Derivation and simulation of thermoelastic Kirchhoff plates
Within the research of the Cluster of Excellence PhoenixD it is of interest to simulate thermoelastic materials on thin optical components which have the structure of Kirchhoff-Plates. This leads to a bothsided nonlinear coupled 2nd order variational system of the heat equation and the elasticity equations. Because of the 2nd order of the system standard FEM cannot be applied directly. However for the biharmonic equation a mixed formulation was developed such that it is reduced to a 1st order variational problem. In this talk we derive a 1st order thermoelastic system on Kirchhoff-Plates by extending the mixed method for the biharmonic equation. This enables the Usage of standard FEM. We finish the talk with an adaptive FEM simulation of the quasistatic problem in deal.ii and an outlook on the dynamic problem.
