A 6‐Parameter Nonlinear Shell Formulation Without Rotational Parametrization by a Hierarchical Quadrature Element Method

ABSTRACT Thickness stretching is indispensable for shell formulations when local three‐dimensional effects are significant. However, a curvature thickness locking phenomenon occurs, and the multiplicative decomposition scheme or assumed strain method is required for the conventional low‐order finite element method. In this article, a 6‐parameter nonlinear shell formulation with extensible thickness is presented. The director field is interpolated directly so that the need for finite rotation parameterization is avoided. To ensure practical applicability, a new robust scheme for applying bending and twisting moments is developed. Benefiting from the high‐order characteristic of the hierarchical quadrature element method adopted in the present formulation, no locking issues (especially the curvature thickness locking) occur. Both Saint‐Venant Kirchhoff and neo‐Hookean models are incorporated to demonstrate the robustness and generality of the proposed formulation. Numerical examples show that it is a reliable and efficient tool for the nonlinear analysis of shells.