Almost Isotropic Perimeters in Topology Optimization: Theoretical and Numerical Aspects

We consider topology optimization of elastic continuum structures including a bound on the perimeter of the structural domain. Such a bound is known to ensure existence of solutions and it stabilizes the behavior of numerical finite element (FE) solutions. However the straightforward way of calculating the perimeter is rotationally mesh-dependent. In this paper we present new perimeter formulae with weaker rotational dependence i.e. perimeters that are almost isotropic. An overview of some theoretical results as well as numerical tests are given