Nonlinear numerical dissipative elastodynamics of an optimal solid shell element

Publisher Summary This chapter presents a simple low-order solid shell element formulation — having only displacement degrees of freedom (dofs) — that has an optimal number of parameters to pass the plate patch tests (both membrane and out-of-plane bending) and therefore allows efficient and accurate analysis of large deformable multilayer shell structures. The formulation is based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle leading to a novel enhancing strain tensor that renders the computation particularly efficient, with improved in-plane and out-of-plane bending behavior. Shear locking and curvature thickness locking are treated using the Assumed Natural Strain (ANS) method. With the dynamics referred to a fixed inertial frame, the elements can be used to analyze multilayer shell structures undergoing large overall motion. The energy-momentum (EM) conserving algorithm in the context of the current solid shell element is presented. Several implicit integration methods with/without numerical dissipation are compared in terms of accuracy, stability and cost in multilayer shell structures.