Introduction
The purpose of this document is to provide guidelines by which to analyze a model aircraft wing
structure in Abaqus. The guide assumes that the user has little experience with Abaqus and/or
may not have encountered many of the features used. The design of the structure is based
largely on previous semesters of AERO 402-Aircraft. It is assumed that the user has already
created a working assembly of the wing structure using CAD software. This document will
assume that the CAD software used is SolidWorks.
The layout of the wing structure used in this example is shown below with the upper surface
skin and sheeting removed. The wing uses the NACA 63-210 airfoil and has a leading edge
sweep of 30 degrees. There is a 12 inch root chord with a taper ratio of 0.5. There is a root
incidence angle of 2 degrees and a wing twist of -2.5 degrees. The tip therefore has an
incidence of -0.5 degrees. These parameters were chosen in order to demonstrate the
techniques that will allow students to analyze a wide variety of wing structures whether simpler
or more complex than this example.
Importing the SolidWorks Model
The model must be saved in a format that is most compatible to be used by Abaqus. Although
there are many formats which can be imported into Abaqus, it should be noted that geometric
features created in Abaqus CAE are stored in ACIS (.sat) format. The Abaqus documentation
therefore suggests using this format for part imports.
Using the ACIS format, every part in an assembly
can be imported into Abaqus at once whereas
importing other part formats may require each
individual part to be saved and imported. In the
case of this structure there are 60 individual
parts that must be imported. Furthermore, the
geometry in stored to an accuracy of 1*10-6 in
ACIS formatting, but according to the Abaqus
documentation other available formats can be
much less accurate.
In SolidWorks, open the wing structure assembly
to be analyzed. Go to File->Save As and use the
pull-down arrow to select ACIS (*.sat) in the
“Save as type:” field. Use the Options button in
the bottom right of the “Save As” window.
Ensure that “Solid/Surface geometry” is selected
for the “Output as:” option and check that the
units are as desired. Check that the highest
number is selected for “Version”. Click “OK” and
save the file.
Open a new model database in Abaqus CAE.
Under the model tree, right click on Parts and
select Import. Ensure that ACIS is selected for
the File Filter and locate the assembly file that
was exported from SolidWorks. If an error is
given that the file is not a valid ACIS file, return
to SolidWorks and resave the file with the next
lower Version in the Export Options and reimport the new file.
Import all parts as 3D, Deformable Solids and in
general do not scale the parts. Select OK and
Abaqus will create a new part for every member of
the assembly. If an error or warning is given that
any of the parts have “imprecise geometry”, there
are two logical courses of action. The first is to use
the “Convert to precise representation geometry”
option when importing. Typically the best action
however is to return to the CAD program and
carefully check the parts for errors. Possible errors
include regions of overlapping volume or selfintersection as well as minute slivers of material
that may be left when using cut features.
Because wing structural assemblies typically consist of
numerous individual parts (in this example there are 60), it is
recommended for each part to right click and rename each
part with a more descriptive name, i.e. “Rib 1 Center”,
“Front Top Spar Cap”, etc.
Partitioning
Partitioning parts is generally recommended when a single part makes contact in a joint with
two or more parts. Partitioning is especially necessary when multiple parts contact a single
surface of another part. Later when contact constraints are added to the model, the need for
partitioning becomes evident and which parts require partitions becomes clearer.
Observe the joints shown to the right. The rib has a partition where it
will join the shear web of the rear shear web because the spar caps also
join the web and the rib. The top spar cap is removed to show the
partitions on the shear web segments. Note that the web segments are
partitioned for the joints with the caps as well as with one another.
To partition for the joints, first select one of the shear web
segments in the part module. Select “Partition Face: Sketch”.
Select the front face (the face with normal vector
approximately in the negative x-direction) and click done.
Choose to select an edge to appear “vertical and on the
left” and select the left edge.
Sketch a simple vertical line, press escape if prompted to enter
the next point, and click done at the “Sketch partition geometry”
prompt.
For the joints between web segments, it is necessary that the
part itself be partitioned into cells rather than just
partitioning the face. To do this, select “Partition Cell:
Extrude/Sweep Edges” as shown.
Select the edge that was created by the face partition, click
“Done”, and select “Extrude Along Direction”. Select the
edge shown to the right for the extrude direction and click
“OK” then click “Create Partition” and “Done”. Use these
steps to partition cells on each shear web segment where it
will join another web segment. Also partition cells on the
rear of the central rib segments as shown at the beginning
of this section. Partition the front faces of all rear shear
web segments as shown at the beginning of the section.
