Energy and momentum conserving elastodynamics of a non-linear brick-type mixed finite shell element

The paper presents aspects of the nite element formulation of momentum and energy conserving algorithms for the non-linear dynamic analysis of shell-like structures. The key contribution is a detailed analysis of the implementation of a Sim o{Tarnow-type conservation scheme in a recently developed new mixed nite shell element. This continuum-based shell element provides a well-de ned interface to strain-driven constitutive stress updates algorithms. It is based on the classic brick-type trilinear displacement element and is equipped with speci c gradient-type enhanced strain modes and shell-typical assumed strain modi cations. The excellent performance of the proposed dynamic shell formulation with respect to conservation properties and numerical stability behaviour is demonstrated by means of three representative numerical examples of elastodynamics which exhibit complex free motions of exible structures undergoing large strains and large rigid-body motions.