A 9-node co-rotational quadrilateral shell element

Abstract

A new 9-node co-rotational curved quadrilateral shell element formulation is presented in this paper. Different from other existing co-rotational element formulations: (1) Additive rotational nodal variables are utilized in the present formulation, they are two well-chosen components of the mid-surface normal vector at each node, and are additive in an incremental solution procedure; (2) the internal force vector and the element tangent stiffness matrix are respectively the first derivative and the second derivative of the element strain energy with respect to the nodal variables, furthermore, all nodal variables are commutative in calculating the second derivatives, resulting in symmetric element tangent stiffness matrices in the local and global coordinate systems; (3) the element tangent stiffness matrix is updated using the total values of the nodal variables in an incremental solution procedure, making it advantageous for solving dynamic problems. Finally, several examples are solved to verify the reliability and computational efficiency of the proposed element formulation.