A simplified co-rotational method for quadrilateral shell elements in geometrically nonlinear analysis

This paper presents a simplified co-rotational formulation for quadrilateral shell elements inheriting the merit of element-independence from the traditional co-rotational approach in literature. With the objective of application to nonlinear analysis of civil engineering structures, the authors further simplify the formulation of the geometrical stiffness using the small strain assumption, which is valid in the co-rotational approach, with the warping effects considered as eccentricities. Compared with the traditional element-independent co-rotational method, the projector is neglected both in the tangent stiffness matrix and in the internal force vector for simplicity in formulation. Meanwhile, a quadrilateral flat shell element allowing for drilling rotations is adopted and incorporated into this simplified co-rotational algorithm for geometrically nonlinear analysis involved with large displacements and large rotations. Several benchmark problems are presented to confirm the efficiency and accuracy of the proposed method for practical applications.