6. Oktober 2022
Abstract:
A new method for performing density based topology optimization is presented. We discuss the approach in the setting of Stokes flow. It is based on classical topology optimization and phase field approaches, and introduces a different way to relax the underlying infinite-dimensional mixed integer problem. We give a theoretically founded choice of the relaxed problems. The density is modeled on a space that allows for jumps along hypersurfaces, such as BV or fractional order Sobolev spaces. We present existence theory for the generalized Stokes equations and discuss the arising optimization problems concerning existence, differentiability and convergence towards solutions of the unrelaxed problem. This motivates the choice of other degrees of freedom in the model. Building on the theoretical findings, we present some numerical results. Moreover, in order to show the potential of the new approach, we do a comparison to a classical approach.