A Lagrangian approach for electrostatic analysis of deformable conductors

Deformable conductors are frequently encountered in microelectromechanical systems (MEMS). For example, in electrostatic MEMS, microstructures undergo deformations because of electrostatic forces caused by applied potentials. Computational analysis of electrostatic MEMS requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to compute the deformation of micromechanical structures. Typically, the mechanical analysis is performed by a Lagrangian approach using the undeformed position of the structures. However, the electrostatic analysis is performed by using the deformed position of the conductors. In this paper, we introduce a Lagrangian approach for electrostatic analysis. In this approach, when the conductors undergo deformation or shape changes, the surface charge densities on the deformed conductors can be computed without updating the geometry of the conductors. The Lagrangian approach is a simple, but critical, idea that radically simplifies the analysis of electrostatic MEMS.