Improvement of Pull-in Voltage of Electromechanical Microbeams Using Topology Optimization

The electrostatic actuation devices used in MEMS are generally based on capacitive systems in which one electrode is mobile and the other one is fixed. Applying voltage between the electrodes generates an electrostatic force which tends to reduce the gap between the electrodes. Due to the non-linearity of the electrostatic force in function of the distance between electrodes, there exists a limit voltage from which there is no equilibrium between the electrostatic and mechanical forces leading to the pull-in phenomenon. In some applications, the pull-in instability is undesirable and maximizing pullin voltage is searched. The pull-in behavior involves a strong coupling between mechanical and electrostatic phenomena. Therefore the computation of the pull-in voltage for a given system requires multiphysics finite element simulations [1]. In addition, to compute efficiently the pull-in conditions, the multiphysics finite elements method is combined with a Riks-Crisfield algorithm [2]. The considered design problem consists in maximizing the pull-in voltage of a microbeam. Indeed, microbeam is the simplest example of electrostatically actuated MEMS exhibiting pull-in and consequently it is suited to serve as test to develop topology optimization of similar devices. Topology optimization is formulated as the research of the optimal distribution of a fixed volume of material. To avoid important modification of the electric field by the optimization process, this first study considers a non design electrode and uses topology optimization to design an optimal suspension structure. In this way, the structural optimization domain is separated from the electrical domain. The solution procedure of the optimization problem is based on CONLIN optimizer using a sequential convex linear programming. On each step of the optimization process, the sensitivity analysis is performed with the formulation of eigenvalue topology optimization problem on the basis of the computed pull-in conditions [3]. Two applications of this new method are finally proposed.