A co-rotational quasi-conforming 4-node resultant shell element for large deformation elasto-plastic analysis

Abstract

A co-rotational, quasi-conforming formulation of a 4-node stress resultant shell element is presented for non-linear analysis of plate and shell structures. The tangent stiffness matrix in this quasi-conforming formulation is explicitly integrated. This makes the element computationally efficient in incremental, non-linear analysis. It includes drilling degrees of freedom, which improves membrane behavior and allows the modeling of stiffened plates and shells. It is also free of shear locking behavior. The formulation of the geometrical stiffness is derived using the full definition of Green strain tensor. The inclusion of the bending moment and transverse shear resultant forces in the geometric stiffness allows effective analysis of stability problems of moderately thick plates and shells. The stresses are accurately taken at the nodal points without extrapolation. The plasticity is traced by applying the von Mises yield condition and Prandtl–Reuss flow rule to discrete points through the thickness. The multi-layered approach is based on equally spaced stations, including extreme fibers. A modified trapezoidal rule is used for the numerical integration of the constitutive relation in the plasticity part. Numerous tests are carried out for the non-linear validation of present 4-node shell element and the results are in good agreement with references.