joint work with Bin Niu
We apply a multi-scale topology optimization method to design an infill structure, which has a solid outer shell, or coating, and a periodic infill pattern. Harmonic-mean based non-linear filters realize length scale control on both the overall macrostructure and the infill design on the microscale. The design optimization of the infill lattice is performed simultaneously with the optimization of the macroscale structure, which also includes the coating.
joint work with Michael Ulbrich
We consider shape optimization for unsteady fluid-structure interaction problems that couple the Navier-Stokes equations with non-linear elasticity equations. We focus on the monolithic approach in the ALE framework. Shape optimization by the method of mappings approach yields an optimal control setting and therefore can be used to drive an optimization algorithm with adjoint based gradient computation. The continuous formulation of the problem and the numerical realization are discussed. Numerical results for our implementation, which builds on FEniCS, dolfin-adjoint and IPOPT are presented.
joint work with Peter Gangl
We present shape and topological sensitivities for a 3D nonlinear magnetostatic model of an electric motor. In order to derive the sensitivities, we use a Lagrangian approach, which allows us to simplify the derivation under realistic physical assumptions. The topological derivative for this quasilinear problem involves the solution of two transmission problems on the unbounded domain for each point of evaluation.