Topology optimization of microstructures with perturbation analysis and penalty methods

Topology optimization at the continuum nano/microscale is of wide interest in designing and developing more efficient micro/nano electromechanical systems. This paper presents a new methodology for topology optimization of microstructures that is based on perturbation analysis and the penalty methods. The homogenized material coefficients are numerically computed based on perturbation analysis, and periodic boundary conditions are imposed by the penalty methods. The sensitivity analysis is implemented directly without the adjoint method. The extension of the proposed method to the design of components for multi-field analysis is straightforward. The capability and performance of the presented methodology are demonstrated through several numerical examples.