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Bending of plates, or plate bending, refers to the deflection of a plate perpendicular to the plane of the plate under the action of external forces and moments. The amount of deflection can be determined by solving the differential equations of an appropriate plate theory.



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Step 2: Define Element Type

  1. In the Main Menu select Preprocessor > Element Type > Add/Edit/Delete

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  2. Click on Add in the dialog box that appears:

  3. Select Solid in the left hand menu and Quad 8 node 183 in the right hand menu and then click OK

  4. This defines element type 1 as a 2D quadratic 8-node quadrilateral element (i.e. a rectangle with curved edges)

  5. Now we must define how this element behaves. Click on Options in the Element Types dialog box:

  6. In the element type options dialog box that appears, make sure that the Element behavior is set to 'Plane Stress with thickness' as shown in the figure below:

  7. Click Close to close the Element Type dialog box.


Step 3: Define The Plate Thickness (Real Constant)

  1. In the Main Menu select Preprocessor > Real Constants > Add/Edit/Delete

  2. Click on Add in the dialog box that appears.

  3. Click on OK to define a real constant for element type 1 PLANE 183.

  4. Enter the value for the plate thickness: 0.001 m and then click OK

  5. Click on Close to close the real constants dialog box.

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Step 4: Define the Material Behaviour

  1. In the Main Menu click on Preprocessor > Material Props > Material Models, the Define Material Model Behaviour dialog box will now appear.

  2. Expand the options in the right hand pane of the dialog box: Structural > Linear > Isotropic

  3. In the dialog box that pops up, enter suitable material parameters for steel ( E = 210 x 109 Pa, Poissons ratio = 0.3):

  4. Click on Ok to close the dialog box in which you entered the material parameters.

  5. Close the Define Material Model Behaviour dialog box by clicking on the X in the upper right corner.

Step 5: Create the Plate Geometry

  1. In the Main Menu click on Preprocessor > Modelling > Create > Areas > Rectangle > By 2 Corners

  2. The WP X and WP Y boxes are used to define the coordinates for the lower left coordinates of the rectangle and the width and height are entered in the other boxes. Set the lower left corner at the coordinates (0,0) and make the width and height equal to 0.1 m, as show below:


  3. You should see a blue square appear on your screen.

  4. We will now create the hole: Preprocessor > Modelling > Create > Areas > Circle > Solid Circle

  5. We must place the centre of the circle at the centre of the square so enter 0.05 for WP X and WP Y. The radius of the circle is 0.005 m :

  6. You should notice the outline of a circle appearing in the centre of the plate.

  7. Now, we are going to subtract the circle area from the rectangular area to give the correct plate with a hole geometry: Preprocessor > Modelling > Operate > Booleans > Subtract > Areas

  8. The Subtract Areas pick box will appear. If you look at the bottom of the main menu you will see a prompt asking you to 'Pick or enter base areas from which to subtract'. This means we need to pick the square first. Click on the square with your mouse.

  9. You will probably find a dialog box like this appearing:

  10. This means that ANSYS is not entirely sure which area you meant to pick (either the circle or the rectangle). Take a look at the screen and if the entire rectangle has changed colour (to indicate that it is picked) then you can just click on OK in this dialog box. If things don't look ok then click on Next or Prev to toggle between selecting the two areas.

  11. Now click on OK in the Subtract Areas pick box.

  12. A new Subtract Areas pick box will immediatly appear and the message at the bottom of the main window will change to 'Pick or enter areas to be subtracted'. This means we need to pick the circle. Click on the circle with your mouse. Use the 'multiple entities' dialog box if required to ensure it is only the circle that is selected and then click on OK to close the Subtract Areas dialog box.

  13. Your geometry should now look like this:

Step 6: Mesh the Geometry

  1. In the Main Menu click on Preprocessor > Meshing > Mesh Tool

  2. This will open the Mesh Tool window.

  3. We are now going to use the Mesh Tool to set the size of the elements to all be a constant size before we begin the meshing process. In the Mesh Tool click on Areas > Set as shown in the figure below:

  4. Use your mouse to click on the plate geometry. Once you have clicked on it, the Element Size at Picked Areas dialog box will appear. Enter 0.001 m for the Element Edge Length to define the size of each element, as shown below:

  5. Click on OK to close the dialog box.

  6. Now we must divide the plate up into elements. In the Mesh Tool window click on Mesh.

  7. You should see the plate divided up into quadrilateral finite elements:

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Step 7: Apply the Boundary Conditions

  1. In the Main Menu click on Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines

  2. Pick the vertical line on the left hand side of the plate and the click OK in the picker dialog box.

  3. In the dialog box that appears make sure that only UX is selected as we only want to constrain this line in the X (i.e. horizontal) direction.

