Topology optimization combined with element‐by‐element solution techniques

Abstract

Topology optimization approaches are commonly used for design problems involving physical phenomena related to solid mechanics, acoustics, electromagnetism, fluid mechanics, and combinations thereof. In computational models of these physical phenomena, the field variables are commonly approximated using spatial discretizations within the domain using the Finite Element Method. Even for topology design problems in which the field variables must only satisfy linear state equations, the storage and solution of the resulting global system of equations can become a computational bottleneck. In this contribution, we investigate a topology optimization approach in which the Solid Isotropic Material with Penalization (SIMP) method is combined with element-wise solution approaches, in order to reduce computational memory requirements.