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Tutorials | Chapter 9. Modal Tutorial |
9.1. Modal Analysis of a Model Airplane Wing
9.1.1. Problem Specification
Applicable ANSYS Products: ANSYS Multiphysics, ANSYS Mechanical, ANSYS Structural, ANSYS ED
Level of Difficulty: easy
Interactive Time Required: 30 to 45 minutes
Discipline: structural
Analysis Type: modal
Element Types Used: PLANE42 and SOLID45
ANSYS Features Demonstrated: extrusion with a mesh, selecting, eigenvalue modal analysis, animation
Applicable Help Available: Modal Analysis in the ANSYS Structural Analysis Guide, PLANE42 and SOLID45 in the ANSYS Elements Reference.
9.1.2. Problem Description
This is a simple modal analysis of a wing of a model airplane. The wing is of uniform configuration along its length and its cross-sectional area is defined to be a straight line and a spline as shown. It is held fixed to the body of the airplane on one end and hangs freely at the other. The objective of the problem is to find the wing's natural frequencies and mode shapes.
9.1.2.1. Given
The dimensions of the wing are as shown above. The wing is made of low density polyethylene with a Young's modulus of 38x103 psi, Poisson's ration of 0.3, and a density of 8.3E-5 lbf-sec2/in4.
9.1.2.2. Approach and Assumptions
Assume the side of the wing connected to the plane is completely fixed in all degrees of freedom. The wing is solid and material properties are constant and isotropic.
Solid modeling is used to generate a 2-D model of the cross-section of the wing. You then create a reasonable mesh and extrude the cross-section into a 3-D solid model which will automatically be meshed.
Additionally, the mesh used in this example will be fairly coarse for the element types used. This coarse mesh is used here so that this tutorial can be used with the ANSYS ED product.
9.1.2.3. Summary of Steps
Use the information in this description and the steps below as a guideline in solving the problem on your own. Or, use the detailed interactive step-by-step solution by choosing the link for step 1.
Input Geometry
1. Read in geometry input file.
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Define Materials
2. Set preferences.
3. Define constant material properties.
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Generate Mesh
4. Define element type.
5. Mesh the area.
6. Extrude the meshed area into a meshed volume.
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Apply Loads
7. Unselect 2-D elements.
8. Apply constraints to the model.
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Obtain Solution
9. Specify analysis types and options.
10. Solve.
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Review Results
11. List the natural frequencies.
12. Animate the five mode shapes.
13. Exit the ANSYS program.
9.1.3. Input Geometry
9.1.3.1. Step 1: Read in geometry input file.
You will begin by reading in a file that includes the model.
Utility Menu> File> Read Input from ...
File name: wing.inp
UNIX version:
/ansys_inc/v100/ansys/data/models/wing.inp
PC version:
\Program Files\Ansys Inc\V100\ANSYS\data\models\wing.inp
[OK]
9.1.4. Define Materials
9.1.4.1. Step 2: Set preferences.
You will now set preferences in order to filter quantities that pertain to this discipline only.
Main Menu> Preferences
(check) “Structural”
[OK]
9.1.4.2. Step 3: Define constant material properties.
Main Menu> Preprocessor> Material Props> Material Models
(double-click) “Structural”, then “Linear”, then “Elastic”, then “Isotropic”
“EX” = 38000
“PRXY” = 0.3
[OK]
(double-click) “Density”
“DENS” = 8.3e-5
[OK]
Material> Exit
9.1.5. Generate Mesh
9.1.5.1. Step 4: Define element types.
Define two element types: a 2-D element and a 3-D element. Mesh the wing cross-sectional area with 2-D elements, and then extrude the area to create a 3-D volume. The mesh will be "extruded" along with the geometry so 3-D elements will automatically be created in the volume.
Main Menu> Preprocessor> Element Type> Add/Edit/Delete
[Add...]
“Structural Solid” (left column)
“Quad 4node 42” (right column)
[Apply] to choose the Quad 4 node (PLANE42)
“Structural Solid” (left column)
“Brick 8node 45” (right column)
[OK] to choose the Brick 8 node (SOLID45)
[Close]
Toolbar: SAVE_DB
9.1.5.2. Step 5: Mesh the area.
The next step is to specify mesh controls in order to obtain a particular mesh density.
Main Menu> Preprocessor> Meshing> Mesh Tool
“Size Controls Global” = [Set]
“Element edge length” = 0.25
[OK]
[Mesh]
[Pick All]
[Close] Warning.
[Close] Meshtool
Toolbar: SAVE_DB
In designing this problem, the maximum node limit of ANSYS ED was taken into consideration. That is why the 4-node PLANE42 element, rather than the 8-node PLANE82 element was used. Note that the mesh contains a PLANE42 triangle, which results in a warning. If you are not using ANSYS ED, you may use PLANE82 during the element definitions to avoid this message. Note however that PLANE82 does not work unless you get rid of the Global Element edge length (which was set to 0.25).
