Unconditionally stable and energy conserving discretization of the dynamic von K\'arm\'an equations

Abstract

A fully discrete approximation of the dynamic von K\'arm\'an equations combines nonconforming Morley finite element methods for spatial discretization with an energy conserving modified unconditionally stable Newmark second- order time-stepping scheme. Brouwer's fixed-point theorem establishes existence of a solution to the fully discrete scheme and further uniqueness and stability estimates follow for small loads. Optimal order a priori error estimates in the piecewise energy norm with quadratic convergence in time are derived for the fully discrete scheme. The results of the numerical experiments validate the theoretical error bounds.