We analyze the nonlinear elliptic problem ∆u = λf(x) (1+u)2 on a bounded domain Ω of R with Dirichlet boundary conditions. This equation models a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at −1. When a voltage –represented here by λ– is applied, the membrane d...

A distributed modeling approach has been developed to describe the dynamic behavior of ring resonators. The model includes the effect of large amplitudes around primary resonance frequencies, material and electrostatic nonlinearities. Through a combination of geometric and material nonlinearities, closed-form expression for third-order nonlinearity in mechanical stiffness of bulk-mode ring reso...

plastic instability which results in the localization and failure of sheet metals has been studied in equibiaxial stretching of commercial purity aluminium sheet. attention was focussed on two main industrial conditions of the material. these were representative of the materials that could be processed by the commercial batchannealing process (slow heating, long time) or by a continuous anneali...

This paper is a continuation of [9], where we analyzed steady-states of the nonlinear parabolic problem ut = ∆u− λf(x) (1+u)2 on a bounded domain Ω of R with Dirichlet boundary conditions. This equation models a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at −1....

In this paper we develop a numerical procedure using finite element and augmented Lagrangian meth-ods that simulates electro-mechanical pull-in states of both cantilever and fixed beams in microelectromechanical systems (MEMS) switches. We devise the augmented Lagrangian methods for the well-known Euler-Bernoulli beam equation which also takes into consideration of the fringing effect of electr...