Monolithic modelling of electro-mechanical coupling in micro-structures

The purpose of the present work is to model and to simulate the coupling between the electric and mechanical fields. A new finite element approach is proposed to model strong electro-mechanical coupling in micro-structures with capacitive effect. The proposed approach is based on a monolithic formulation: the electric and the mechanical fields are solved simultaneously in the same formulation. This method provides a tangent stiffness matrix for the total coupled problem which allows to determine accurately the pull-in voltage and the natural frequency of electro-mechanical systems such as MEMs. To illustrate the methodology results are shown for the analysis of a micro-bridge.