Development of a non-linear triangular prism solid-shell element using ANS and EAS techniques

Abstract

This paper extends a previous triangular prism solid element adequate to model shells under large strains to become a solid-shell element, i.e., that discretizations may include just one element across the thickness. A total Lagrangian formulation is used based on a modified right Cauchy-Green deformation tensor (C). Three are the introduced modifications: (a) an assumed mixed strain approach for transverse shear strains, (b) an assumed strain approach for the in-plane components using a four-element patch that includes the adjacent elements, and (c) an enhanced assumed strain approach for the through the thickness normal strain (with just one additional degree of freedom). One integration point is used in the triangle plane and as many as necessary across the thickness. The intention is to use this element for the simulation of shells avoiding transverse shear locking, improving the membrane behavior of the in-plane triangle, alleviate the Poisson effect locking and to handle quasi-incompressible materials or materials with isochoric plastic flow. Several examples are presented that show the transverse shear and Poisson effect locking free behavior, how the improvement in the membrane approach alleviates the volumetric locking and the very good performance of the introduced element for the analysis of shell structures for both geometric and material non-linear behavior.