Multi-layer multi-director concepts for D-adaptivity in shell theory

Solid mechanics problems use to be formulated in tensor notation in three-dimensional (3D) Euclidean space. But engineering practice favors reduced dimensional models, in order to describe deformation processes in its most natural way by surface- and line-like geometries, mainly for ease of error controling. Modern surface-like structures, e.g. shells, often show a layered structure or are computed––in case of inelastic materials––by use of virtual layers. The present paper thus is devoted to shells in layered representation. After demonstrating the equivalence of six-parameter, 4-noded shell elements with 3D hexahedron elements as fundamental model constituents, the treatment introduces two different layer-wise refinement concepts, one for modeling of complicated stress profiles, the other one for improvement of model deformability. Such concepts admit the simulation of rather arbitrary shell responses including all kinds of perturbations, like thickness jumps, points of single loads or loci of material damage. In order to validate this model, the paper will systematically transform all sets of basic mechanical conditions of a 3D solid of arbitrary material into corresponding two-dimensional sets of a multi-director shell theory. Aim is the evaluation of bounds for the convergence error.