account for the contact region and
assumes that the part is only constrained around the bolt hole. The calculated von Mises
stress is then assumed to be a fully reversing alternating stress (Rratio=-1) in all locations.
It will be shown analytically that this is not case.
𝜎
𝑅𝑟𝑎𝑡𝑖𝑜 = 𝜎 𝑚𝑖𝑛 [1]
𝑚𝑎𝑥
To evaluate the effect of contact on a bolted joint two different models of the same part
were created. One contained contact and the other did not.
The model containing
contact will be referred to as the complex model and the one without contact will be
referred to as the simplistic model. Contact was able to be including in the complex
model because it was solved for a static solution so the stiffness matrix updated. A
method was devised to load the complex static model in a way to simulate harmonic
loading. The simplistic model was creating using typical industry methods. A series of
test cases were analyzed to determine if certain parameters affected the results.
1
The same method of creating two different models of one part to study the effect of
contact was then done for a commercial piece of hardware. The results show that the
current industry method over predicts the alternating stress in a significant portion of the
bracket when compared to the results from the complex model. The results show that in
order to better predict the stress, the analyst needs a method to account for the contact
region. This method needs to lead to a linear solution so the method can be used in a
harmonic analysis.
Linear methods of modifying the simplistic model to improve
correlation to the complex model results are investigated. The investigation shows one
promising method that improves correlation of the linear solution to the non-linear
solution.
2
2. Analysis of Single Bolted Bracket
Analysis results were compared for a series of parts that were analyzed as simplistic and
complex models. The overall geometric dimensions and shape were selected to be
representative of a typical sheet metal bracket fastened with a single bolt as shown in
Figure 1. Various configurations were analyzed to determine if the part thickness,
length, and bolt size had any effect. The configurations examined are summarized in
Table 1.
Figure 1: Bracket Geometric Configuration
1
2
3
4
5
6
Flange Thickness
(in)
0.062
0.062
0.062
0.125
0.125
0.125
Bolt Diameter
(in)
0.190
0.190
0.190
0.250
0.250
0.250
Bolt Preload
(lbs)
1129
1129
1129
2154
2154
2154
Applied
Force (lb)
40
20
15
100
75
50
Table 1: Single Bolt Conditions Considered
3
Load
Overhang (in)
0.00
0.50
1.00
0.00
0.50
1.00
The complex and simplified models were created using ANSYS version 10.0 software.
Table 2 details the attributes common to all models. The material mechanical properties
were selected to be representative of a titanium bracket.
Modulus (psi)
Poisson's Ratio
1.65E+07
0.33
Table 2: Analysis Material Properties
2.1 Complex 3-D Solid Model:
The complex model used 3-D solid elements to model the bracket, flange, and bolt as
designated in Figure 2. The model includes the following contact pairs; bolt-bracket,
bracket-flange, and bolt-flange. The bolt-flange contact is modeled using always bonded
contact. Bonded contact is the equivalent of the two solid bodies being glued together.
The model has surface to surface contact definition between the bolt head and bracket, as
well as between the bracket and flange. In both contact definitions friction has been
included using a coefficient of 0.36. Pretension elements are included in the bolt. The
pretension elements put the bolt shank into tension, compressing the joint. The amount
of tension applied varied with the size of the bolt as defined in Table 1. These preload
values are based on the recommended installation torque for the given bolt size.
The complex 3-D solid model consists of the following attributes:
1.
2.
3.
4.
Sheet metal bracket – 10 node tetrahedral elements (ANSYS Solid 92)
0.400 in. thick “flange” – 8 Node brick elements (ANSYS Solid 45)
Bolt model with pretension – 10 node tetrahedral elements (ANSYS Solid 92)
Surface to surface contact – (ANSYS Contact 174 and Target 170)
The model is constrained in 3 DOF (x, y, and z) only on the back side of the flange as
shown in Figure 3. Rotational constrains are not required because solid elements do not
have rotational degrees of freedom.
4
bracket
bolt
flange
Figure 2: Model Description
Constrained face of flange
Figure 3: Displacement Boundary Conditions
The complex model was solved for multiple load steps to simulate harmonic loading. In
the first load step, preload was applied to the bolt to clamp down the joint. This was
done using the pretension elements. The bolt remained locked (pretension load constant)
for the proceeding load steps. In the second load step, a positive force was applied to the
part as shown in Figure 4. A positive force is defined as a load resulting in joint opening.
In the third load step, the direction of the applied force was reversed. The reversed force
5
creases a load on the part that wants to close the joint and it is defined as a negative load.
The difference between load step 2 and load step 3 simulates the effect of harmonic
loading since the direction of the load is alternating.
Negative Load
Positive Load
Figure 4: Load Description
After running the three load steps the stress components (x, y, z, xy, yz, zx) along a
path of nodes on the bracket from both the bolt head and flange face side are extracted
from the model for each load case. See Figure 5 for path description.
6
Path Coordinates - .125” Thick
2.83”
“Flange Side”
Stresses obtained
from nodes along path
(both top and bottom
surface of solid)
“Bolt Side”
1.675”
1.26”
0.85”
0.538”
0.35”
0.00”
Figure 5: Path Description
The path data was used to calculate the mean and alternating von Mises stress using the
results from load step 2 and 3 for each data point along the path. The von Mises stress
can not directly be taken from the model to determine the alternating stress since it by
definition is always a positive value. Subtracting the von Mises stress values from the
Positive and Negative load cases would not make any sense.
Using the classical definition of von Mises stress in a local coordinate system the
individual alternating stress components are combined to determine the von Mises
equivalent alternating stress value for each node along the path according to equation 5.
In equation 5 each stress component is the difference between load step 2 and load step
3.
 VM 
alt
1
2

xalt
  yalt
  
2
y alt
  zalt
  
2
z alt
  xalt

2


 6  xy2 alt   yz2 alt   zx2 alt [5]
Since the Positive and Negative stress component values are not equal and opposite (or
fully reversing R = -1) the mean stress was calculated for each stress direction in a
similar fashion.
7
x

y

mean
mea n
z
 yz
mean
mea n
 zx
mea n
po s

[6]
 y  y
pos
n eg
[7]
2


neg
2

mean
 xy
x x
z z
po s
neg
2
[8]
 xy   xy
pos
n eg
2
 yz   yz
pos
[9]
n eg
[10]
2
 zx   zx
pos
n eg
2
[11]
And the von Mises equivalent mean stress was calculated as:
 VM
mean

1
2

 
 



  ymean   ymean   zmean   zmean   xmean  6  xy2 mean   yz2 mean   zx2 mean [12]
2
xmean
2
2
See the supporting files for the actual spreadsheets used to calculate the alternating and
mean stress values for all solid models.