Note
The mesh you see on your screen may vary slightly from the mesh shown above. As a result of this, you may see slightly different results during postprocessing. For a discussion of results accuracy, see Planning Your Approach in the ANSYS Modeling and Meshing Guide.
9.1.5.3. Step 6: Extrude the meshed area into a meshed volume.
In this step, the 3-D volume is generated by first changing the element type to SOLID45, which is defined as element type 2, and then extruding the area into a volume.
Main Menu> Preprocessor> Modeling> Operate> Extrude> Elem Ext Opts
(drop down) “Element type number” = 2 SOLID45
“No. Elem divs” = 10
[OK]
Main Menu> Preprocessor> Modeling> Operate> Extrude> Areas> By XYZ Offset
[Pick All]
“Offsets for extrusion” = 0, 0, 10
[OK]
[Close] Warning.
Using SOLID45 to run this problem in ANSYS ED will produce this warning message. If ANSYS ED is not being used, then SOLID95 (20-node brick) can be used as element type 2. Using PLANE82 and SOLID95 produces a warning message about shape warning limits for 10 out of 127 elements in the volume.
Utility Menu> PlotCtrls> Pan, Zoom, Rotate
[Iso]
[Close]
Toolbar: SAVE_DB
9.1.6. Apply Loads
9.1.6.1. Step 7: Unselect 2-D elements.
Before applying constraints to the fixed end of the wing, unselect all PLANE42 elements used in the 2-D area mesh since they will not be used for the analysis.
Utility Menu> Select> Entities
(first drop down) “Elements”
(second drop down) “By Attributes”
(check) “Elem type num”
“Min,Max,Inc” = 1
(check) “Unselect”
[Apply]
9.1.6.2. Step 8: Apply constraints to the model.
Constraints will be applied to all nodes located where the wing is fixed to the body. Select all nodes at z = 0, then apply the displacement constraints.
(first drop down) “Nodes”
(second drop down) “By Location”
(check) “Z coordinates”
“Min,Max” = 0
(check) “From Full”
[Apply]
Main Menu> Preprocessor> Loads> Define Loads> Apply> Structural> Displacement> On Nodes
[Pick All] to pick all selected nodes.
“DOFs to be constrained” = All DOF
[OK] Note that by leaving “Displacement” blank, a default value of zero is used.
Now, reselect all nodes.
(second drop down) “By Num/Pick”
[Sele All] to immediately select all nodes from entire database.
[Cancel] to close dialog box.
Toolbar: SAVE_DB
9.1.7. Obtain Solution
9.1.7.1. Step 9: Specify analysis type and options.
Specify a modal analysis type.
Main Menu> Solution> Analysis Type> New Analysis
(check) “Modal”
[OK]
Main Menu> Solution> Analysis Type> Analysis Options
(check) “Block Lanczos” (Block Lanczos is the default for a modal analysis.)
“No. of modes to extract” = 5
“No. of modes to expand” = 5
[OK]
[OK] All default values are acceptable for this analysis.
Toolbar: SAVE_DB
9.1.7.2. Step 10: Solve.
Main Menu> Solution> Solve> Current LS
Review the information in the status window, then choose:
File> Close (Windows),
or
Close (X11 / Motif), to close the window.
[OK] to initiate the solution.
[Yes]
[Yes]
Based on previous discussions, the warnings are accepted. The messages presented in the verification window are due to the fact that PLANE42 elements have been defined but not used in the analysis. They were used to mesh a 2-D cross-sectional area.
[Close] to acknowledge that the solution is done.
9.1.8. Review Results
9.1.8.1. Step 11: List the natural frequencies.
Main Menu> General Postproc> Results Summary
[Close] after observing the listing.
9.1.8.2. Step 12: Animate the five mode shapes.
Set the results for the first mode to be animated.
Main Menu> General Postproc> Read Results> First Set
Utility Menu> PlotCtrls> Animate> Mode Shape
[OK]
Observe the first mode shape:
Make choices in the Animation Controller (not shown), if necessary, then choose Close.
Animate the next mode shape.
Main Menu> General Postproc> Read Results> Next Set
Utility Menu> PlotCtrls> Animate> Mode Shape
[OK]
Observe the second mode shape:
Repeat red steps 4 through 7 above, and view the remaining three modes.
Observe the third mode shape:
Observe the fourth mode shape:
Observe the fifth mode shape:
9.1.8.3. Step 13: Exit the ANSYS program.
Toolbar: QUIT
(check) “Quit - No Save!”
[OK]
Congratulations! You have completed this tutorial.
Even though you have exited the ANSYS program, you can still view animations using the ANSYS ANIMATE program. The ANIMATE program runs only on the PC and is extremely useful for:
Viewing ANSYS animations on a PC regardless of whether the files were created on a PC (AVI files) or on a UNIX workstation (ANIM files).
Converting ANIM files to AVI files.
Sending animations over the web.
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