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.