2.2 Simplistic Shell Model:
The simplistic model uses shell elements. The model consists only of the bracket. The
bolt and flange have been omitted from this model since contact will not be included.
The lack of contact means that there is no way for these bodies to interact with each
other so including them in the model would not improve results and would only increase
8
the computational time required for the model to solve since number of nodes in the
model would increase. The bracket is modeled using ANSYS 8 noded elements (Shell
93). The nodes on the bolt-hole edge are connected to a center node using a rigid
constraint equation. The center node is fixed in all 6 DOF (x, y, z, rx, ry, rz). Since the
center node of the rigid region is constrained, the model behaves like the edges of the
bolt hole are constrained. The benefit of constraining the center node instead of the hole
edges directly is that all of the load has to react through a point which makes it easier to
determine what load is being exerted on the bolt and to verify that the model is behaving
as expected by checking the reaction loads.
Figure 6 shows the shell model used. The
input file used to build the model is in the Appendix.
Rigid region
Figure 6: Shell Model
This model is constructed in a manner commonly used in industry because of its speed
and efficiency.
It is efficient because shell elements have fewer nodes then solid
elements, leading to faster solve times, and produce similar results. Omitting contact
keeps the solution linear, so numerous iterations are not required to reach a solution,
significantly reducing solve time.
9
Since the shell element model is linear-elastic the force was applied only in one direction
(Negative). The von Mises equivalent stress will be the same if the load is applied in the
opposite direction. This is because von Mises stress is always positive. Changing the
direction of the applied load will change the sign of the individual stress components,
but not their magnitude, so the calculated von Mises stress remains unchanged. This
behavior was verified in the model. The von Mises stress was obtained for the shell top
and bottom using a path method similar to that described in Figure 5 for the solid model.
Since the stresses are assumed to be fully reversing for the shell model, the mean stress
is zero for all nodes and the alternating stress is the von Mises stress directly obtained
for each node at the top and bottom of the shell.
2.3 Analysis Results
The results indicate that the stresses in the contact region on the 3-D solid model are not
fully reversing. The alternating stress component from the 3-D model is much lower
than is predicted in the shell element model.
The alternating stress in the area beyond the contact region of the 3-D solid model are
effectively fully reversing (R = -1) and closely match the shell element model. The Rratio is shown for the 0.125” thick, 1” overhang case in Figure 7 where the blue shaded
region is where the stress is fully reversing and the red shaded region is where the stress
is steady.
10
Figure 7: R-ratio for 0.125”- 1.00” Overhang
Figure 10 through Figure 14 plot the alternating stress component in the bracket vs. path
position. Note that the path starts at the heel edge (Figure 5) and the values in the bolthole part of the model are plotted as a zero stress since there is no material in the
bracket. As expected, the simplistic shell element model shows very high stress at the
bolt-hole edge. This is expected because it is common to see artificially high stress in
elements attached to fixed nodes due to the singularity created by the constraint. This is
typically accounted for by ignoring stress in elements that would be under the bolt, since
these elements would be in compression due to preload of the bolt.
11
Figure 8: Bracket Nomenclature
The stress from the simplistic model does not match the complex model in the entire
region of contact. The plots include the stress on both the side of the bracket that is
contact with the flange (flange side) and exposed side of the bracket (top side) as
denoted in Figure 8.
The predicted alternating stress on the flange side is almost
identical to the top side. The end of the contact region is at path location 0.85”; the edge
of the bolt-hole (location of highest stress in shell model) is at 0.465”.
12
Figure 9: Bracket Without Overhang
The stress contour of the bracket, when the bracket does not overhang the flange, as
shown in Figure 9, is different from when the bracket does overhang the flange. When
the bracket does not overhang the flange the maximum alternating stress occurs near the
bolt head as shown in Figure 10 and Figure 11.
13
Reversing Stress Study
Alternating Stress vs. Position
.062" thick bracket, no overhang
100
90
Simplified Model, Flange Side
80
Alternating Stress (ksi)
Complex Model, Flage Side
70
Complex Model, Top Side
60
Simplified Model, Top Side
50
40
30
20
10
0
0
0.25
0.5
0.75
1
1.25
Path Location (in)
1.5
1.75
2
Figure 10: Alternating Stress vs. Location 0.062” – No overhang
Reversing Stress Study
Alternating Stress vs. Position
.125" thick bracket, 0" overhang
35
Simplified Model, Flange Side
30
Alternating Stress (ksi)
Complex Model, Flange Side
Complex Model, Top Side
25
Simplified Model, Top Side
20
15
10
5
0
0
0.25
0.5
0.75
1
1.25
1.5
1.75
Distance from Heel Edge (in)
Figure 11: Alternating Stress vs. Location 0.125” – No overhang
14
2
When the bracket overhangs the flange, as shown in Figure 2, the location of the
maximum stress shifts. This shift occurs in the complex model. With an overhang the
maximum alternating stress occurs at the edge of the contact region. This is because the
transition creates a stress concentration region. This behavior is shown in Figure 12
through Figure 14 where there is a peak at position 0.85, the end of the contact region.
This highlights a particular significant shortfall of the simplistic shell model because it
predicts the maximum stress location in another location.
Reversing Stress Study
Alternating Stress vs. Position
.062" thick bracket, 0.5" overhang
70
Simplified Model, Flange Side
Alternating Stress (ksi)
60
Complex Model, Flange Side
50
Complex Model, Top Side
40
Simplified Model, Top Side
30
20
10
0
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Path Location (in)
Figure 12: Alternating Stress vs. Location 0.062” – 0.5” Overhang
15
2.25
2.5
Reversing Stress Study
Alternating Stress vs. Position
.062" thick bracket, 1" overhang
120
Simplified Model, Flange Side
Alternating Stress (ksi)
100
Complex Model, Flange Side
80
Complex Model, Top Side
60
Simplified Model, Top Side
40
20
0
0
0.25 0.5 0.75
1
1.25 1.5 1.75
Path Location (in)
2
2.25 2.5 2.75
Figure 13: Alternating Stress vs. Location 0.062” – 1.00” Overhang
The bracket thickness has no significant effect on the general trend of the predicted
alternating stress. Figure 13 and Figure 14 both show the predicted alternating stress for
a one inch overhang, where Figure 13 is for 0.062 inch thick bracket and Figure 14 is for
a 0.125 inch thick bracket. While the magnitude of the values is different, the trend is
same. The maximum stress occurs at the same position. The section of the path where
the complex and simplified model match is also the same.
