Recent Improvements in Hu-Washizu Shell Elements with Drilling Rotation

Abstract

Enhanced four-node shell elements based on the Hu-Washizu (HW) functional are developed for the Green strain and constitutive laws modified by the zero-normal-stress condition. They have six dofs/node, i.e. the drilling rotation is included. The key features of the approach are as follows: 1. For the membrane part of HW shell elements, we use the 7-parameters stress, 9-parameter strain and 2-parameter EADG enhancement, which are selected as optimal for the 2D elements with drilling rotations. This ensures excellent accuracy and robustness to shape distortions for coarse meshes and very good performance for finite deformations. 2. The assumed representations of stress and strain are defined in skew coordinates, which not only improves accuracy, but also implies, as checked for 2D elements, that the homogenous equilibrium equations and the compatibility condition are satisfied point-wise for an arbitrary shape of an element. The skew coordinates are also easy to implement. 3. The bending/twisting and transverse shear parts are treated either by the HW functional or by the potential energy functional, in order to select the formulation which performs best for a reduced number of parameters. The performance of the shell HW elements is illustrated on several numerical examples and compared to the EADG elements in such aspects as: accuracy, radius of convergence, required number of iterations of the Newton method, and time of computation.