Implementation of the refined zigzag theory in shell elements with large displacements and rotations

Abstract

This work shows a possible implementation of the refined zigzag theory in elements based on Simo’s shell theory. Refined zigzag theory can deal with composite laminate economically, adding only two nodal degrees of freedom, with very good accuracy. Two existing elements are considered, a four-node bi-linear quadrilateral and a six-node linear triangle. This geometry is enhanced with a hierarchical field of in-plane displacement expressed in convective coordinates. The objective is to have simple and efficient elements to analyze composite laminates under large displacements and rotations but small elastic strains. General aspects of the implementation are presented, and in particular the assumed natural strain technique used to prevent transverse shear locking. Several examples are considered to compare on the one hand with analytical static solutions and natural frequencies of plates, and on the other hand to observe the buckling loads and non-linear behavior with large displacement in double curved shells. In these latter cases comparisons are against numerical solutions obtained with solid elements. The results obtained are in a very good agreement with the targets used.