Four‐node mixed Hu–Washizu shell element with drilling rotation

SUMMARY In this paper, enhanced four‐node shell elements with six DOFs/node based on the Hu–Washizu (HW) functional are developed for Green strain. The drilling rotation is included through the drilling rotation constraint equation. The key features of the approach are as follows. The shell HW functional is derived from the shell potential energy functional, which is an alternative to the derivation from the three‐dimensional HW functional. This method is more versatile as it enables the derivation of the so‐called partial HW functionals, with different treatment of the bending/twisting part and the transverse shear part of strain energy. For the membrane part of HW shell elements, a seven‐parameter stress, a nine‐parameter strain and a two‐parameter enhanced assumed displacement gradient enhancement are selected as optimal. The assumed representations of stress and strain are defined in skew coordinates in the natural basis at the element's center. This improves accuracy and has positive theoretical consequences. The drilling rotation constraint equation is treated by the perturbed Lagrange method. The faulty term resulting from the equal‐order approximations of displacements and the drilling rotation is eliminated, and one spurious mode is stabilized using the gamma method. The proposed formulation is insensitive to the element's distortions and yields a large radius of convergence in the examples involving in‐plane bending. The performance of 4 four‐node shell HW elements, having different bending/twisting and transverse shear parts, is analyzed on several numerical examples. Such aspects are considered as: accuracy, radius of convergence, required number of iterations of the Newton method or the arc‐length method and time of computations. The element with 29 parameters (HW29) is selected as the best performer. Copyright © 2011 John Wiley & Sons, Ltd.