16
Reversing Stress Study
Alternating Stress vs. Position
.125" thick bracket, 1" overhang
Alternating Stress (ksi)
90
80
Simplified Model, Flange Side
70
Complex Model, Flange Side
60
Complex Model, Top Side
Simplified Model, Top Side
50
40
30
20
10
0
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
Path Location (in)
Figure 14: Alternating Stress vs. Location 0.125” – 1.00” Overhang
The simplified shell model and complex solid model only show good correlation in the
non contact region. In Figure 14 and Figure 15 the non-contact region stats at position
0.85. Starting as this location the simplified and complex models correlate very well
with each other. Between the edge of the bolt hole (position 0.5) and the end of the end
of the contact region (position 0.85) the correlation is poor. The simplified model over
predicts the alternating stress in this entire region
17
Reversing Stress Study
Alternating Stress vs. Position
.125" thick bracket, .5" overhang
80
Simplified Model, Flange Side
70
Complex Model, Flange Side
Alternating Stress (ksi)
60
Complex Model, Top Side
50
Simplified Model, Top Side
40
30
20
10
0
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
Path Location (in)
Figure 15: Alternating Stress vs. Location 0.125” – 0.5” Overhang
To verify that there was sufficient mesh density to produce accurate results the mesh
density was increased to see if the results changed significantly. The baseline model has
the same mesh size as all of the thus far presented results. In the refined model the mesh
density was increased and everything else remained unchanged. This was done for both
the simplified shell model and the complex solid model. The comparison was done for a
0.125 inch thick bracket with a 1.0 inch overhang. The node and element count of each
model is listed in Table 3. The total element count was increased by at least a factor four
in the refined version for both the shell and solid model. In the refined version of the
solid model, the mesh density of the bracket was increased by a greater factor then the
other bodies in the model. The number of elements defining the bracket increased from
18,561 to 106,605. The majority of the elements were concentrated in the bracket
because that is where the stress is being reported.
18
Model Description
Node Count
Element Count
Baseline Mesh, Solid Model
32,471
29,503
Refined Mesh, Solid Model
182,135
139,191
Baseline Mesh, Shell Model
7,642
2,448
Refined Mesh, Shell Model
30,631
10,013
Table 3: Mesh Density Statistics
The predicted alternating stress in the refined version of the shell model was practically
identical to the baseline mesh. Figure 16 shows a comparison between the two different
meshes for the shell model. The alternating stress as a function of position is same along
the entire path. The path is defined in Figure 5. Since there is no change in the results
the mesh used in the study is sufficient and there is no need to increase it.
Alternating Stress vs. Position
90
80
baseline mesh, shell model
70
refined mesh, shell model
Alternating Stress (ksi)
60
50
40
30
20
10
0
0
0.5
1
Position (in)
Figure 16: Mesh Density Effect, Shell Model
19
1.5
2
The predicted alternating stress in the refined version of the solid model was very similar
to the baseline mesh. Figure 17 shows a comparison between the two different meshes
for the solid model. The alternating stress as a function of position is similar along the
entire path. The path is defined in Figure 5. The only deviation occurs near the bolt
head, but this deviation is not significant. The predicted alternating stress in the majority
of the bracket is identical for both mesh densities. Since there is no significant change in
the results the mesh used in the study is sufficient and there is no need to increase it.
Alternating Stress vs. Position
35
Refind Mesh, Solid Model
30
Baseline Mesh, Solid Model
Alternating Stress (ksi)
25
20
15
10
5
0
0
0.5
1
Position (in)
Figure 17: Mesh Density Effect, Solid Model
20
1.5
2
3. Analysis of Commercial Typical Hardware
The techniques developed in Section 2 were applied to the analysis of a commercial part.
This part is made of 0.093 inch thick sheet stock AMS 5599, Inconel 625 and is shown
in Figure 18. A load of 40 lbs was applied normal to the bracket base. The load was
applied to a node that was attached using rigid constraints to the secondary holes as
shown in Figure 19. The material properties used are show in Table 4. The major
difference between this part and those considered in Section 2 is that there are now 2
bolts and that the part is not symmetric about the load point. A shell model without
contact and solid model with contact were created. The shell model is shown in Figure
19 and the solid model is shown in Figure 20.
Figure 18. Commercial Bracket
Elastic Modulus (psi) 2.97E+7
Poission’s Ratio
0.28
Table 4: Material Properties Production Bracket
21
Figure 19: FE Mesh of shell model
Figure 20: FE mesh of solid model with contact
The alternating stress for the shell model is shown in Figure 21. This plot shows that the
stress is very at the bolt hole where the constraint is applied, which is consistent with the
test cases detailed in Section 2. The alternating stress for the solid model cannot be
22
directly shown in ANSYS for the reasons described in the Section 2.1. The path method
used to map stress in the previous section is not a good solution due to the non
symmetric nature of the part. An alternate method is used in this section to present the
alternating stress. The stress parameters needed to calculate the stress in Equation 5
were stored in an element table within ANSYS. These values were then written to a text
file which was imported into Microsoft Excel.
Within Excel the calculation was
performed and the solution was saved as a text file. This text file was read back into
ANSYS as an array. The array was then used to populate an element table so the data
could be plotted in ANSYS. The alternating stress values for the solid model are plotted
in Figure 22.
Figure 21: Shell model Von Misses Stress
23
Units: ksi
Figure 22: Alternating Stress Solid Model
The stress predicted in the shell model is significantly higher than in the solid model.
The gray area in Figure 23 and Figure 24 indicate the region of the shell model where
the stress is greater than the maximum predicted alternating stress in the solid model.
Figure 23 and Figure 25 plot alternating stress on the same scale for the shell and solid
model. The difference in stress is most significant in the contact region near the left
bolt.
