A comparative study of continuum-mechanics-based and structural-mechanics-based absolute nodal coordinate formulations for quadrature shell elements

In this paper, a structural-mechanics-based shell element is developed by combining the absolute nodal coordinate formulation and the weak-form quadrature element method. Incorporating simplifying assumptions, the elastic strain energy formulation for shells based on three-dimensional continuum mechanics degenerates into the one based on structural mechanics approach. The plane stress assumption and the constant thickness stress assumption are introduced to modify the constitutive relations between in-plane and through-thickness stresses and strains, addressing the Poisson locking issue. A comprehensive comparison between the structural-mechanics-based and the continuum-mechanics-based formulations for quadrature shell elements is made. Examples including static, post-buckling, and dynamic analysis of conventional thin and moderately thick shell structures, as well as nonconventional shell structures, are presented. Elements of either formulation are capable of accurately modeling shear deformable shells undergoing large displacements and rotations. Nevertheless, quadrature elements of each formulation exhibit peculiar strengths and weaknesses in terms of computational efficiency and practical applicability.