On the Advantages of Using a Strong Coupling Variational Formulation to Model Electro-Mechanical Problem

This paper presents the advantages of a strong coupled formulation to model the electro-mechanical coupling appearing in MEMS. Usually the classical softwares use a staggered methodology iterating between two different codes to obtain the solution of the coupled problem. In this research a strong coupled formulation is proposed and a tangent stiffness matrix of the whole problem is computed. Using this matrix, nonlinear algorithms such as the Riks-Crisfield algorithm may be applied to solve the static nonlinear problem and determine accurately the static pull-in voltage. Moreover, the natural frequencies may be computed around each equilibrium positions. The dynamic behaviour of the structure may also be studied and two new parameters are defined: the dynamic pull-in voltage and the dynamic pull-in time. This strong coupled methodology deriving from variational principle may also be used for topology optimisation and extended finite elements.