Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach

In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain-stress pair. A plane stress behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed EBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhanced rotation-free shell triangle.