Solid shell prism elements based on hierarchical, heterogeneous, and anisotropic shape functions

The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As with other solid shell formulations, only displacement degrees of freedom are required to describe the shell kinematics and general three-dimensional material laws can be adopted. However, the novelty of this formulation is the ability to capture complex shell behaviour and avoid locking phenomena, without the need to use reduced integration or adopt additional natural strain or enhanced strain fields. Thus, this element is ideally suited for geometrically and physically nonlinear problems. This is achieved by constructing independent approximation shape functions on both the prism element's triangular faces and through the thickness, where the latter is associated with a local coordinate system that convects with deformation of the shell. The element is extremely efficient, with the hierarchical property lending itself to an efficient and highly scalable multigrid solver, and the heterogeneity property enables local p-adaptivity. The paper demonstrates performance of the element for a number of linear and geometrically nonlinear problems, benchmarked against well established problems in the literature. The formulation has been implemented in the MoFEM.