A New 4-node Co-rotational Quadrilateral Composite Shell Element

A new 4-node quadrilateral composite shell element using vectorial rotational variables is presented. An advanced co-rotational approach adopts the local coordinate system defined by the two vectors generated by the four corner nodes, rotating together with the rigid body rotation of the element, which can eliminate the influence of rigid body displacement in the calculation of nodal variables, greatly simplifies the calculation of the element formulations in the local coordinate system. Utilizing vectorial rotational variables makes the relationship between the local variables and the global variables much simpler, meanwhile, the increment of vectorial rotation can be directly superimposed. Different from all other existing co-rotational approach, the tangent stiffness matrix of the present element was calculated as the second derivatives of the Hellinger-Reissner mixed functional with respect to local nodal variables, which makes the resulting element tangent stiffness is symmetric. In the analysis of the small strain/large rotation problems in the composite laminated plate and shell structure, the co-rotational element formulations based on the first order shear deformation theory can have very high computational performance.To alleviate the membrane and shear locking phenomena seriously affecting the calculation accuracy and efficiency of the element, the reduced integration method and the assumed strain method are adopted to improve the performance of finite element computation, where assumed strains replace the membrane strains and the shear strain in calculating the element strain energy, In the incremental solution procedure, the generalized displacement control method is employed in tracing nonlinear equilibrium path. Finally, reliability, accuracy and efficiency of the proposed CR shell formulation is verified through solving several benchmark numerical problems.