Author: Sebastien LachanceBarrett, Cornell University
Problem Specification
1. PreAnalysis & StartUp
2. Initial Solution
3. Input & Output Parameters
4. Design of Experiments
5. Response Surface
6. Optimization
7. Verification & Validation
Exercises
Comments
This tutorial was created with an older version of ANSYS (14.5), where the mesh generator and the refinement process was not as strong as it is now. This will result in a different solution than the one shown. (In ANSYS 16.1, the optimization results in a radius of ~1.25in1.27in and in ANSYS 2019 R2 the optimization results in a radius of ~1.111.13in)
Verification & Validation
As with any numerical method verification and validation of great significance. As mentioned earlier, there is no analytical solution for the finite plate with a hole. Thus, the results can not be compared to theory. Thus, in this section other verification and validations will be used. First, the solution will be examined as the mesh is refined to see if it has converged. Additionally, the optimization results will be verified by using different optimization methods and comparing results.
Mesh Refinement
The convergence criteria which was inserted earlier was used to view the effect of mesh refinement with a radius of 1.4853 inches.
Number of Elements  Equivalent Von Mises Stress (PSI)  Percent Change 

244  32,495 

775  32,712  0.6656 
As one can see from the data above, over the course of the mesh refinement, the equivalent Von Mises Stress only changes by less than one percent. Thus, the solution has been verified with respect to mesh refinement. However, notice how the equivalent Von Mises Stress now lies above our constraint. While our optimization looked promising, we had not taken into account the slight change in results from a finer mesh.
Optimization Methods
The optimization was carried using each of the four optimization methods offered in ANSYS workbench. Note that the default optimization method in ANSYS was Screening but now is MOGA.
Optimization Method  Radius (In)  Volume (In^3)  Equivalent Von Mises Stress (PSI) 

Screening  1.3278  9.8615  32,484 
MOGA  1.3267  9.8618  32,500 
NLPQL  1.3291  9.8613  32,503 
As one can see from the table above, there is no significant differences between the results from the four methods.