Advanced nine-node co-rotational quadrilateral elasto-plastic shell element

A nine-node co-rotational quadrilateral shell element for elasto-plastic shell structures undergoing arbitrarily large rotations was presented. Different from other existing co-rotational shell element formulations, additive vectorial rotational variables were employed in the proposed formulation, thus, updating nodal variables in a nonlinear incremental solution procedure becomes very simple, and symmetric element tangent stiffness matrices were achieved in both local and global coordinate systems, resulting in better computational efficiency. For analyses of elasto-plastic shell problems, the von Mises yield criterion was introduced, and an implicit integration of the flow rules using the backward-Euler return approach was employed, meanwhile, consistent tangent moduli were derived. An assumed strain method was used to overcome locking phenomena, and the computational efficiency and accuracy of the present element were verified through several elasto-plastic shell problems undergoing arbitrarily large rotations.