Structural optimization of electrostatic actuators based on the level set method

This paper presents a level set-based structural optimization method for electrostatic actuator problems. Electrostatic actuators are electromechanical systems that are actuated by electrostatic forces. The development of MEMS (Micro Electro Mechanical Systems) device production techniques has spurred widespread deployment of small-sized electrostatic actuators. This paper proposes a level set-based structural optimization method for electrostatic actuators that provides optimal configurations with clear boundaries. The main difficulty when applying a level set-based structural optimization method to electrostatic actuator design problems is the calculation of actuation forces, because these appear on structural boundaries that move during the optimization. Thus, the nodes of the finite element mesh may be displaced from the level set boundaries, causing inaccuracies. To accurately calculate the actuation forces on these surfaces, we develop an adaptive meshing scheme so that the nodes closest to the structural boundaries snap to the boundaries after each update of level set function. In our study, the electrostatic and elastic displacement fields are coupled. The sensitivity is derived using the adjoint variable method, and Maxwell's stress tensor is used to calculate actuation forces. We provide two numerical examples to verify the effectiveness of our proposed method.