24
Units: ksi
Figure 23: Alternating Stress Shell Model Top Surface
Units: ksi
Figure 24: Alternating Stress Shell Model Bottom Surface
25
Units: ksi
Figure 25: Alternating Stress Solid Model Top View
The peak alternating stress in the solid model occurs on the top surface in the beginning
of the bend as shown in Figure 26. The highest stress on the bottom surface is at the end
of the contact region as show in Figure 27. This model shows more of discrepancy
between the upper and lower surface then the test case shown in Figure 10 through
Figure 14. The mismatch does not occur directly in front of the bolt and is off to the
side. The asymmetric geometry could account for the difference in results.
26
Beginning of bend
Units: ksi
Figure 26: Alternating Stress Solid Model Top View
Beginning of bend
Units: ksi
Figure 27: Alternating Stress Solid Model Bottom View
27
4. Practical Methods for Improved Results
The method of taking a harmonic load and breaking it into static steps so contact can be
included is not a practical approach for solving most problems. This can only be applied
when the force is known. In many instances this is not the case. It is therefore desirable
to have a method that will improve the accuracy of the results that is linear so harmonics
stress can be directly solved. Several different methods of accomplishing this were
considered.
1. Including springs to provide additional stiffness on the contact area
2. Increase region constrained around the bolt
The first method was evaluated by creating spring elements (Combin 14) that have
stiffness normal to the contact region. A spring element was attached to each node of the
shell elements that define the bracket in the contact region. The other end of the spring
was fixed. These modifications were made to the 0.125” thick 1.00” overhang model
described in Section 2.2 and are shown in Figure 28.
Figure 28: Model with springs in contact region
28
The stiffness of the spring was varied to see how this would affect the behavior of the
part. The stiffness of the individual spring elements was varied from 10 lbs/in to
100,000 lbs/in. The stress as a function of position up until the bend as shown in Figure
5 for varying spring stiffness values is shown in Figure 29. As the stiffness was
increased the stress near the bolt hole decreased and the peak stress location translated to
the end of the contact region. The stress profile changed along the entire contact region
but remained constant in the overhang portion.
This indicates that this is a good
potential solution to improve results.
Alternating Stress vs. Position
80000
k=10 lbs/in
70000
k=100 lbs/in
k=1000 lbs/in
60000
k=10000 lbs/in
Alternating Stress (psi)
50000
k=100000 lbs/in
40000
30000
20000
10000
0
0
0.5
1
Position (in)
1.5
2
Figure 29: Alternating stress vs. position for varying spring stiffness
The second method was implemented by applying a degree of freedom constraint in the
normal direction to nodes on the contact surface. The peak stress always occurred at the
constrained nodes closest to the applied load.
In order to predict the maximum
alternating stress at the same location as the solid model, the entire contact surface had
to be constrained in the normal direction.
For this boundary condition the peak
alternating stress was slightly over predicted and the stress in the contact region was
29
under predicted as indicated in Figure 30. Given the poor correlation over the majority
of the surface length for the constrained model, it was determined that the spring method
was superior.
Alternating Stress vs. Position
35,000
Solid Model
30,000
Shell Contrained
25,000
Alternating Stress (psi)
20,000
15,000
10,000
5,000
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Position (in)
Figure 30: Alternating Stress; Solid Model vs. Shell Model Constrained
4.1 Spring Method
The initial study of the effects of including springs presented in Figure 29 showed the
results for varying the stiffness of the spring constant of the individual springs. A more
meaningful value is the equivalent stiffness (Keq) of the spring field. There is a spring
element at every node on the contact surface. Each spring acts in parallel to the others.
The equivalent stiffness can be calculated by equation 13.
𝐾𝑒𝑞 = 𝐾1 + 𝐾2 + ⋯ 𝐾𝑛 [13]
30
By the process of iteration, the optimum spring stiffness was determined. The criteria
for the optimal solution was that it should error on the conservative side by over
predicting the stress in more locations then under predicting, not over predict the
maximum stress by more than 10%, never under predicted the maximum stress and
match the location of maximum stress as much as possible. Based on these criteria an
equivalent spring stiffness of 1.65E6 lbs/in should be applied.
This value was
determined using the 0.125” thick and 1” overhang model. A comparison between the
results of the solid model and the shell model with springs of the optimal stiffness is
shown in Figure 31. This equivalent spring stiffness meets the criteria since there is only
a very small region where the stress is under predicted. The error bars included in
Figure 31 are minus 10%, so the stress is never over predicted by more than 10% except
near the bolt head.
Alternating Stress v. Position
35000
30000
ShellSpring
Alternating Stress (psi)
25000
Solid
Model
20000
15000
10000
5000
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Position (in)
Figure 31: Alternating Stress Comparison; Solid Model vs. Shell with Springs
The optimum equivalent spring stiffness value is 10% of the elastic modulus used in the
solid model for the bolt, bracket, and base. To determine how the elastic modulus of the
31
components that define joint affect the results, the complex solid model was ran again
for different values. To make any trends obvious, non realistic values were selected for
the elastic modulus. When components were made stiff, the modulus was increased by
two orders of magnitude and when they were made flexible the modulus was decreased
by two orders of magnitude. When the stiffness of all of the components was increased
the results were identical. Increasing the bolt stiffness had local effects around the bolt
but did not change the overall stress in the part significantly. Increasing the stiffness of
the base also did not have an effect. Making the bracket stiffer then the base, either by
increasing the stiffness of the bracket, or decreasing the stiffness of the base did increase
the stress in the entire contact region. These results are summarized in Figure 32. This
study is focusing on alternating stress in a bolted stack were all of the components are
assumed to be metal. Given this assumption the elastic modulus of the bracket will be
similar to that of the base. This similarity means that the elastic modulus will not be 2
orders of magnitude greater and thus the effects of a significant mismatch between the
two materials will not be evaluated. The recommendations made going forward will be
based on this, and may not be the best solution if the bracket and base are made of
dissimilar materials where the bracket is much stiffer then the base.
32
Alternating Stress vs. Position
35.0
baseline
30.0
Alternating Stress (ksi)
all stiff
bolt stiff
25.0
base stiff
20.0
bracket stiff
base soft
15.0
10.0
5.0
0.0
0
0.5
1
Position (in)
1.5
2
Figure 32: Alternating Stress Solid Model Modified Elastic Modulus
The iterations performed on the solid model showed that the predicted alternating stress
remained constant as the elastic modulus of all the parts that define the bolted joint were
changed. In the shell spring model, as the elastic modulus of the bracket changes the
equivalent stiffness of the springs needs to change as well to keep the results consistent.