Material Properties
The structure of this example consists of materials that are primarily used in creating model
aircraft: balsa wood, birch ply-wood, and Monokote skin. Because wood is highly orthotropic, it
is critical that orthotropic material properties be specified for all wooden components and that
material directions be specified to simulate the wood grain directions.
Use the pull-down arrow to go to the Property
module and create a new material for each of
balsa, birch, and Monokote.
Choose to define elastic mechanical
properties as shown.
For the woods, select Type: Orthotropic using
the pull-down menu.
Orthotropic material behavior is defined by:
Where the D matrix for balsa is given using values from the USDA Enycyclopedia of Wood as:
544477.0317
8464.503486
15429.48139
0
0
0
8464.503486
9609.681717
5447.54364
0
0
0
15429.48139
5447.54364
260031.5336
0
0
0
0
0
0
1.99E+04
0
0
0
0
0
0
2.91E+04
0
0
0
0
0
0
2.70E+03
Similarly the D matrix for birch, calculated using values from the USDA, is:
2306606.945
138833.8032
195951.2595
0
0
0
138833.8032
161031.5298
79197.24615
0
0
0
195951.2595
79197.24615
253126.8765
0
0
0
0
0
0
1.50E+05
0
0
0
0
0
0
1.64E+05
0
0
0
0
0
0
3.76E+04
If basswood should instead be used for any components, the D matrix using USDA values is:
1657603.957
81770.03951
130932.8106
0
0
0
81770.03951
64579.6542
40144.71305
0
0
0
130932.8106
40144.71305
158411.8644
0
0
0
0
0
0
7.39E+04
0
0
0
0
0
0
8.99E+04
0
After using the above properties to define the wood
materials, create Monokote as an isotropic material with the
properties shown. Distributors of Monokote acknowledge
that it is a Mylar film, but will not provide specific
properties. The properties shown are therefore taken from
information for Mylar films manufactured by DuPont Teijin
Films.
Material Libraries
In Abaqus versions 6.7EF and later, material properties can managed
through the use of Material Libraries. Material Libraries allow the
use of consistent material properties without the need to research
properties for each individual material. Because of the number of
values required to define orthotropic materials, libraries are
especially useful for these materials. While in the Property module,
note that there is a tab for Material Library.
0
0
0
0
0
1.61E+04
In the work directory create a folder named “abaqus_plugins” if there is not one already there.
Go to the Material Library tab and use the “Material Library Manager” button.
Create a new Material Library using the “Create”
button. Select each material and use the “ < ”
button to add the material to the library. Save
the library and the materials in it can be added to
any other project. Again, this is primarily to
ensure consistent properties are used and to save
time in finding the necessary parameters.
To use materials from a library in a project, first ensure that the .lib
file is saved in the “abaqus_plugins” folder. In the Material Library
Tab use the pull-down arrow to select the desired library (if there
are multiple in the plugin folder). Select the material and use the
“Add Material to Curent Model” button.
Material Directions
In order to accurately apply the material properties to the parts,
material directions must be assigned for each orthotropic part. To
demonstrate this, first go to the model tab and find one of the spar
caps in the Parts list, right click on it, and select “Switch Context”.
Use the “Create Datum CSYS: 3 Points” button as shown
and choose to create a Rectangular coordinate system.
Choose the origin as any point along one of the long
edges of the part. When prompted to select a point
along the x-axis, choose any other point that lies along
the same edge as already chosen. Choose the third
point as any point on an edge which is parallel to the
edge already chosen. The desired result is that the xaxis should lie along the longitudinal direction of the
part. All other spar caps and all stringers should have
datum coordinate systems added in a like manner. Each
piece of the upper surface and lower surface sheets for
each leading edge and trailing edge should have
coordinate systems added in a similar manner.
For each spar cap, stringer, and leading and trailing edge sheets go
to the Property module and choose to Assign Material Orientation.
Select the part as the highlighted region, click on
the “Datum CSYS List” button in the bottom right,
and select the datum coordinate system that was
created with the three points. Leave the default
options in the “Edit Material Orientation” window
and click OK.
Adding material directions for the
center rib segments and leading edge
segments can also be accomplished with
the same procedure. As shown, the
corner notches provide the three points
to define the coordinate system.
As the trailing edge segments do not have such
notches, other techniques can be used to create
logical material directions. For the trailing edge
segments, the desired material directions are
such that one axis lies along the left edge, one
axis lies perpendicular to that edge and in the plane of the face shown, and one axis is normal to
the face shown.
