Topology optimization of electrostatically actuated microsystems

This study addresses the design of electrostatically actuated microelectromechanical systems by topology optimization. The layout of the structure and the electrode are simultaneously optimized. A novel, continuous, material-based description of the interface between the structural and electrostatic domains is presented that allows the optimization of the interface topology. The resulting topology optimization problem is solved by a gradient-based algorithm. The electromechanical system response is determined by a coupled high-fidelity finite element model and a staggered solution procedure. An adjoint formulation of the coupled electromechanical design sensitivity analysis is introduced, and the global sensitivity equations are solved by a staggered method. The proposed topology optimization method is applied to the design of mechanisms. The optimization results show the significant advantages of varying the interface topology and the layout of the electrode versus conventional approaches optimizing the structural layout only.