A hybrid finite element strategy for the simulation of MEMS structures

Abstract

SummaryThis work describes the development of a hybrid finite element strategy for modeling the nonlinear, strongly coupled electromechanical equations governing micro‐electro‐mechanical systems (MEMS) structures in general and the phenomena of static and dynamic pull‐in exhibited by such structures in particular. It is known that conventional finite elements ‘lock’ severely for thin plate or shell‐type structures (which is typical of geometries that occur in microsystems). The developed hybrid finite element formulation is based on a two‐field variational formulation and involves an independent interpolation of the displacement and stress fields. In a conventional structural analysis, it is known that hybrid finite elements are much more immune to volumetric, shear, and membrane locking compared with conventional elements. This work extends the hybrid finite element method to the analysis of MEMS structures. Such an extension is not straightforward due to the strong coupling with the electric field variables. The formulation is based on a total Lagrangian description and is monolithic. This combination of the hybrid strategy and the monolithic scheme results in very good coarse‐mesh accuracy and quadratic convergence both within the context of the static and transient formulations that have been developed. Numerous examples from the literature are considered to demonstrate the high efficacy of the developed method. Copyright © 2015 John Wiley & Sons, Ltd.