First choose to create a point using “Create Datum Point:
Project Point On Line”.
Choose the point shown and the left
edge. The use the projected point,
the original point, and another point
along the left edge to define the
datum coordinate system. Assign
material directions with the same
steps as above.
Define material coordinates for the leading edge dowel such
that the x-axis coincides with the longitudinal direction of the
part.
Sections and Composite Layups
In the Property module, use the Create
Section button to create a Solid,
Homogeneous section of balsa material.
Assign this section to each spar cap and to
each stringer. Create another Solid,
Homogeneous section of birch and assign it
to the leading edge dowel rod
For the leading and trailing edge sheets,
create a Homogeneous, Shell section and
note that it is considered to be type:
Continuum Shell. Since the sheets are 1/32
inch balsa, enter .03125 for the thickness and
balsa material. Since this is a Continuum Shell
section, the true thickness is calculated based
on the dimensions of the part to which it is
assigned. The entered value is considered an
initial value for the calculations. Assign this
section to each of the upper and lower
surface leading and trailing edge sheets.
Create another Continuum Shell section for
the shear webs. Use a thickness of 1/16 inch
(.0625) and balsa material. Assign this
section to each of the three segments of the front shear web and the three segments of the rear
shear web. Create a Continuum Shell section with 0.002 thickness and Monokote/Mylar
material. Assign this section to the wing skin.
The rib segments should be modeled as 1/16 inch thickness
birch plywood with 3 plies oriented at 0-90-0 degrees. The most
accurate way to model these therefore is to use the composite
layup feature in Abaqus. In the property module, select “Create
Composite Layup” as shown
Create a 3-ply Continuum Shell layup.
Right click the Region box, select Edit Region,
highlight the entire part, and click done to set the
entire column. Right click the Material box, select
birch, and click OK to set the entire column. Since
the part is 1/16 inch thick, assign 0.020833,
0.020834, and 0.020833 for the thicknesses.
Near the top of the window, use the pull-down
arrow to set “Definitition: Coordinate system”.
Click the “Select” button, choose “Datum CSYS
List”, select the datum coordinate system
previously defined, and click OK. Set the rotation
angles for the plies to 0, 90, and 0. Click OK and
the part is now defined as a 3-ply composite. Use
the same sequence of steps to apply composite layups to each leading edge rib segment and
each trailing edge rib segment.
Meshing
Notice that of all the parts that compose the structural assembly, the majority of them are
plate-like, thin structures. All of the ribs and shear web segments are simple flat plates while
the leading and trailing edge sheeting and the skin are curved shell structures. All of these type
components can be analyzed in Abaqus using Continuum Shell Elements.
To use Continuum Shells in the analysis, mesh controls must be
assigned to each part that will use the shell elements. For each
plate-like and shell-like part, go to the Mesh modules and select
“Assign Mesh Controls”
Highlight the entire part and click done. Make sure that
the technique to be used is Sweep. On parts such as the
rib segments, Sweep meshing may have been selected as
the default.
Choose “Assign Element Type”, highlight the entire part, and
click done.
Choose Continuum Shell, Hex and leave the
other options at the default settings. Note
that on parts that contain a cusp such as on
the trailing edge sheets, it is often desirable
to partition the cusp from the rest of the part.
Continuum Shell, Wedge elements can then
be applied to the cusp in order to provide a
better quality mesh than if only hex elements
were used.
Apply this sequence of steps to each of the rib segments, the shear web segments, the sheeting
and the skin. The stringers, spar caps, and leading edge dowel can simply be assigned 3D Stress
elements.
The parts of this example can be seeded by
specifying the approximate global size as shown.
Avoid meshing too finely on the ribs segments as
the Academic Teaching License is limited to
100000 nodes for the entire assembly. The
curvature of the wing skin will dictate a very fine
mesh that will easily lead to a node count near
that limit. Higher quality meshes can often be
obtained using careful partitioning and edge
seeds, but doing so can be quite tedious and
often yields little benefits to the analysis.
Assembly
The first step in assembling the model is to create an Instance for each and every part.
Go to the Assembly module, right click on
Instances, and select “Create Instance” as
shown. Left click on the first part in the list,
scroll to the bottom, hold the Shift key, and left
click on the bottom-most part. Choose
Dependent Instance Type and click OK. This will
create all 60 Instances at once
At this point each of the parts will be placed in
the position that the part held in the SolidWorks
assembly and therefore in the ACIS .sat file that
was used to import the geometry. By default, all
of the datum coordinate systems that were
created for the material directions are also
shown in the assembly. This clutter can make
assigning constraints more annoying.
