An Advanced Co-rotational Curved Quadrilateral Shell Element Based On Assumed Strains

An advanced co-rotational curved quadrilateral shell element based on assumed strains is proposed to solve large-displacement and large-rotation problems. With this co-rotational framework, the effect of rigid-body motion on the nodal variables computing can be excluded in advance, which makes a great simplification in establishing the element tangent stiffness matrix. Furthermore, by utilizing vectorial rotational variables which are additive in an incremental solution procedure, the relationship between the local variables and the global variables becomes much simpler. Meanwhile, the internal force vector and the element tangent stiffness matrix could be obtained from calculating directly the first derivative and second derivative of the element strain energy with respect to the nodal variables, respectively. Different from most other existing co-rotational element formulations, all nodal variables in the present curved quadrilateral shell formulation are commutative in calculating the second derivative of the strain energy. As a result, the element tangent stiffness matrix is symmetric and is updated by using the total values of the nodal variables in an incremental solution procedure. Such update procedure is advantageous in solving dynamic problems.To alleviate the membrane and shear locking phenomena, the membrane strains and the out-of-plane shear strains are replaced with assumed strains in calculating the element strain energy. The strategies used in the mixed interpolation of tensorial components approach and enhanced interpolation of membrane and shear strain method are employed in defining the assumed strains in the natural coordinates. Finally, several elastic plate and shell problems are solved to demonstrate the reliability, efficiency, and convergence of the present formulation.