Prism solid-shell with heterogonous and hierarchical approximation basis

A solid-shell element which does not possess rotational degrees of freedom (DOFs) and which is applicable to thin plate/shell problems is considered. The element approximation is constructed in prisms, where displacements on the upper and lower surfaces are approximated in the global coordinate system. In addition, two other fields are defined in the shell natural (local) coordinate system that represent the components of the displacement vector in both the current shell normal direction and the current shell tangent plane. To each field, an arbitrary order of approximation can be defined, and all fields reproduce a complete and conforming polynomial approximation basis for the solid prism element. It is not necessary to augment the formulation with an assumed natural strain (ANS) field or enhanced assumed strain (EAS) field or to use reduced integration, making the element ideally suited for geometrically and physically nonlinear problems.