TUTORIAL 3: Third Time is a Charm

Design of Cross-Section to Meet Specific Stress Requirements ANSYS has many tools that help designers determine near-optimal cross-sections, lengths, loads, etc. for specific design problems. In this Tutorial you will try out the Direct Optimization Tool in ANSYS. This tool will help you determine the width of the I-shape cross-section that is needed to meet specific stress limits at the extreme fiber of the cross-section. The beam problem is still the 120-inch long cantilever with the 1000 lb load applied to its end made out of Lafayette Aluminum.

To start the process, create a Duplicate of the Static Structural block you just completed for Homework Problem 2 (120-inch, Lafayette Aluminum Cantilever Beam Model, Major Axis bending) in the ANSYS workspace.

Now open up the DesignModeler by double clicking on the Geometry menu item of the new Static Structural block. In order to optimize the cross-section shape, ANSYS needs to be told which dimensions of the cross-section should it keep the same and which dimensions it can try to change during the search process for a cross-section that better meets stated design requirements. In this tutorial example, there will only be two cross-section dimensions that will be considered as design variables, which means they can be changed by ANSYS. These two dimensions are the width of the top flange and the width of the bottom flange. The other cross-sectional dimensions will be kept fixed at their original values.

To assign the top and bottom cross-section width dimensions as variables, you need to double click on the + before the Cross Section leaf in the LHS menu in order to expand the list and then click on the I1 leaf. This opens up a lower, LHS menu that provides a Details View showing the cross-section dimension values that you created in the previous tutorial for the I-shape section.

Click on the check box next to the W1 entry line that corresponds to the top flange width dimension value. A D will show up in this box and a popup dialog will appear in the window. Click OK to create a new design parameter tied to the top flange width. Repeat this process by clicking in the check box next to the W2 entry line that corresponds to the bottom flange width dimension value. Note that a D also appears and click OK in the popup dialog to create another new design parameter that will be tied to the bottom flange width.

Save your Project.

Now open the main ANSYS window. You will see that a Parameter Set has been added to the project.

Double-click on the Parameter Set box in this main ANSYS window view. This will open up a new window in which you can confirm that W1 and W2 dimensions on the cross-section are now the Input design variables that will be used in the optimization process. You will now add the Output Parameters to the optimization process. Check that two IDs have been created, P1 and a P2, and that these are related to the Parameter Names I1_Plane.W1 and I1_Plane.W2, respectively.

Close the Parameter Set Tab (X) and then double-click on the Model item in the current Project in the main ANSYS window. This will open up the Mechanical model window. You will use the Mechanical window options to now tell ANSYS what the specific Output Parameters are for the optimization process.

To do this double click on the Geometry leaf in the LHS tree to get to the Line Body leaf. Click on Line Body. This will open the lower, LHS view of the Details of Line Body. Expand the Properties menu item and click on the check box next to Mass. This will place a P in the check box and will assign the mass of the beam element as an Output Design Parameter value that can be changed by ANSYS during optimization. You should see a view similar to the one below at this point.

Now go back to the top LHS tree view. Double click on the Beam Tool Viewer to expand it. Click on Minimum Bending Stress leaf to open the lower, LHS view of the Details of Minimum Bending Stress. Click on the check box before the Results->Minimum entry to have ANSYS place a P in the box.

Then in the top LHS tree view, click on the Maximum Bending Stress leaf to open the lower, LHS view of the Details of Maximum Bending Stress. Click on the check box before the Results->Maximum entry to have ANSYS place a P in the box.

Once you have finished these two steps, Save your Project. Then open the main ANSYS window and double-click on Parameter Set to open it. You will see that three Output parameters (P3, P4, and P5) were created with the steps just completed. One parameter is tied to the Mass, a second is tied to the minimum bending stress and the third is tied to the maximum bending stress.

Click on the Project tab in the Main ANSYS window from the current Parameter Set tab to go back to the main project window.

In the main ANSYS window, expand the LHS menu item Design Exploration if it is not expanded and then double-click on the Direct Optimization option under this heading.

Double-clicking on the Direct Optimization option will add another block to your project. This block should be titled Direct Optimization and should be connected to the Parameter Set with arrows as shown in the view provided.

At this point double-click on the Optimization menu item in this new menu. This will allow you to set up the Optimization details that ANSYS will need to know in order to find a new top and bottom flange width for the I-section that meets specific bending stress limits.

A new window view will have appeared after you double-clicked above. In this new view, click on the Optimization text box item in the top menu. This will open the following lower menu details.

