Advantages of an Energetic Approach to derive the Electro-Mechanical Coupling

This paper presents the advantages of a strong coupled formulation derived from the energy to
model the electro-mechanical coupling appearing in MEMS. Usually classical softwares use a staggered
methodology iterating between two different codes to obtain the solution of the coupled problem.
Others use some additional links between the two fields to obtain a stronger coupling. In this
research a strong coupled formulation derived from the total energy of the problem is proposed and
has been presented by the author in paper.1 In this approach a new formulation of the electrostatic
force is obtained and an analytical expression of the tangent stiffness matrix of the whole problem
is derived. It has also been shown that this formulation of electrostatic forces provides a better convergence
around corner.2 This paper will highlight the advantage to use this method in static, modal
and dynamic simulation. Indeed using the tangent stiffness 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 easily computed around
each equilibrium positions. The dynamic behaviour of the structure may also be studied and two
characteristic parameters are computed: 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.