A STABILIZED FOUR-NODE CO-ROTATIONAL QUADRILATERAL SHELL ELEMENT FOR SMOOTH AND NON-SMOOTH SHELL STRUCTURES

Abstract

A four-node co-rotational quadrilateral shell element for smooth and non-smooth shell structures is presented. Each node of the element has three translational degrees of freedom and two or three vectorial rotational degrees of freedom. For the nodes of smooth shells or nodes away from the intersection of non-smooth shells, the two smallest components of the mid-surface normal vector are defined as the nodal rotational variables. For the nodes at intersections of non-smooth shells, two smallest components of one orientation vector, together with one smaller or the smallest component of another nodal orientation vector, are employed as rotational variables. In a nonlinear incremental solution procedure, the vectorial rotational variables are additive and the symmetric tangent stiffness matrices are obtained in both global and local coordinate systems, thus, one-dimensional linear storage scheme can be adopted, saving computer storage and computing time effectively. To alleviate membrane and shear locking phenomena, one-point quadrature is adopted in calculating the element tangent stiffness matrices and the internal force vector, and the physically stabilized method is employed to avoid the occurrence of spurious zero energy modes. The reliability and computational accuracy are verified through two smooth shell problems and two non-smooth shell problems undergoing large displacements and large rotations.