This is illustrated in Figure 33. In order to keep the results consistent the equivalent
stiffness of the springs needs to remain 10% of the elastic modulus of the bracket. It is
recommended that a spring field should be created in the contact region that has an
equivalent stiffness that is 10% of the elastic modulus of the bracket material.
33
Alternating Stress vs. Position
35000
30000
Baseline
Alternating Stress (psi)
EX/1000
25000
EX/1000, Keq/1000
20000
15000
10000
5000
0
0
0.5
1
Position (in)
1.5
Figure 33: Shell Spring Model, Bracket and Spring Stiffness Relationship
34
2
5. Conclusion
The analysis conducted with non-linear static FEA models has successfully
demonstrated the trends that should be observed in a harmonic analysis. The alternating
stress is not fully reversing in the contact region. The peak alternating stress location
should be predicted to be at the end of the contact region, not the bolt hole. The length
of the overhang, the thickness of the bracket and the size of the bolt hole have no
significant effect on the behavior of the alternating stress field.
This trend was
consistent for a range of single bolted, symmetric models and a double bolted non
symmetric model.
Modeling the joint without contact and constraining the bracket only at the bolt hole
does not exhibit the same trend described above. When the FEA model is constructed
this way the stress is over predicted in the entire contact region. The peak stress occurs
at the bolt hole instead of at the end of the contact region. The results do correlate well
to the FEA model with contact in the non contact region. These results show that
modifications need to be made to the model to improve the accuracy of the results.
An investigation into methods to improve the correlation of results generated by a linear
solution to those obtained by a non-linear solution has shown promising results.
Including one dimensional spring elements along the contact surface that have stiffness
normal to the surface can change the predicted alternating stress in the model. By
adjusting the stiffness of these spring elements the results of the linear model can
produce results that closely mirror the non-linear model. The best correlation was
obtained when the equivalent stiffness of the spring elements was set to 10% of the
elastic modulus of the bracket. This was considered to be the best correlation because it
did not underestimate the stress, followed the same trend, and did not overestimate the
stress by more than 10%. Creating a spring field that has an equivalent stiffness of 10%
of the elastic modulus of the bracket results in an accurate solution as long as the bracket
does not have an elastic modulus that is significantly greater than the base it bolts to.
Most bolted joints have similar material properties between the parts that define a bolted
joint so the solution presented should be valid for most real world applications.
35
Including spring elements in a harmonic model would lower the predicted alternating
stress in the contact region. Predicting a lower alternating stress would reduce material
costs and generate weight savings by allowing thinner parts to be used.
In many
applications, particularly the gas turbine jet engine industry, alternating stress is the main
driver in static structures containing bolted joints. The use of springs that have an
equivalent stiffness of 10% of the elastic modulus of the bracket provides the
opportunity to improve results by better estimating part life while still remaining
conservative since the stress will not be underestimated in critical areas.
36
References
1. Experimental and Theoretical Studies of a bolted Joint Excited by a Torsional
Harmonic Load. H. Ouyang. International Journal of Mechanical Sciences,
2006.
2. Finite Element Analysis and Modeling of Structure with Bolted Joints. Jeong
Kim. Applied Mathematical Modeling, 2007.
3. Mechanical Behavior of Materials. Morman Dowling. Pearson Prentice Hall,
2007.
4. Mechanical Vibrations. Singiresu Rao. Pearson Prentice Hall, 2004.
5. Military Handbook – MIL-HDBK-5H: Metallic Materials and Elements for
Aerospace Vehicle Structures. Works of the U.S. Department of Defense.
December 1998.
37
