Shape Optimization of a Rail Joint Shape optimization requires you to have knowledge of the kind of shape you would like to change in the structure. This may include finding the optimum shape to reduce stress concentrations to changing the cross-sections to meet specific design requirements. Therefore, you need to define the shape modifications and the nodal movements to reflect the shape changes. Shape optimization requires the use of two cards DESVAR and DVGRID. They can be defined using HyperMorph. These cards are included in the OptiStruct input file along with the objective function and constraints to run the shape optimization.

In this exercise you will perform a shape optimization on a rail-joint. The rail-joint is made of shell elements and has one load case. The shape of the joint is modified to satisfy stress constraints while minimizing mass.

Rail joint

The optimization problem for this exercise is stated as: Objective: Minimize mass

Constraint: Maximum von Mises stress of the joint < 200 MPa

Design variables: Shape variables

Problem Setup You should copy the file: rail_joint.hm

Step 1: Import rail_joint.fem into HyperMesh Desktop

Step 2: Display Node Numbers 1. From Tool page, select numbers panel.

2. Click nodes and select by sets.

3. Select node set by clicking the check box to the left of node.

4. Click select. 16 nodes are highlighted on screen.

5. Click on to display node IDs.

6. Click return.

Step 3: Build 2-D Domains on the Rail 1. In the Model Browser window, expand the Component list.

2. Right-click on the component PSHELL and click on Isolate.

All other components are turned off for ease of visualization.

3. From the Analysis page, select the optimization panel.

4. Go to the HyperMorph panel, and select domains.

5. Toggle the radio button on the left to partitioning.

6. Verify that domain angle = 50.

7. Verify that curve tolerance = 8.0000.

8. Toggle back the radio button to create.

9. Click the switch (small triangle) and select 2D domains.

10. Toggle all elements to elems.

11. Click elems and select by sets from the pop-up window.

12. Check the boxes for rail_set1 and rail_set2.

13. Click select. 14. Click create.

Rail domains

Step 4: Split the Circular Edge Domains Around the Opening of the Rail The following steps show the procedure to split each of the two circular domains (as shown in the previous figure) into four curved edge domains.

1. Toggle the radio button to edit edges subpanel.

2. Verify the top selector is split. 3. Click domain and select the circular edge-domain passing through nodes 1300, 1305, 1311,

1316.

4. Click node and select node 1311 from the display. Refer to the previous figure.

5. Click split. The circular domain is split at Node 1311 and a new handle is created at node1311.

6. Select the circular edge between node 1311 and the other handle.

The edge is highlighted.

7. Click node 1316 to split the domain.

8. Similarly (as in steps 6-7), split the curved edge at nodes 1305 and 1300, respectively. Refer to the previous figure.

A similar process is followed to split the circular domain using the four nodes on the other side of the rail.

9. Click domain and select the circular domain passing through nodes 931, 926, 937 and 942.

10. Click node and select node 931 on screen.

11. Click split. 12. Select the circular edge between node 931 and the other handle.

The edge is highlighted.

13. Click node 926 to split the domain.

14. Similarly (as in steps 11-14), split the curved edge at nodes 937 and 942, respectively.

The following figure shows the image after the circular edge domains are split.

Rail domains after the circular edge have been split

Step 5: Merge Edge Domains Each circular domain on the rail has been split at four nodes and four new handles have been added to each circular domain. This operation results in five curved edge domains on each circular edge on the rail. The objective is to have only four domains. The following steps show the procedure to merge domains.

1. Toggle the left switch and select to merge edges.

2. Click the left domain below merge and select the outer red curve from node 926 to pre-existing handle (refer to previous figure).

3. Click the right domain and select the outer red curve from pre-existing handle to node 942.

4. Verify that retain handles is unchecked.

5. Click merge.

Notice the pre-existing handle is removed.

6. Repeat steps 1 through 5 to merge two edge domains between node 1316 and node 1300 on the other side of the rail.

Rail domains after few domains are merged

Step 6: Build 2-D Domains on the Tube 1. In the Model Browser window, expand the Component. 2. Right-click on the component PSHELL.1 and click Show.

3. Toggle back the radio button to create.

4. Make sure the switch (small triangle) is selected to 2D domains.

5. Click elems and select by sets from the pop-up window.

6. Check the boxes for elem_set1 and elem_set2.

7. Click select. 8. Click create.

9. Repeat steps 5 through 8 to create two more 2-D domains for elements in sets elem_set3 and elem_set4, respectively.

10. Click return and go back to the HyperMorph module.

Domains on Rail and Tube Joint

Step 7: Create Shapes In this step, three shapes are created using the created domains and handles.

1. Click morph.

We use the alter dimensions subpanel in HyperMorph to modify the curvatures of selected edge domains.

2. Toggle to alter dimensions.

3. Toggle the right switch and select curve ratio.

4. Toggle center calculation and change the setting to by edges.

5. Toggle the switch below and select hold ends.

Holding two ends of a selected edge domain allows a change of curvature of the selected edge without altering its end points.

6. Leave the other settings with the defaults.

7. Under edges only, click domains and select red edge-domains as shown in the following figure. You might need to zoom in for easier picking operation.

8. Verify that a total of eight edge domains are selected and highlighted on screen.

Morph edge domains

9. Click curve ratio = and enter 20.

10. Click morph.

A new curvature is applied to the selected eight edge domains. See the following figure below.

