A Universal and Efficient Quadrilateral Shell Element Based on Absolute Nodal Coordinate Formulation for Thin Shell Structures with Complex Surfaces

This work proposes a new quadrilateral shell element to analyze large deformations or rotations of membrane or shell structures. The element is an improvement of the previously proposed gradient deficient quadrilateral elements. The proposed element adopts three techniques to enhance its universality and efficiency. Firstly, an enriched field is added to make the element immune to in-plane mesh distortions. Secondly, local numerical curvilinear coordinates are used for curved surfaces where global curvilinear coordinates cannot be obtained analytically. Thirdly, the slope vector of the element is obtained by the cross-product of the two gradient vectors on each node, but interpolated inside the element to ensure continuity, especially for complex quadrilateral meshes. Additionally, this processing maintains the linear relationships between the shape functions and nodal coordinates, resulting in constant stiffness matrices. Several numerical examples show that this new element is universal for those irregularly curved surfaces and immune to mesh distortions. In addition, the efficiency is much higher compared to the traditional quadrilateral element.