To remove the clutter from the
assembly, go to View->Assembly
Display Options. Go to the
Datum tab and unselect “Show
datum coordinate system”.
Changing the View Manipulation Options can often make
constraining the assembly much less of an annoyance. To do
this, go to Tools->Options. There one can set the mouse
controls to coincide with controls in a number of CAD
programs with which the user may be more familiar such as
SolidWorks or Catia.
Properly constraining the assembly requires a rather lengthy
sequence of constraints between the various parts. It is
generally easier to work with constraining some parts when
other parts not in the view. In the Model tree, under Instances
right click on the upper surface piece of the wing skin and
select “Suppress”. Do the same for the two pieces of upper
surface sheeting. This will allow the underlying structure to be
visible. To add each part back to the assembly, simply right
click and select “Resume”.
To assign the constraints, the parts should be separated enough to
select the contact surfaces. For example, select the “Translate
Instance” shown.
Select the top cap of the front spar, click done, enter
(0,0,0) for the translation vector start point, enter (0,3,0)
for the translation vector end point, and click OK.
In the Interaction module, use the “Create
Constraint” button to create a Tie Constraint.
Click continue, choose Surface for the master type, and
left click on the bottom surface of the spar cap.
Choose Surface for the slave type and select the top
surface for each of the front shear web segments. Also
select the top surface of the corner notch on each leading
edge rib segment and center rib segment as shown. To
select multiple surfaces simply click a surface, hold the
Shift key, and left click the next surface. To deselect one
of the surfaces hold the Ctrl key and left click on the
undesired surface.
Click Done to access the Edit Constraint window. The Position
Tolerance option should be set based upon the manner in
which the parts are assembled. In many cases the computed
default is sufficient especially when this is no separation or
negligible separation. In some assemblies, however, the
convergence calculations are helped by instead adding a small
separation between parts and then specifying the Position
Tolerance as slightly larger than the separation. In many cases
the “Adjust slave surface initial position” option will aid the
calculations. However, care should be taken especially in
contact between curved or complex surfaces as this option may
occasionally cause errors due to “Negative Element Volume”.
Once the constraint is completed the part should be translated
back to its original position. Constraints should then be added in
the same manner to define each joint between parts. As was
shown previously, a single constraint can be added to define
several joints that a single part has with several others. Multiple
master surfaces can also be chosen in defining a single
constraint, thereby further reducing the number of individual
constraints which are to be used in defining the assembly. The
list of constraints which were used in creating this example is
shown to the right in order to demonstrate a possible
combination of constraints to define the assembly. One primary
concern in defining the constraints is that no node should have
more than one master, although a master node may have any
number of slave nodes.
Loads and Boundary Conditions
The loads and boundary conditions chosen for this example were somewhat simple.
Go to the Step module and use the “Create Step” button to create
a Static, General Step. The default options are sufficient to conduct
basic analysis.
Go to the Load Module and use the “Create Load” button
to create a concentrated force in the Step that was just
created.
Make the load a 2lb force at the tip, centered about
the quarter-chord by selecting the two points shown
and entering a magnitude of 1 for CF2.
Use the “Create Boundary Condition” button to create
a boundary condition in the same step. Select the
Mechanical Category and Choose
Symmetry/Antisymmetry/Encastre.
Select the regions shown and choose the Encastre
boundary condition.
Stresses and Strains in Local Part Coordinate Directions
In the job module create a job and simply use the default options.
Submit the job for analysis. Once the analysis is complete, right click to view
the results. The “Plot Contours on Deformed Shape” button is quite useful for
locating stress concentrations and areas of high strain. Use Result-> Field
Output to choose which variable is displayed. The invariant variables can be of
particular interest.
Because the global coordinate system is used in expressing the stress
and strain components, these variables typically are not useful.
Instead it is much more useful to consider the stress and strain
components of various parts in context of the material coordinate
systems which were previously defined. To obtain these values, first
use the “Create Field Output From Fields”.
In the Create Field Output
window select whether which
set of variables to transform
(stress or strain or others).
Select Transformation for the
Function and the select the
coordinate system to which
the variables should be
transformed.
Clicking OK creates a Session Step in the Output Database
tree. In this Session Step using Results->Field Output
allows one to instead plot the variable components in the
transformed material direction. This information is
invaluable in any analysis which incorporates material
grain directions.