Solid-to-shell transition elements for the computation of interlaminar stresses

Abstract

This paper presents an accurate and practical technique for coupling shell element models to three-dimensional continuum finite element models. The compatibility between these two types of formulations is enforced by degenerating a continuum element through kinematic constraints compatible with shell deformations. Two formulations of two-dimensional/three-dimensional transition elements are presented. The first and simplest formulation is based on the Mindlin-Reissner plate assumptions, and is found to perform well in a variety of problems involving the analysis of geometrically linear/non-linear laminated structures. The second formulation is based on a higher-order shell theory that allows stretching in the through-the-thickness direction. This additional freedom virtually eliminates the interlaminar normal stress boundary layer that can form in lower-order transition elements. Finally, the coupling of two-dimensional to three-dimensional subdomains is enriched with the use of an interface element, which can be used in conjunction with either transition formulation. The interface element improves the efficiency of the solid-to-shell transition modeling scheme by allowing the independent selection of optimal mesh sizes in the shell and the three-dimensional regions of the model.