Shape optimization for thermoelasticity with temperature-dependent material parameters

We consider the numerical solution of shape optimization problems for thermoelasticity with temperature-dependent material parameters.

We show the existence of the shape derivative and derive an expression for generic functionals of domain integral type.

Numerical results are presented for two settings: minimization of the compliance under a volume constraint, and minimization of the volume under a constraint on the $L^2$-norm of the von Mises stress.

We use the finite element method for solving the underlying boundary value problems and the level set method for the representation of the actual domain.