Appendix
ANSYS Input file for shell model
http://www.rh.edu/~petrab/project/supporting_files/ANSYS_inpute_files/make_shell.mac
Full text below
ANSYS Input file for solid model
http://www.rh.edu/~petrab/project/supporting_files/ANSYS_inpute_files/make_solid.mac
Full text below
ANSYS Input file for shell model with springs
http://www.rh.edu/~petrab/project/supporting_files/ANSYS_inpute_files/shell_springs.mac
Full text below
ANSYS Input file for shell model:
/PREP7
*SET,thk,.125
*SET,bdia, .250
*SET,lenght, 1
*SET,preload,2154
*SET,load,50
!**Bracket
*SET,bendrad,.1
RECTNG,0,.566,0,.85+lenght-(thk/2)-bendrad,
CYL4,.566/2,.35,(bdia+.031)/2
ASBA,1, 2
k,9,0,.85+lenght-(thk/2),bendrad
k,10,.566,.85+lenght-(thk/2),bendrad
k,11,0,.85+lenght-(thk/2),1-(thk/2)
k,12,.566,.85+lenght-(thk/2),1-(thk/2)
a,9,10,12,11
k,13,0,lenght-(thk/2)-.02,bendrad
k,14,.566,lenght-(thk/2)-.02,bendrad
larc,4,9,13,bendrad
38
larc,3,10,14,bendrad
al,3,14,9,13
!** define element type and real constants
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,1,,16.5e6
MPDATA,PRXY,1,,.33
ET,1,SHELL93
ET,2,MASS21
R,1,thk, , , , , ,
R,2,0,0,0,0,0,0,
!* creat mass element at center of hole
n,1,.566/2,.35,0
type,2
real,2
e,1
type,1
real,1
esize,.025
amesh,all
lsel,s,,,5,8,1
nsll,s,1
nsel,a,,,1
cerig,1,all,all
areverse,2,0
!** apply loads
d,1,all
lsel, s,,,11
lsum
*get, x_, line, 0, cent, x
*get, y_, line, 0, cent, y
*get, z_, line, 0, cent, z
ALLSEL,ALL
*set, cent_node, node(x_, y_, z_)
F,cent_node,FZ,load
!** Path
LSEL, S, , , 1
39
lsum
*GET,xt_1, LINE , 0, CENT, X
*GET,yt_1, LINE , 0, CENT, Y
*GET,zt_1, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_1, node(xt_1, yt_1, zt_1)
LSEL, S, , , 3
lsum
*GET,xt_2, LINE , 0, CENT, X
*GET,yt_2, LINE , 0, CENT, Y
*GET,zt_2, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_2, node(xt_2, yt_2, zt_2)
LSEL, S, , , 9
lsum
*GET,xt_6, LINE , 0, CENT, X
*GET,yt_6, LINE , 0, CENT, Y
*GET,zt_6, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_6, node(xt_6, yt_6, zt_6)
LSEL, S, , , 11
lsum
*GET,xt_7, LINE , 0, CENT, X
*GET,yt_7, LINE , 0, CENT, Y
*GET,zt_7, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_7, node(xt_7, yt_7, zt_7)
asel, s,,,2
allsel, below, area
asum
*get, xt_4, area, 0, cent, x
*get, yt_4, area, 0, cent, y
*get, zt_4, area, 0, cent, z
ALLSEL,ALL
*set, cent_4, node(xt_4, yt_4, zt_4)
*set, cent_3, node(xt_4, yt_4-.01, zt_4-.01)
*set, cent_5, node(xt_4, yt_4+.01,zt_4+.01)
40
*SET,cent_k1, 3314
*set,cent_k2,3277
/solu
solve
/POST1
!*****BOLT HEAD PATH
ALLSEL, ALL
SET,LIST,999
SET,,, ,,, ,1
/graphics,off
shell,top
PLNSOL, S,eqv, 0,1
PATH,bolt_head,9,30,20,
PPATH,1,cent_1
PPATH,2,cent_k1
PPATH,3,cent_k2
PPATH,4,cent_2
PPATH,5,cent_3
PPATH,6,cent_4
PPATH,7,cent_5
PPATH,8,cent_6
PPATH,9,cent_7
AVPRIN,0, ,
PDEF, ,S,eqv,AVG
PAGET,TRACDATA,TABL
*MWRITE, tracdata, top_von, txt, , ,,,
%G
%G
%G
%G
SET,LIST,999
SET,,, ,,, ,1
shell,bot
PLNSOL, S,eqv, 0,1.0
PATH,bolt_head,9,30,20,
PPATH,1,cent_1
PPATH,2,cent_k1
PPATH,3,cent_k2
PPATH,4,cent_2
41
%G
PPATH,5,cent_3
PPATH,6,cent_4
PPATH,7,cent_5
PPATH,8,cent_6
PPATH,9,cent_7
AVPRIN,0, ,
PDEF, ,S,eqv,AVG
PAGET,TRACDATA1,TABL
*MWRITE, tracdata1, bot_von, txt, , ,,,
%G
%G
%G
%G
ANSYS Input file for solid model
/PREP7
*SET,thk,.125
*SET,bdia, .250
*SET,lenght, 1
*SET,preload,2154
*SET,load,50
!**Boss
RECTNG,0,1.25,0,1,
CYL4,.625,.5,(bdia+.031)/2
ASBA,1,2
VOFFST,3,-.4,
!**Bracket
RECTNG,.908,.342,-lenght,thk-lenght,
VOFFST, 11, 1
RECTNG,.908,.342,-lenght,.85,
CYL4,.625,.5,(bdia+.031)/2
ASBA,17, 18
VOFFST, 19, thk
vadd, 2, 3
lfillit,26,62,0.05
42
%G
lfillit,69,73,0.05
l,26,43
l,25,44
al,40,36,46,33
vext,13,,,-(.908-.342)
VPTN, 2,4
VDELE,
5, , ,1
VADD, 3,7,6,8
WPCSYS,-1
!**Bolt
wpoff, , ,thk
CYL4,.625,.5,(bdia+.2)/2
VOFFST, 11, .30
CYL4,.625,.5,(bdia+.031)/2
VOFFST, 27, -.7
VADD, 3, 4
ET,1,SOLID45
ET,2,SOLID92
ET,3,SOLID92
ET,99,MASS21
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,1,,16.5e6
MPDATA,PRXY,1,,.33
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,2,,16.5e6
MPDATA,PRXY,2,,.33
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,3,,16.5e6
MPDATA,PRXY,2,,.33
!**MESH
!**BRACKET
VSEL, R,,,2
ALLSEL,BELOW,VOLU
43
VATT, 1,,3,0
AESIZE,16,thk/5,
AESIZE,18,thk/5,
AESIZE,62,thk/3,
