A palette of methods for computing pull-in curves for numerical models of microsystems

Modeling micro-electromechanical systems (MEMs) with Finite Elements is a widely used approach to analyze their behavior, particularly to compute quasi-static instabilities such as pull-in originating from the strong electro-mechanical coupling between conducting and deforming parts. In this paper we discuss several solution techniques to compute the quasi-static response of MEMs. Depending on the type of simulation (staggered or fully coupled), on the solution strategy (monolithic or staggered) and on the load parameter chosen to drive the system (applied potential, charge or displacement), we show that one can build a palette of solvers. Some of the methods outlined here are standard whereas other are novel approaches. We discuss the methods with respect to their ability to compute the pull-in voltage and we illustrate their applicability and efficiency on an electro-mechanically coupled beam, structurally linear and non-linear.