Analysis of Nonlinear Electrostatic Membranes

摘要

We give a concise treatment of the interaction of a nonlinear elastic membrane with an electrostatic field. The focus is on the generation of reduced dimension model equations for continuum electrodynamics based on the methodology used by Steigmann (2007) in the purely mechanical context. We formulate the background theory for reduced dimension models pertaining to continuum electrostatics and implement the resulting equations numerically for an example problem of practical interest.