AESIZE,36,thk/3,
VMESH,2
ALLSEL, ALL
!**BOSS
VSEL, R, ,,1
ALLSEL,BELOW,VOLU
VATT, 1, , 1, 0
ESIZE,0..05,0,
VSWEEP,1
ALLSEL, ALL
!**BOLT
VSEL, R,,,5
ALLSEL,BELOW,VOLU
VATT, 1, , 2,0
ESIZE, 0.1, 0
VMESH,5
ALLSEL, ALL
!****CONTACT PAIRS
!****Bracket to Bolt
/COM, CONTACT PAIR CREATION - START
CM,_NODECM,NODE
CM,_ELEMCM,ELEM
CM,_KPCM,KP
CM,_LINECM,LINE
CM,_AREACM,AREA
CM,_VOLUCM,VOLU
/GSAV,cwz,gsav,,temp
MP,MU,1,.36
MAT,1
MP,EMIS,1,7.88860905221e-031
R,3
REAL,3
ET,100,170
44
ET,101,174
R,3,,,1.0,0.1,0,
RMORE,,,1.0E20,0.0,1.0,
RMORE,0.0,0,1.0,,1.0,0.5
RMORE,0,1.0,1.0,0.0,,1.0
KEYOPT,101,4,0
KEYOPT,101,5,3
KEYOPT,101,7,1
KEYOPT,101,8,0
KEYOPT,101,9,1
KEYOPT,101,10,2
KEYOPT,101,11,0
KEYOPT,101,12,0
KEYOPT,101,2,0
KEYOPT,100,5,0
! Generate the target surface
ASEL,S,,,62
CM,_TARGET,AREA
TYPE,100
NSLA,S,1
ESLN,S,0
ESLL,U
ESEL,U,ENAME,,188,189
ESURF
CMSEL,S,_ELEMCM
! Generate the contact surface
ASEL,S,,,34
CM,_CONTACT,AREA
TYPE,101
NSLA,S,1
ESLN,S,0
ESURF
ALLSEL
ESEL,ALL
ESEL,S,TYPE,,100
ESEL,A,TYPE,,101
ESEL,R,REAL,,3
45
/PSYMB,ESYS,1
/PNUM,TYPE,1
/NUM,1
EPLOT
ESEL,ALL
ESEL,S,TYPE,,100
ESEL,A,TYPE,,101
ESEL,R,REAL,,3
CMSEL,A,_NODECM
CMDEL,_NODECM
CMSEL,A,_ELEMCM
CMDEL,_ELEMCM
CMSEL,S,_KPCM
CMDEL,_KPCM
CMSEL,S,_LINECM
CMDEL,_LINECM
CMSEL,S,_AREACM
CMDEL,_AREACM
CMSEL,S,_VOLUCM
CMDEL,_VOLUCM
/GRES,cwz,gsav
CMDEL,_TARGET
CMDEL,_CONTACT
/COM, CONTACT PAIR CREATION - END
!****Boss to Bracket
/COM, CONTACT PAIR CREATION - START
CM,_NODECM,NODE
CM,_ELEMCM,ELEM
CM,_KPCM,KP
CM,_LINECM,LINE
CM,_AREACM,AREA
CM,_VOLUCM,VOLU
/GSAV,cwz,gsav,,temp
MP,MU,1,0.36
MAT,1
MP,EMIS,1,7.88860905221e-031
R,4
46
REAL,4
ET,102,170
ET,103,174
R,4,,,1.0,0.1,0,
RMORE,,,1.0E20,0.0,1.0,
RMORE,0.0,0,1.0,,1.0,0.5
RMORE,0,1.0,1.0,0.0,,1.0
KEYOPT,103,4,0
KEYOPT,103,5,3
KEYOPT,103,7,1
KEYOPT,103,8,0
KEYOPT,103,9,1
KEYOPT,103,10,2
KEYOPT,103,11,0
KEYOPT,103,12,0
KEYOPT,103,2,0
KEYOPT,102,5,0
! Generate the target surface
ASEL,S,,,3
CM,_TARGET,AREA
TYPE,102
NSLA,S,1
ESLN,S,0
ESLL,U
ESEL,U,ENAME,,188,189
ESURF
CMSEL,S,_ELEMCM
! Generate the contact surface
ASEL,S,,,36
CM,_CONTACT,AREA
TYPE,103
NSLA,S,1
ESLN,S,0
ESURF
ALLSEL
ESEL,ALL
ESEL,S,TYPE,,102
47
ESEL,A,TYPE,,103
ESEL,R,REAL,,4
/PSYMB,ESYS,1
/PNUM,TYPE,1
/NUM,1
EPLOT
ESEL,ALL
ESEL,S,TYPE,,102
ESEL,A,TYPE,,103
ESEL,R,REAL,,4
CMSEL,A,_NODECM
CMDEL,_NODECM
CMSEL,A,_ELEMCM
CMDEL,_ELEMCM
CMSEL,S,_KPCM
CMDEL,_KPCM
CMSEL,S,_LINECM
CMDEL,_LINECM
CMSEL,S,_AREACM
CMDEL,_AREACM
CMSEL,S,_VOLUCM
CMDEL,_VOLUCM
/GRES,cwz,gsav
CMDEL,_TARGET
CMDEL,_CONTACT
/COM, CONTACT PAIR CREATION - END
!****Boss to Bolt
/COM, CONTACT PAIR CREATION - START
CM,_NODECM,NODE
CM,_ELEMCM,ELEM
CM,_KPCM,KP
CM,_LINECM,LINE
CM,_AREACM,AREA
CM,_VOLUCM,VOLU
/GSAV,cwz,gsav,,temp
MP,MU,1,0.36
MAT,1
48
MP,EMIS,1,7.88860905221e-031
R,5
REAL,5
ET,104,170
ET,105,174
R,5,,,1.0,0.1,0,
RMORE,,,1.0E20,0.0,1.0,
RMORE,0.0,0,1.0,,1.0,0.5
RMORE,0,1.0,1.0,0.0,,1.0
KEYOPT,105,4,0
KEYOPT,105,5,3
KEYOPT,105,7,1
KEYOPT,105,8,0
KEYOPT,105,9,1
KEYOPT,105,10,2
KEYOPT,105,11,0
KEYOPT,105,12,5
KEYOPT,105,2,0
KEYOPT,104,5,0
! Generate the target surface
ASEL,S,,,29
ASEL,A,,,31
ASEL,A,,,32
ASEL,A,,,33
CM,_TARGET,AREA
TYPE,104
NSLA,S,1
ESLN,S,0
ESLL,U
ESEL,U,ENAME,,188,189
ESURF
CMSEL,S,_ELEMCM
! Generate the contact surface
ASEL,S,,,7
ASEL,A,,,8
ASEL,A,,,9
ASEL,A,,,10
49
CM,_CONTACT,AREA
TYPE,105
NSLA,S,1
ESLN,S,0
ESURF
ALLSEL
ESEL,ALL
ESEL,S,TYPE,,104
ESEL,A,TYPE,,105
ESEL,R,REAL,,5
/PSYMB,ESYS,1
/PNUM,TYPE,1
/NUM,1
EPLOT
ESEL,ALL
ESEL,S,TYPE,,104
ESEL,A,TYPE,,105
ESEL,R,REAL,,5
CMSEL,A,_NODECM
CMDEL,_NODECM
CMSEL,A,_ELEMCM
CMDEL,_ELEMCM
CMSEL,S,_KPCM
CMDEL,_KPCM
CMSEL,S,_LINECM
CMDEL,_LINECM
CMSEL,S,_AREACM
CMDEL,_AREACM
CMSEL,S,_VOLUCM
CMDEL,_VOLUCM
/GRES,cwz,gsav
CMDEL,_TARGET
CMDEL,_CONTACT
/COM, CONTACT PAIR CREATION - END
!****Bracket to Bolt (Shank)
WPCSYS,-1
ALLSEL, ALL
50
PSMESH,10,preten, ,VOLU,5, 0,Z,thk/2, , , , ,
finish
allsel, all
/prep7
asel, s,,,12
allsel, below, area
asum
*get, x_, area, 0, cent, x
*get, y_, area, 0, cent, y
*get, z_, area, 0, cent, z
ALLSEL,ALL
*set, cent_node, node(x_, y_, z_)
!*******TOP PATH
LSEL, S, , , 47
lsum
*GET,xt_1, LINE , 0, CENT, X
*GET,yt_1, LINE , 0, CENT, Y
*GET,zt_1, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_1, node(xt_1, yt_1, zt_1)
LSEL, S, , , 79
