Analysis of electrostatic MEMS using meshless local Petrov–Galerkin (MLPG) method

We analyze electrostatic deformations of rectangular, annular circular, solid circular, and elliptic micro-electromechanical systems (MEMS) by modeling them as elastic membranes. The nonlinear Poisson equation governing their deformations is solved numerically by the meshless local Petrov–Galerkin (MLPG) method. A local symmetric augmented weak formulation of the problem is introduced, and essential boundary conditions are enforced by introducing a set of Lagrange multipliers. The trial functions are constructed by using the moving least-squares approximation, and the test functions are chosen from a space of functions different from the space of trial solutions. The resulting nonlinear system of equations is solved by using the pseudoarclength continuation method. Presently computed values of the pull-in voltage and the maximum pull-in deflection for the rectangular and the circular MEMS are found to agree very well with those available in the literature; results for the elliptic MEMS are new.