Nonlinear Dynamics of Shells: Theory, Finite Element Formulation, and Integration Schemes

Abstract

The paper is concerned with a dynamical formulation of a recently established shell theory capable to catch finite deformations and falls within the class of geometrically exact shell theories. A basic aspect is the design of time integration schemes which preserve specific features of the continuous system such as conservation of momentum, angular momentum, and energy when the applied forces allow to. The integration method differs from the one recently proposed by Simo and Tarnow in being applicable without modifications to shell formulations with linear as well as nonlinear configuration spaces and in being independent of the nonlinearities involved in the strain-displacement relations. A finite element formulation is presented and various examples of nonlinear shell dynamics including large overall and chaotic motions are considered.