1. Project 2: Torque-Arm Modeling, Simulation and Optimization
Date: April 3

2. Report Format
Formal report, including title, summary, introduction, approach, results, discussion, appendix (programs), and/or references.
Report must be self-explanatory; define all terms that you use and explain clearly what you did.
Submit report (Word or PDF file, Max 10 pages) and CAE file of optimum design by 12:00 PM in Sakai
Penalty or extra credit
There will be additional extra credit of up to 10% for easy-to-understand (and grade) reports that would be given to at least 20% of the reports.
4/19
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4/27 +6 +5 +4 +3 +2 +1 -5
-10

3. Design of Torque Arm
Used for transmitting load from a shaft to a wheel
Goal: design the lightest structure with stress constraints
Material properties
E = GPa, Poisson’s ratio = 0.29, thickness = 1.0cm, density = 7850 kg/m3
Use cm for the length unit and make other units consistent (need to convert all values in cm units).

4. Preliminary Analysis
At the initial design (x1 = 12, x2 = 1, x3 = 27), estimate the vertical displacement at the center of the right hole and maximum von Mises stress using Mechanics of Materials.
Explain your assumptions and approaches in the report.
Later, compare your hand calculation with FE results and discuss the difference between them
Remember that the purpose of preliminary analysis is to estimate the locations of max stress and displacement as well as their levels.

5. Abaqus Modeling
First task is to sketch the section geometry with fully constrained (curves will change to green color)
This is necessary because you will change design and regenerate models several times
How to apply BCs and loads?
MPC constraint (control point = reference point, slave nodes = nodes on the circumference of the hole, MPC type = Beam).

6. Effect of Element Types
Compare results using different elements (CST, LST, Q4 and Q8).
Turn off “reduced integration” option in Element Type command
Use plane stress element type
Compare the maximum displacement at the load application point and maximum von Mises stress (provide a table)
Try to use approximately the same number of nodes for all element types.

7. Convergence Study
FEA at the initial design (x1 = 12, x2 = 1, x3 = 27) with Q4
Carry out convergence study on the vertical displacement at the center of right shaft
Determine reasonable mesh size (you are limited to 1,000 nodes!). Use this mesh size in the parameter study later.
Use Richardson’s extrapolation to estimate the accurate vertical displacement at the load application point
No. of Elements
Displacement

8. Parameter Study Designer wants
We simplify the design problem by one function with one variable (penalty parameter a = 100)
The relationship between d and design variables is
Change in d  changes in x  changes in FE geometry

9. Parameter Study
Perform a parameter study by changing d between 0 and 1 with 10 increments
Plot a graph d versus f(d) and find an optimum design dopt that minimizes f(d) (graphically or approximated by polynomials)
Report optimum design in terms of mass, stress and (x1, x2, x3)
f(d) d
dopt