  4. You should notice some blue triangles appearing on the line indicating that it has been constrained.

  5. If we only applied this displacement then there would be nothing to stop the entire model from moving in the vertical direction even though we will not be applying any loads in the vertical direction. This could occur due to imbablances in the mesh as internal forces work their way through the mesh etc. In order to prevent this from happening we need to constrain at least one more node in the vertical direction also. We are going to constrain a node at the centre of the left hand vertical line in the Y direction:

  6. Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Nodes

  7. Click on the node at the centreline of the plate on the left hand edge and then click on OK

  8. In the dialog box that appears make sure the DOFs to be constrained is set to UY only and then click on OK.

  9. You will probably get a warning saying that 'Both solid model and finite element boundary conditions have been applied to this model. As solid loads are transferred to the nodes or elements, they can overwrite directly applied loads'. This is OK just click on Close to dismiss this dialog.

Step 8: Couple the Nodes on the Right Hand Edge and Apply the Force

  1. In the Main Menu click on Preprocessor > Coupling/ Ceqn > Couple DOF

  2. Make sure that the box option is selected in the Define Coupled DOFs pick box, as shown below:

  3. Draw a box around the nodes on the right hand edge of the plate finite element model by clicking your left mouse button and holding it down to draw the box. Release the left mouse button when the box is the size you require.

  4. Now, click on OK to close the picker dialog box.

  5. The next dialog box asks you for a Set Reference Number - enter any number you wish (I have used 99 in the image below). The dialog box also asks you which degree of freedom you wish to couple: make sure that this is set to UX, as shown below.

  6. You should notice green arrows appearing on all the nodes on the right hand edge of the plate, indicating that their UX degree of freedom has been coupled.

  7. We can now apply the required force to any one of the coupled nodes: Preprocessor > Loads > Define Loads > Apply > Structural > Force/Moment > On Nodes

  8. Click on any of the nodes on the right hand edge of the plate and then click on OK to close the picker dialog.

  9. Change the force direction to FX and enter a Force/Moment value of 1000 in order to apply 1000 N.

  10. You should notice a read arrow appearing on your screen pointing to the right.

    Your screen should now look like this:

Step 10: Solve the Problem

  1. In the Main Menu select Solution > Analysis Type > New Analysis

  2. Make sure that Static is selected in the dialog box that pops up and then click on OK to dismiss the dialog.

  3. Select Solution > Solve > Current LS to solve the problem

  4. A new window and a dialog box will pop up. Take a quick look at the infromation in the window ( /STATUS Command) before closing it.

  5. Click on OK in the dialog box to solve the problem.

  6. Once the problem has been solved you will get a message to say that the solution is done, close this window when you are ready.

Step 11: Examine the Results

  1. In the Main Menu select General Postproc > Plot Results > Deformed Shape

  2. Select Def + undef edge in order to show both the deformed and undeformed shapes.

  3. Your screen should look something like this:

  4. Notice that the plate has reduced height and elongated in the horizontal direction. The hole has changed shape from a perfect circle to an ovoid shape. This is all as we would expect.

  5. In the Main Menu select General Postproc > Plot Results > Contour Plot > Nodal Solu > Stress > X-Component of Stress

  6. You should see a plot similar to this:

  7. Notice that the maximum stress is approximately 30 MPa and is at the top and bottom of the hole. This is the result that was predicted by our analytical theory.

Step 12: Change the Model to take advantage of Symmetry

  1. We are now going to remove 3/4 of the model and use a 1/4 symmetry model of the plate to obtain the same result as above.

  2. We must first clear the mesh: Main Menu select Preprocessor > Meshing > Clear > Areas and click on Pick All in the picker dialog box.

  3. You will get a message telling you that the coupled set has been deleted - this is ok, just click on close to get rid of this message.

  4. In order to display the geometry again: Utility Menu > Plot > Areas

  5. We are going to use the workplane to cut the existing model into four quarters. Turn on the workplane by selecting: Utility Menu > WorkPlane > Display Working Plane

  6. By default, the workplane is located and aligned with the global origin. We must now move it to the centre of the plate: Utility Menu > WorkPlane > Offset WP to > XYZ Locations

  7. Enter the coordinates 0.05,0.05 in the pick dialog box that appears:

  8. You should notice the workplane move to the centre of the hole in the centre of the plate.

  9. By default ANSYS uses the XY plane of workplane to cut through an object. We must now rotate the workplane so that it's XY plane cuts through the plate. Utility Menu > WorkPlane > Offset WP by increments..

  10. In the dialog box that appears change the number of degrees to 90 and then rotate the workplane in the positive X - direction, as shown below:

  11. Click on OK to close the Offset WP dialog box.

  12. Now let's start cutting up the plate: Main Menu > Preprocessor > Modelling > Operate > Booleans > Divide > Area by Workplane

  13. Click on the plate and then click on OK.

  14. The plate is now divided vertically into two halves. Let's now delete the lower half: Main Menu > Preprocessor > Modelling > Delete > Area and Below

  15. Click on the lower half of the plate and click on OK. Your screen should now look like this:

  16. We will now repeat a lot of the above process to remove the left hand 1/4 of the plate: Utility Menu > WorkPlane > Offset WP by increments..

