SIMP-ALL: A generalized SIMP method based on the topological derivative concept

Abstract

Topology optimization has emerged in the last years as a promising research field with a wide range of applications. One of the most successful approaches, the SIMP method, is based on regularizing the problem and proposing a penalization interpolation function. In this work, we propose an alternative interpolation function, the SIMP-ALL method that is based on the topological derivative concept. First, we show the strong relation in plane linear elasticity between the Hashin-Shtrikman (H-S) bounds and the topological derivative, providing a new interpretation of the last one. Then, we show that the SIMP-ALL interpolation remains always in between the H-S bounds regardless the materials to be interpolated. This result allows us to interpret intermediate values as real microstructures. Finally, we verify numerically this result and we show the convenience of the proposed SIMP-ALL interpolation for obtaining auto-penalized optimal design in a wider range of cases. A MATLAB code of the SIMP-ALL interpolation function is also provided.