I'd rather to go with open source solvers.

What is the meaning of open source solvers? I did not understand . I use Arena simulation program not excel or other solvers.

https://en.wikipedia.org/wiki/List_of_optimization_software#Free_and_open-source_software

I do not get the aim of the optimization by changing stiffness. If you're looking for the best material for a construction there will probably be only a discrete set of possible ones, so a normal continuous optimization would not work.

With regard to the minimization of compliance (if it concerns a solid body) I'd expect the aim would be shape optimization, look e.g. at papers here

https://ins.uni-bonn.de/staff/rumpf

The approach is different from changing matrial characteristics (in practice it would be rather hard to produce the optimal material for a construction).

With that aim of finding the optimal shape of a part you'd need to work with a shape derivative.

Hi Farzad Torabi

I think you need at first an idea of your optimization problem. What do you want to optimize (only mass or more e.g. multiple objectives?), what are your variables and how many (thickness, topology, ..., continuous or discrete) and what are the constraints (number and linear or nonlinear) you want to consider.

Than roughly select an optimization method (gradient based, evolutionary,...). Than find a optimization toolbox providing a method you want (nlopt, Pyopt, pyoptsparse, scipy, midaco ...).In general you have to provide a function returning your objective and the constraints (e.g. max stresses, ...) based on a given variable vector. Sometimes objective and constraints are divided in two functions, depending on the toolbox.

Now, in the function providing the objective and constraints you have to set up the FE run with the new variables (e.g. change the input file) and then solve the system running FEM. After finished FEM, you have to read the results back into Python (e.g. reading an ASCII-File) and provide the desired data as return values of your function.Starting FEM from Python is possible via "subprocess" module which is a build in module. Via e.g. subprocess.run(["path/to/executable", "input_file.xyz"]) you run your executable with a given input_file depending on your FEM solver.

I hope this answers your question. More details depending on your concrete optimization problem.

Kind regards

Sascha

I assume you need to code an interfacing with Ansys, see e.g. in MatLab one example described at https://www.researchgate.net/post/How_can_we_couple_ANSYS_with_MATLAB_to_perform_optimization_processes

There are available in the net a few more actual ways/codes, so look for: Python interface Ansys, and after give here some feedback on your achievements.

I'd suggest you to perform any optimization algorithm in Matlab and then 'couple' it in ansys by using 'dos' command.