In the lower menu Optimization items, expand the options available next to Method Name and select NLPQL (Nonlinear Programming – Quadratic Lagrangian Method) , which is a gradient based search method. For our problem this method will start with a new top and bottom width and evaluate how close this new cross-section is to meeting the set stress limits, it will then modify the width to a new value and evaluate how close this next cross-section is to meeting the set stress limits, and then modify the width again. The search process will end when it finds a width that meets very closely the set stress limits.

Lower Menu Items

Once you have set the method to NLPQL, go back to the top menu options and click on the item Objectives and Constraints. This action will open a new table in the RHS of the window. As in the view shown below, right now that table is empty in your view.

Edit the Name, Parameter, Objective, and Constraint Table Entries in the empty table to create a table containing the information shown in the screen shot on the next page. This view is a blowup of the table text and value entries. Note that many of the entries were not typed in the text boxes but were selected from the pull down menus available in some of the columns. For example the Parameter is set by using the Select a Parameter pull down menu and selecting the needed parameter for each of the three rows created. The first row defines the search objective for ANSYS. ANSYS will try to minimize the Mass of the beam element during the search process by changing the top and bottom flange widths. The second and third rows define constraints on this minimization search. To meet these constraints ANSYS must find the smallest top and bottom flange width that will cause the bending stress to not be above 5000 psi on the cross-section.

The last thing to set up for ANSYS is to tell it what the range of values to consider when it searches for a new top and bottom flange width. You will tell ANSYS not to consider flange widths less than 1” or greater than 20”. To set these input parameter range limits click back in the top, LHS menu under the Domain heading on the P1 entry. If you do not see this entry then expand the options under the Domain heading. This will open a lower menu that holds the properties for this input parameter.

In the boxes provided in this lower menu, type 1 as the Lower Bound and 20 as the Upper Bound.

These range values will change in both the lower menu and is the RHS table provided in this view as shown in the next view.

Lower Menu Items

Repeat this process by selecting the P2 input design variable in the top menu and entering the same lower and upper bound values (1 and 20) in the lower menu boxes.

Once all of this is complete, click on the Update (lightening bolt) in the upper toolbar in this view. When you click Update you are actually asking ANSYS to perform the optimization process and search for the smallest width of the top and bottom flanges that meets the stated objectives and constraints you provided above.

Note that ANSYS likes to take its time searching. This process may take up to five to ten minutes to complete depending on your machine speed. This gradient search process is pretty slow – I have wrote programs faster than this one for optimization using genetic algorithms. To speed it up some we could add a constraint that P1 = P2 (i.e. that the top flange width should be the same as the bottom flange width). For now we will let it proceed as defined.

You can view the progress being made by the search process by viewing the Table of Schematic values. This tracks the current solutions as there are being found and then improved upon if possible. You should notice that in order to get to the lower stress limit imposed on the cross-section, the width of cross-section is increased during the search process. This means that the mass of the beam element increases as the search proceeds also.

Once the search process is over, click on the menu item Candidate Points in the menu in the top LHS menu to view the search results. This item will open up the RHS table shown in the view below. This table provides information about two candidate solutions: The first is the original starting design point (i.e. width of 4 inches) and second provided the design width found by the search process that meets the stated constraints and objectives. Therefore, the top and bottom flange width that is required to have the maximum and minimum bending stresses in the beam be limited to 5000 psi for both tension and compression is 5.8018 inches.

To select the solution found by ANSYS as the new Design, you will need to right-click somewhere on that specific row entry and select Insert as a Design Point as shown below.

After selecting this as the new Design Point you can change back to the Project Tab in the top toolbar and double click on Parameter Set.

In the RHS Table provided in this view you should see the new Design Point listed having the newly found width for the top and bottom flanges of the cross-section.

Right-click on the DP1 box and select Copy Inputs to Current as shown below. This selection will change your ANSYS model Geometry to be the new top and bottom flange width.

Change back again to the Project Tab and double click on Geometry in your current project. Click OK for any popup windows that appear. In the DesignModeler stay in the Modeling view and click on the CrossSection leaf and then on the I1 leaf to confirm that dimensions of the top and bottom flanges of the I-shaped cross-section have been changed to the optimized value found by ANSYS.

Change back to the main ANSYS window and update the Model by right-clicking on Model and selecting Update. Then double-click on Model to open the Mechanical window. Right click on Solutions and select Solve to get the analysis results for the modified flange cross-section. If necessary use Clear Generated Results and then Solve. Using the result view for the Maximum and Minimum Bending Stress you can check to see that the 5000 psi stress limit as set as an optimization constraint is meet by this new cross-section.

Save your model and enjoy the rest of the day or evening!