  17. Click on the +Y rotation button to rotate the workplane so the XY plane is in the vertical direction on the screen then click on OK to close the dialog box.

  18. Now let's cut the plate again: Main Menu > Preprocessor > Modelling > Operate > Booleans > Divide > Area by Workplane

  19. Click on the plate and then click on OK.

  20. The plate is now divided horizontally into two halves. Let's now delete the left hand half: Main Menu > Preprocessor > Modelling > Delete > Area and Below

  21. Click on the left hand side of the plate and click on OK.

  22. It is good practice to put the workplane back in its original position when you are finished using it:

  23. Your screen should now look like this: Utility Menu > WorkPlane > Align WP with > Global Cartesian

  24. You can also turn off the workplane again: Utility Menu > WorkPlane > Display Working Plane

  25. Now, let's do a replot to tidy up our display: Utility Menu > Plot > Areas

  26. Your screen should now look like this:


  27. We want to ensure that we get a nice regular mesh when we mesh this 1/4 of the plate. A very regular mapped mesh would be desireable here but a mapped mesh is only possible with a four sided area and our area has five sides. In order to overcome this we are going to concatanate the lines on the top and the right (i.e. merge them into one line). This way we can 'trick' the mesher into thinking it is a four sided object and obtain a nice mapped mesh.

  28. Main Menu > Preprocessor > Modelling > Operate > Booleans > Add > Lines

  29. Pick the lines at the top and right of the 1/4 plate and then click on OK

  30. A dialog box will appear asking you if you want to keep or delete the existing lines: make sure 'Deleted' is selected and then click on OK

  31. You will get a warning message telling you that the lines do not share a common slope at the upper right hand corner and this will cause problems if you try to sweep the new line to form another object. This doesn't apply here, as we won't be doing this, so we can just ignore this warning and close the warning.

  32. We can now begin to mesh our 1/4 plate: Main Menu > Preprocessor > Meshing > Meshtool

  33. In the MeshTool, under 'Size Controls' click on Lines > Set

  34. Click on the line at the bottom of the plate and click on OK. In the dialog box that appears enter 20 for the number of divisions and 5 for the spacing ratio. This will ensure that this line is divided into 20 elements and that the elements at one end of the line will be 5 times bigger than the elements at the other end.

  35. Make sure that the small elements are near the hole: Utility Menu > Plot > Lines If they are not in the right place then use the Flip button on the meshtool to flip the spacing over.

  36. Repeat steps 33-35 with the line at the left hand edge of the 1/4 plate.

  37. Now, we will set the number of divisions on the curved line that defines the hole: this time enter 20 for the number of divisions and set the spacing ratio to 1 as we don't want the elements to change size over the length of this line.

  38. We can now mesh the 1/4 plate: In the Meshtool make sure that the Shape is set to 'Quad' and that 'Mapped' meshing is selected, then click on Mesh.

  39. Pick the 1/4 area and then click on OK. Your screen should look like this:

  40. Now, apply a symmetry boundary condition to the lines on the left and the bottom of the 1/4 plate: Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > Symmetry BC > On Lines

  41. Pick the lines on the left and the bottom of the 1/4 plate and then click on OK. You should see small 's' symbols appear along these lines to show that a symmetry constraint has been applied.

  42. Now, we must couple the nodes on the right hand line together and apply the load as we did above. Repeat the steps detailed above to do this, but this time, take care to only apply a load of 500 N, as due to the symmetry boundary conditions, any load we applied will be effectively doubled.

  43. Now, solve the problem as usual and then check the deformed shape and the stress in the X-direction.

  44. The deformed shape:

  45. This is as expected

  46. The stress in the x-direction:

  47. Again, as expected and with a magnitude of 29.7 MPa. This is slightly below what we expected 30 MPa but is still 99% accurate. We could possibly improve the accuracy by changing the mesh.

This tutorial has given you the following skills:

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  1. The ability to model plane stress problems in ANSYS.
  2. The ability to generate finite element models by meshing a solid model (in this case an area)
  3. The ability to apply loads to 2D models using coupled DOF.
  4. The ability to produce contour plots of stress in 2D plane models.
  5. The ability to divide and manipulate a model using the ANSYS workplane.
  6. The ability exploit symmetry in a model using appropriate boundary conditions.
  7. The ability to produce a mapped mesh by concatinating lines
  8. Experience in comparing the results obtained from your finite element model with other results and validating your results against the other results.

Log Files / Input Files

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The log file for this tutorial may also be used as an input file to automatically run the analysis in ANSYS. In order to use this file as an input file save it to your working directory and then select Utility Menu > File > Read input from.. and select the file. You should notice ANSYS automatically building the finite element model and issuing all the commands detailed above.

Quitting ANSYS

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To quit ANSYS select Utility Menu > File > Exit... In the dialog box that appears click on Save Everything (assuming that you want to) and then click on Ok

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