Modelling Using Axisymmetry

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Introduction

This tutorial was completed using ANSYS 7.0 This tutorial is intended to outline the steps required to create an axisymmetric model.

The model will be that of a closed tube made from steel. Point loads will be applied at the center of the top and bottom plate to make an analytical verification simple to calculate. A 3/4 cross section view of the tube is shown below.

As a warning, point loads will create discontinuities in the your model near the point of application. If you chose to use these types of loads in your own modelling, be very careful and be sure to understand the theory of how the FEA package is appling the load and the assumption it is making. In this case, we will only be concerned about the stress distribution far from the point of application, so the discontinuities will have a negligable effect.

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Preprocessing: Defining the Problem

1. Give example a TitleUtility Menu > File > Change Title ...
   /title, Axisymmetric Tube
2. Open preprocessor menuANSYS Main Menu > Preprocessor
   /PREP7
3. Create AreasPreprocessor > Modeling > Create > Areas > Rectangle > By Dimensions
   RECTNG,X1,X2,Y1,Y2For an axisymmetric problem, ANSYS will rotate the area around the y-axis at x=0. Therefore, to create the geometry mentioned above, we must define a U-shape.
   We are going to define 3 overlapping rectangles as defined in the following table:
   
   

   Rectangle	X1	X2	Y1	Y2
   1	0	20	0	5
   2	15	20	0	100
   3	0	20	95	100

4. Add Areas TogetherPreprocessor > Modeling > Operate > Booleans > Add > Areas
   AADD,ALLClick the Pick All button to create a single area.
5. Define the Type of Element
Preprocessor > Element Type > Add/Edit/Delete...For this problem we will use the PLANE2 (Structural, Solid, Triangle 6node) element. This element has 2 degrees of freedom (translation along the X and Y axes).
Many elements support axisymmetry, however if the Ansys Elements Reference (which can be found in the help file) does not discuss axisymmetric applications for a particular element type, axisymmetry is not supported.

6. Turn on Axisymmetry
While the Element Types window is still open, click the Options... button.Under Element behavior K3 select Axisymmetric.


7. Define Element Material PropertiesPreprocessor > Material Props > Material Models > Structural > Linear > Elastic > IsotropicIn the window that appears, enter the following geometric properties for steel:
   
   1. Young's modulus EX: 200000
   2. Poisson's Ratio PRXY: 0.3
8. Define Mesh SizePreprocessor > Meshing > Size Cntrls > ManualSize > Areas > All AreasFor this example we will use an element edge length of 2mm.
9. Mesh the framePreprocessor > Meshing > Mesh > Areas > Free > click 'Pick All'Your model should know look like this:
   

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Solution Phase: Assigning Loads and Solving

1. Define Analysis Type
Solution > Analysis Type > New Analysis > Static
ANTYPE,0

2. Apply Constraints
• Solution > Define Loads > Apply > Structural > Displacement > Symmetry B.C. > On LinesPick the two edges on the left, at x=0, as shown below. By using the symmetry B.C. command, ANSYS automatically calculates which DOF's should be constrained for the line of symmetry. Since the element we are using only has 2 DOF's per node, we could have constrained the lines in the x-direction to create the symmetric boundary conditions.
  


• Utility Menu > Select > EntitiesSelect Nodes and By Location from the scroll down menus. Click Y coordinates and type 50into the input box as shown below, then click OK.
  
  Solution > Define Loads > Apply > Structural > Displacement > On Nodes > Pick All
  Constrain the nodes in the y-direction (UY). This is required to constrain the model in space, otherwise it would be free to float up or down. The location to constrain the model in the y-direction (y=50) was chosen because it is along a symmetry plane. Therefore, these nodes won't move in the y-direction according to theory.


3. Utility Menu > Select > EntitiesIn the select entities window, click Sele All to reselect all nodes. It is important to always reselect all entities once you've finished to ensure future commands are applied to the whole model and not just a few entities. Once you've clicked Sele All, click on Cancel to close the window.
   
4. Apply Loads
• Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints
  Pick the top left corner of the area and click OK. Apply a load of 100 in the FY direction.
• Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints
  Pick the bottom left corner of the area and click OK. Apply a load of -100 in the FY direction.
• The applied loads and constraints should now appear as shown in the figure below.


5. Solve the System
Solution > Solve > Current LS
SOLVE

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Postprocessing: Viewing the Results

1. Hand CalculationsHand calculations were performed to verify the solution found using ANSYS:
   The stress across the thickness at y = 50mm is 0.182 MPa.
   
   
2. Determine the Stress Through the Thickness of the Tube
   • Utility Menu > Select > Entities...Select Nodes > By Location > Y coordinates and type 45,55 in the Min,Max box, as shown below and click OK.
     
     
   • General Postproc > List Results > Nodal Solution > Stress > Components SCOMPThe following list should pop up.
     
     
   • If you take the average of the stress in the y-direction over the thickness of the tube, (0.18552 + 0.17866)/2, the stress in the tube is 0.182 MPa, matching the analytical solution. The average is used because in the analytical case, it is assumed the stress is evenly distributed across the thickness. This is only true when the location is far from any stress concentrators, such as corners. Thus, to approximate the analytical solution, we must average the stress over the thickness.
3. Plotting the Elements as AxisymmetricUtility Menu > PlotCtrls > Style > Symmetry Expansion > 2-D Axi-symmetric...The following window will appear. By clicking on 3/4 expansion you can produce the figure shown at the beginning of this tutorial.
   
4. Extra ExerciseIt is educational to repeat this tutorial, but leave out the key option which enables axisymmetric modelling. The rest of the commands remain the same. If this is done, the model is a flat, rectangular plate, with a rectangular hole in the middle. Both the stress distribution and deformed shape change drastically, as expected due to the change in geometry. Thus, when using axisymmetry be sure to verify the solutions you get are reasonable to ensure the model is infact axisymmetric.
   
   
   
   

   ANSYS Command Listing

   finish
   /clear
   
   /title, Axisymmetric Tube
   /prep7
   /triad,off   ! Turns off origin triad marker
   
   rectng,0,20,0,5   ! Create 3 overlapping rectangles
   rectng,15,20,0,100
   rectng,0,20,95,100
   
   aadd,all   ! Add the areas together
   
   et,1,plane2   ! Define element type
   keyopt,1,3,1   ! Turns on axisymmetry
   mp,ex,1,200000   ! Young's Modulus
   mp,prxy,1,0.3   ! Poisson's ratio
   
   esize,2    ! Mesh size
   amesh,all   ! Mesh the area
   
   finish
   /solu
   
   antype,0   ! Static analysis
   
   lsel,s,loc,x,0   ! Select the lines at x=0
   dl,all,,symm   ! Symmetry constraints
   lsel,all   ! Re-select all lines
   
   nsel,s,loc,y,50   ! Node select at y=50
   d,all,uy,0   ! Constrain motion in y
   nsel,all   ! Re-select all nodes
   
   fk,1,fy,-100   ! Apply point loads in center
   fk,12,fy,100
   
   solve
   finish
   
   /post1
   nsel,s,loc,y,45,55  ! Select nodes from y=45 to y=55
   prnsol,s,comp   ! List stresses on those nodes
   nsel,all   ! Re-select all nodes
   
   /expand,27,axis,,,10  ! Expand the axisymmetric elements
   /view,1,1,2,3   ! Change the viewing angle
   /replot