Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics

Abstract

We are presenting a simple low-order solid-shell element formulation––having only displacement degrees of freedom (dofs), i.e., without rotational dofs––that has an optimal number of parameters to pass the patch tests, and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio. With the dynamics referred to a fixed inertial frame, the elements can be used to analyze multilayer shell structures undergoing large overall motion. The formulation of this element is based on the mixed Hu-Washizu variational principle leading to a novel enhancing strain tensor (enhanced assumed strain (EAS) method) that renders the computation particularly efficient, with improved in-plane and out-of-plane bending behavior (Poisson thickness locking), especially in refined analyses of composite structures involving a large number of high aspect-ratio layers. The energy–momentum conserving algorithm in the context of current solid shell element is presented. We discuss the EAS formulation based on the displacement gradient and its complexity compared to formulation on the Green–Lagrange strain. Shear locking and curvature thickness locking are treated using the assumed natural strain (ANS) method. The element has an optimal combination of the ANS method and the minimal number of EAS parameters required to pass the plate bending patch test. Numerical examples involving dynamic analyses (with conservation of energy and momentum) of multilayer shell structures having a large range of element aspect ratios are presented. Several implicit direct integration methods with/without numerical dissipation are used and compared in terms of the accuracy, stability and cost in multilayer shell structure. Finally, we note that the topic in this paper is a fitting dedication to Professor Ekkehard Ramm, who has made important pioneering contributions in this research direction.