Multiphysics for structural topology optimization

Coupled simulation environment for MEMS devices are already available in a variety of commercial and freeware software packages. However, structural optimization for the multiphysics case has not been fully discussed yet. In most published cases, the optimization algorithm merely follows the traditional single-field problem case, in which design variable and sensitivity are updated sequentially. This paper presents a promising method to implement structural topology optimization via a fully coupled partial differential equation (PDE) expression. The multiphysical structural optimization is integrated via derivation of a suitable Lagrangian-Euler equation. The update of the structural topology is implemented through evolving material boundaries with the level set method. The accuracy of the boundary position is preserved with the h-adaptive mesh refinement method. A benchmark example of structural topology optimization which includes coupled effects is presented in order to demonstrate the feasibility of this method.