ES 230 Strengths – Intro to Finite Element Modeling & Analysis Homework Assignment 7 Stress Concentrations and Design Modifications – Designing Around Stress Concentrations

Start by creating a Duplicate of your Seat Belt Tab model from this last Tutorial 7 in the ANSYS Project environment. Make sure to check that the material is ‘Elastic-Plastic Lafayette Steel’ and that the Units are set to US Customary.

Look at the current Equivalent Stress results you obtained at the end of Tutorial 7. Note that the blue areas of the view indicate locations of the seat belt tab that are not under very much stress from the loads applied. Also, note that the stress concentrations around each opening, which are a function of the fillet radius of each of these, plays a large role in the higher stress levels acting in these regions. At this time, write down the Maximum Equivalent Stress in the Seat Belt Tab having the original geometry for use in future comparisons.

Also write down the current total volume of material used in the seat belt tab. You can view the Volume under the Properties of the Solid Part in the current Mechanical window. Expand the Geometry leaf to see the Solid Part. Click on the Solid leaf and then expand the Properties information block in the lower LHS menu showing the Details of ‘Solid’. The Volume is listed as shown in the view below.

Imposing Design Change 1 to the Seat Belt Tab Model – Overall Shape In design you will be able to tailor the shape of the seat belt tab through a process called shape optimization. This can be automated using optimization programs in ANSYS, but in this homework we will try out some of this process in a couple of trial stages. All of the changes will be modifications to the Geometry. Therefore, you will need to create a Duplicate system in the ANSYS Project Space for each Trial Design. By having separate systems you will be able to more easily compare the stresses obtained in each Trial Design. So to start this process, make a copy of your current Seat Belt Tab model.

Open up the Geometry in the DesignModeler for this new project. As the first step, right click on the current Extrude leaf in the LHS menu and select Delete. This will allow you to modify the Sketch of the cross-section of the tab and then generate a new extruded part from the Sketch.

Now click on the Sketching tab to get to the Draw, Dimension, Modify options. Draw two new side lines on the XZ sketch as shown below. Just connect the existing points on the current sketch. Use Auto Constraints to help with selecting the specific points.

Now delete the other side lines that are not needed in the model anymore to get the cross-section shown below. Use the Modify Cut tool available to delete these extra lines.

In this process you lost the main total side length dimension. So you will need to add this back to this new cross-section. Use the Vertical Dimension tool to add the side dimension of 4 inches back to the Sketch of the cross-section as shown in the next view.

Now as the additional part modification, change the distances of each of the holes from the edges to 0.5 inches instead of the original 0.75 inches for the seat belt tab. This change will position the holes closer to the sides of the tab as shown below.

You will need to Extrude this Sketch by 0.25 inches and then select Generate to develop the new Seat Belt Tab part as shown in the next view.

Save the project geometry and then Update the model in the Main ANSYS Project window.

Once the update is complete, open the Model Mechanical window. Depending the changes you make to the Geometry, you may need to Update the Model in the main ANSYS Project tab as well as Generate a New Mesh for the part, Re-Apply the specific surfaces to apply the forces to, and rerun Solve to get new results. You can track the unhappy (non-green check mark) tags in the different items in the LHS menu. From the Results you get for this first Geometry modification, record the new Total Volume and Maximum Equivalent Stress obtained. Imposing Design Change 2 to the Seat Belt Tab Model - Geometry of Opening The goal of the geometry design change this time is to reduce the maximum equivalent stress by changing the geometry of one of the holes. To do this you redraw the larger hole in the tab and re-dimension the width and length and also the fillet radii. To start create a Duplicate of the current Angled Seat Belt Tab Model in the ANSYS Project window and then open the Geometry of this new project in the DesignModeler. Delete the Extruded part and change to the Sketch view in the sketching tab. Delete all of the lines, points and dimensions associated with the larger hole as shown below.

Draw in a new rectangle that is dimensioned to a 1.6” width and 0.9” height that is centered on the axis and also has 0.4” fillets at all four corners. This hole should be dimensioned at a location 0.5” from the far edge as before. Your new part should look like the one below.

Extrude this Sketch by 0.25 inches and then select Generate to develop the new Seat Belt Tab part as shown in the next view.

Save the project geometry and then Update the model in the Main ANSYS Project window.

Once the update is complete, open the Model Mechanical window. Depending the changes you make to the Geometry, you may need to Update the Model in the main ANSYS Project tab as well as Generate a New Mesh for the part, Re-Apply the specific surfaces to apply the forces to, and rerun Solve to get new results. You can track the unhappy (non-green check mark) tags in the different items in the LHS menu. From the Results, write down the new Total Volume and the new Maximum Equivalent Stress obtained for this specific modification.

Note that the maximum equivalent stress in the part is now located at the other hole opening in the Seat Belt Tab, but the overall maximum equivalent stress has been reduced to around 21,000 psi, which is a reduction.

BONUS Work The BONUS for this homework is to find a geometry of the Seat Belt tab that has the same outside shape and dimensions as above but that minimizes the value of the maximum equivalent stress anywhere in the plate while providing holes that are at a minimum 1.5” x 0.5” for the larger hole and 1” x 0.5” for the smaller hole. These minimum dimensions provided follow the current rectangle layout of each hole for the proportions.

The BONUS points received will depend on the % reduction in the Maximum Equivalent Stress obtained. The greater the reduction achieved, the greater the points obtained to a maximum of 20 points.

Homework 7 Assignment Part to Turn In – A) and BONUS: Due no later than Monday, December 14th Turn in the following items in hard copy form (print out) for grading. You will compare the maximum equivalent stress values for all three models, but you only need ANSYS screen captures for the 2nd Change imposed on changing the geometry of the opening.

A) Screen Captured ANSYS analysis results to turn in for the ‘Opening Geometry’ Seat Belt Tab Model:

Screen-capture and print-out a view showing results for the Directional Deformation in the x-axis direction on the seat belt tab for this 2nd Design change model. Use the Max and Min specific Probes to identify where the maximum and minimum x-axis deformations act. Circle the units on the printed copy.

Screen-capture and print-out a view showing results for the Equivalent Stress on the seat belt tab for this 2nd Design change model. Use the Max and Min specific Probes to identify where the maximum and minimum equivalent stresses act. Circle the units on the printed copy.

Compare the values of the maximum equivalent stresses obtained from the Original Tutorial ‘Boxy’ Seat Belt Tab, the Simplified ‘Angled’ Seat Belt Tab, and the ‘Opening Geometry’ Seat Belt Tab (the three models run in the tutorial and this homework assignment). State the percent change in the maximum equivalent stress and the total volume for the ‘Angled’ and ‘Opening’ models with respect to the values obtained for the Original Tutorial ‘Boxy’ Seat Belt Tab.

BONUS - Screen Captured ANSYS analysis results to turn in for BONUS modified geometry: Screen-capture and print-out a view showing results for the Equivalent Stress on your ‘Bonus’ Seat Belt

Tab Design. Use the Max and Min specific Probes to identify where the maximum and minimum equivalent stresses act. Circle the units on the printed copy.

Compare the value of the maximum Equivalent Stress for your ‘Bonus’ Seat Belt Tab Design versus the ‘Opening’ Seat Belt Tab and report the percent change in the maximum equivalent stress that you obtained.