Implicit/explicit elastodynamics of isotropic and anisotropic plates and shells using a solid-like shell element

This paper presents a full three-dimensional solid-like shell element for dynamic analysis of isotropic, orthotropic and anisotropic laminated composites. The dynamic variational formulation is based on a degenerated-shell concept which uses a compatible displacement field varying quadratically in the through-the-thickness direction in order to overcome Poisson-thickness locking. Mass discretization schemes for implicit and explicit dynamic analysis are presented. A selective mass scaling scheme is proposed for explicit analysis to avoid the use of extremely small time steps needed to resolve high element eigenfrequencies, introduced by the presence of internal degrees of freedom and a small thickness of the element. It is further explained, that a mid-surface and plane-stress constitutive law assumption lead to inaccurate results compared to realistic cases where the Neumann and Dirichlet boundary conditions are applied at the surface of the plates and shells.