# Simultaneous Material and Topology Optimization

Jannis Greifenstein*, Michael Stingl and Fabian Wein

A general setting for simultaneous material and topology optimization in linear elasticity with different regularization methods is presented. The admissible material tensors are represented using a parametrization of the tensor and, if needed, feasibility constraints. The topology optimization is done multiplying the material tensor with a topological design variable. The presented setting provides for an independent use of well known regularization techniques (density filters, slope constraints) for each design parameter. Existence of solutions and convergence of an associated finite element scheme can be proven. $\\$ As an example for a parametrization, a simple class of microstructures is homogenized for a grid of sizing parameters and interpolated. Finally, numerical results are shown for the microstructures and a parametrizaton of orthotropic material.

Mathematics Subject Classification: 49J20

Keywords: material optimization; topology optimization; regularization method; finite element approximation; existence of solutions

Minisymposion: Material and Topology Optimization: Theory, Methods and Applications