11. Toggle the radio button to save shape.

12. Click on shape =, enter the name sh1.

13. Toggle as handle perturbation to as node perturbation.

14. Click on the color button and change the color of the shape vectors or leave the default color.

15. Click save.

Shape vectors (arrows) are created of the selected color.

16. Click undo all to prepare for the generation of the next shape.

17. Click the Model Browser tab, right-click on Shape and select Hide.

First shape variable, sh1.

18. Toggle the radio button to alter dimensions.

19. Under edges only, click reset .

This will clean up previous selection from buffer.

20. Click domains and select the red edge curves, as shown the following figure.

Morph edge domains for the second shape.

21. Click morph.

A new curvature is applied to the selected eight edge domains. See the following figure below.

22. Toggle the radio button to save shape.

23. Click on shape =, enter the name sh2.

24. Toggle as handle perturbation to as node perturbation.

25. Click on the color button and change the color of the shape vectors or leave the default color.

26. Click save.

Shape vectors (arrows) are created of the selected color.

27. Click undo all to prepare for the generation of the next shape.

28. Click the Model Browser tab, right-click on Shape and select Hide.

Refer to the following figure for the new shape changes.

Second shape variable, sh2.

29. Toggle the radio button to apply shapes.

In HyperMorph, a new shape can be created as a linear combination of existing shapes.

30. Click shapes and select both sh1 and sh2.

31. Click Select. Verify that the multiplier is 1.0.

32. Click apply.

33. Toggle the radio button to save shapes.

34. Click shape = and enter sh3.

35. Make sure that the toggle is set to node perturbations.

The new shape sh3 includes influences from both sh1 and sh2 shapes, as shown in the next figure.

36. Click save.

37. Click the Model Browser tab, right-click on Shape and select Hide.

Do NOT click undo all at this moment because we will create one more shape based on this third shape change.

The third shape variable, sh3, converts the tube to a square cross-section

An additional shape variable is created using the shape created in the previous step.

38. In the Model Browser window, right-click on the component PSHELL and select Hide.

These components are turned off for ease of visualization.

39. Toggle the radio button to alter dimensions.

40. Under edges only, click reset .

This will clean up previous selection from buffer.

41. Switch the top selector from curve ratio to distance =.

This feature allows you to shorten the distance between selected domains.

42. Switch the end a: selector from two handles to nodes and handles.

43. Click node a and pick node as shown in the next figure.

44. Click node b and pick node as shown in the next figure.

Setup for the fourth shape variable, sh4

Once nodes a and b are selected, the distance between node a and node b is measured automatically and appears in distance = field.

The distance between node a and node b is about 43.

45. Click handles under node a, and select the 8 handles shown by the downward pointing arrows in the previous figure.

To select, click the handles on the screen until they are highlighted.

46. Click handles under node b and similarly as in the previous step, select the 8 handles near the opposite face of the tube.

47. Toggle the bottom selector and select hold middle.

48. In the Model Browser window, right-click on the component PSHELL and click on Show.

These components are turned on for ease of visualization.

49. Click distance = and enter 20.

50. Click morph.

A rectangular shape appears to the joint as shown in the next figure.

51. Toggle the button to save shape.

52. Click shape = and enter sh4.

53. Make sure that the toggle is set to node perturbations.

54. Click save.

55. Click undo all to restore the mesh to the baseline configuration.

56. Click the Model Browser tab, right-click on Shape and select Hide.

57. Click return three times to return to the main menu.

Fourth shape variable, sh4

Step 8: Define the shape design variables with lower and upper bounds -1 and 1, initial value 0, including all shapes created (sh1-sh4)

Step 9: Create a total mass response named mass

Step 10: Create a static stress response Stress for property PSHELL.1 of type vonMises using stress measurement option both surfaces

Step 11: Constrain response Stress with an upper bound of 200 for subcase STEP

Step 12: Create the objective to min mass

Step 13: Run the optimization

Step 14: Define Control Cards Required for Shape Optimization 1. From the Analysis page, click the control cards panel.

2. Click the Next button twice and chose the PARAM card.

3. Check the box next to CHECKEL.

4. Click the YES button under CHECKEL_V1 to change to NO.

5. Click return twice.

Step 13: Run the optimization

Step 14: Review the Shape Change results contour in Hyperview

Shape change contour in HyperView

Optional: View a Contour Plot of the Stress on Top of the Shape Optimized Model 1. Click the Next Page arrow in the toolbar to move to the next page.

2. Click the Contour toolbar button.

Note the Result type: is Element Stresses [2D & 3D] [t]. The second pull-down menu shows von Mises.

3. At the bottom of the GUI, click on the name Subcase 1 (STEP) <> Model Step to activate the Load Case and Simulation Selection dialog.

4. Select the last iteration by double-clicking on the last Iteration listed.

5. Click Apply.

The stress contour shows on top of the shape changes applied to the model. Verify that this value is around the constraint value specified.

Von Mises Stress for the last iteration (Max < 200 MPa)

Reviewing the Results Is your design objective of minimizing the volume obtained? If not, can you explain why?

Are your design constraints satisfied?

Which shape has the most influence in this problem setup?

What is the percentage decrease in compliance?

Can size optimization be introduced to the joint?