lsum
*GET,xt_2, LINE , 0, CENT, X
*GET,yt_2, LINE , 0, CENT, Y
*GET,zt_2, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_2, node(xt_2, yt_2, zt_2)
LSEL, S, , , 78
lsum
*GET,xt_6, LINE , 0, CENT, X
*GET,yt_6, LINE , 0, CENT, Y
*GET,zt_6, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_6, node(xt_6, yt_6, zt_6)
LSEL, S, , , 31
lsum
*GET,xt_7, LINE , 0, CENT, X
51
*GET,yt_7, LINE , 0, CENT, Y
*GET,zt_7, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_7, node(xt_7, yt_7, zt_7)
asel, s,,,16
allsel, below, area
asum
*get, xt_4, area, 0, cent, x
*get, yt_4, area, 0, cent, y
*get, zt_4, area, 0, cent, z
ALLSEL,ALL
*set, cent_4, node(xt_4, yt_4, zt_4)
*set, cent_3, node(xt_4, yt_4+.01, zt_4-.01)
*set, cent_5, node(xt_4, yt_4-.01,zt_4+.01)
!*******BOTTOM PATH
LSEL, S, , , 39
lsum
*GET,xb_8, LINE , 0, CENT, X
*GET,yb_8, LINE , 0, CENT, Y
*GET,zb_8, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_8, node(xb_8, yb_8, zb_8)
LSEL, S, , , 80
lsum
*GET,xb_9, LINE , 0, CENT, X
*GET,yb_9, LINE , 0, CENT, Y
*GET,zb_9, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_9, node(xb_9, yb_9, zb_9)
asel, s,,,18
allsel, below, area
asum
*get, xt_11, area, 0, cent, x
*get, yt_11, area, 0, cent, y
*get, zt_11, area, 0, cent, z
ALLSEL,ALL
52
*set, cent_11, node(xt_11, yt_11, zt_11)
*set, cent_10, node(xt_11, yt_11+.01, zt_11-.01)
*set, cent_12, node(xt_11, yt_11-.01,zt_11+.01)
LSEL, S, , , 77
lsum
*GET,xb_13, LINE , 0, CENT, X
*GET,yb_13, LINE , 0, CENT, Y
*GET,zb_13, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_13, node(xb_13, yb_13, zb_13)
LSEL, S, , , 29
lsum
*GET,xb_14, LINE , 0, CENT, X
*GET,yb_14, LINE , 0, CENT, Y
*GET,zb_14, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_14, node(xb_14, yb_14, zb_14)
/SOL
DA,1,ALL,0
DA,47,UX,0
DA,48,UX,0
allsel,all
ANTYPE,0
nlgeom,on
NSUBST,10,20,5
AUTOTs,ON
SLOAD,ALL,9,LOCK,FORC,preload, 1,2
SOLVE
SAVE
F,cent_node,FZ,load
SOLVE
SAVE
fdele,cent_node,all
F,cent_node,FZ,-load
SOLVE
53
SAVE
FINISH
ANSYS Input file for shell model with springs
/clear
/PREP7
*SET,thk,.125
*SET,bdia, .250
*SET,lenght, 1
*SET,preload,2154
*SET,load,50
*SET,tstiffness,16.5e5
*set,locCountParam,10
*set,factor,1
!**Bracket
*SET,bendrad,.1
RECTNG,0,.566,0,.85+lenght-(thk/2)-bendrad,
CYL4,.566/2,.35,(bdia+.031)/2
ASBA,1, 2
k,9,0,.85+lenght-(thk/2),bendrad
k,10,.566,.85+lenght-(thk/2),bendrad
k,11,0,.85+lenght-(thk/2),1-(thk/2)
k,12,.566,.85+lenght-(thk/2),1-(thk/2)
a,9,10,12,11
54
k,13,0,lenght-(thk/2)-.02,bendrad
k,14,.566,lenght-(thk/2)-.02,bendrad
larc,4,9,13,bendrad
larc,3,10,14,bendrad
al,3,14,9,13
!** define element type and real constants
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,1,,16.5e6
MPDATA,PRXY,1,,.33
wpoff,0,.85,0
wpro,,-90.000000,
ASBW,
3
ET,1,SHELL93
ET,2,MASS21
R,1,thk, , , , , ,
R,2,0,0,0,0,0,0,
!* creat mass element at center of hole
n,1,.566/2,.35,0
type,2
real,2
e,1
type,1
real,1
esize,.025
amesh,all
lsel,s,,,5,8,1
nsll,s,1
nsel,a,,,1
cerig,1,all,all
areverse,2,0
!** apply loads
d,1,all
lsel, s,,,11
lsum
*get, x_, line, 0, cent, x
*get, y_, line, 0, cent, y
55
*get, z_, line, 0, cent, z
ALLSEL,ALL
*set, cent_node, node(x_, y_, z_)
F,cent_node,FZ,load
!**make springs
asel,s,,,5
nsla,s,0
*get,nsprings,node,0,count
stiffness=tstiffness/nsprings
NGEN,2,7609,ALL, ,,0,0,0,1,
ET,3,COMBIN14
!*
KEYOPT,3,1,0
KEYOPT,3,2,3
KEYOPT,3,3,0
R,3,stiffness, , ,
type,3
real,3
eintf,.001,low
nsla,u
d,all,all
allsel
!** Path
LSEL, S, , , 1
lsum
*GET,xt_1, LINE , 0, CENT, X
*GET,yt_1, LINE , 0, CENT, Y
*GET,zt_1, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_1, node(xt_1, yt_1, zt_1)
LSEL, S, , , 17
lsum
*GET,xt_2, LINE , 0, CENT, X
*GET,yt_2, LINE , 0, CENT, Y
*GET,zt_2, LINE , 0, CENT, Z
ALLSEL, ALL
56
*SET,cent_2, node(xt_2, yt_2, zt_2)
LSEL, S, , , 3
lsum
*GET,xt_3, LINE , 0, CENT, X
*GET,yt_3, LINE , 0, CENT, Y
*GET,zt_3, LINE , 0, CENT, Z
ALLSEL, ALL
*SET,cent_3, node(xt_3, yt_3, zt_3)
/solu
antype,0
solve
/POST1
!*****BOLT HEAD PATH
ALLSEL, ALL
SET,LIST,999
SET,,, ,,, ,1
/graphics,off
shell,top
PLNSOL, S,eqv, 0,1
PATH,bolt_head,3,30,50,
PPATH,1,cent_1
PPATH,2,cent_2
PPATH,3,cent_3
AVPRIN,0, ,
PDEF, ,S,eqv,AVG
PAGET,TRACDATA,TABL
*MWRITE, tracdata, top_von_%stiffness%, txt, , ,,,
%G
%G
%G
%G
finish
57
%G