Weak form quadrature shell elements based on absolute nodal coordinate formulation

Abstract Weak form quadrature elements for moderately thick shells with arbitrary initial configurations are developed under the framework of continuum mechanics and the absolute nodal coordinate formulation (ANCF). Nodal variables of the element consist of the position vector, the transverse gradient vector and the transverse derivatives thereof at the shell mid-surface. In-plane gradient vectors which are not taken as nodal variables are obtained with the aid of the differential quadrature analog. Using the transverse gradient vector and one in-plane gradient vector, joint constraint equations for shells with discontinuous slopes are established. Simplified equations of motion with constant mass matrix result. The elements are applicable to analysis of shell structures undergoing large displacements and rotations. Five examples encompassing static and dynamic shell analysis, post-buckling analysis of shells, as well as analysis of shells with discontinuous mid-surface slopes are examined to assess the performance of the proposed elements. Satisfactory results are obtained, validating the efficacy of the proposed elements.