Innovative numerical methods for nonlinear MEMS: the Non-Incremental FEM vs. the Discrete Geometric Approach

Electrostatic microactuator is a paradigm of MEMS. Cantilever and double clamped microbeams are often used in microswitches, microresonators and varactors. An efficient numerical prediction of their mechanical behaviour is affected by the nonlinearity of the electromechanical coupling. Sometimes an additional nonlinearity is due to the large displacement or to the axial-flexural coupling exhibited in bending. To overcome the computational limits of the available numerical methods two new formulations are here proposed and compared. Modifying the classical beam element in the Finite Element Method to allow the implementation of a Non incremental sequential approach is firstly proposed. The so-called Discrete Geometric Approach (DGA), already successfully used in the numerical analysis of electromagnetic problems, is then applied. These two methods are here formulated, for the first time, in the case of strongly nonlinear electromechanical coupling. Numerical investigations are performed to find the pull-in of microbeam actuators experimentally tested. The non incremental approach is implemented by discretizing both the structure and the dielectric region by means of the FEM, then by meshing the electric domain by the Boundary Element Method (BEM). A preliminary experimental validation is finally presented in the case of planar microcantilever actuators.