Geometrically non-linear finite element modeling of microelectromechanical structures subjected to electrostatic loading

A general and consistent hybrid non-linear finite element/boundary element method is developed for the purpose of modeling the deformations in an elastic structure under the action of electrostatic forces. Problems of this type occur frequently in the analysis and design of microelectromechanical systems (MEMS) in which electrostatic actuation is used. Numerous MEMS structures, such as spatial light modulators, deformable micromirrors, and microvalves, have been developed in recent years which use an electrostatic actuation scheme. Because of the highly non-linear nature of the electroelastic behavior of these systems, the process of designing such structures requires a general and powerful numerical technique. An incremental non-linear finite element method is formulated which uses a boundary element solution at each load step to update the electrostatic force on the body and the simple example of a deformable diaphragm is investigated