I am not sure, what your question exactly is :), but if you are looking for commercial software, which suits your tasks, the most used will be Abacus, Ansys and maybe Comsol. You should be aware that there are two methods for modelling 2D plate, "generalised plain strain" and "generalised plain stress". So you should read about the assumptions made in the two models regarhding to the plate dimensions and take the proper model. Good luck!
I am working on a metallic plate, say Cu, which is clamped at the edges and is subject to temperature increase. Since the edges are constrained we would have a temperature increase; and I am trying to model that stress.
Yes, commercial FEA is a way, but I was looking if there are any analytic solutions to approach this problem.