A 4-node assumed strain quasi-conforming shell element with 6 degrees of freedom

Quasi-conforming formulations of 4-node stress-resultant shell elements are presented. The element formulations use interrelated displacement-rotation interpolations. The formulation also includes drilling degrees of freedom, which improves membrane behavior and allows the modeling of stiffened plates and shells. The proposed treatment for bending provides very good results in the 4-node shell element. The stiffness matrices for the present elements are explicitly expressed and the stresses are taken accurately at the nodal points. Compared to elements using Gauss integration, where the stresses are most accurate at the integration points, the extrapolation procedure needed for post-processing is eliminated in the present shell element. A lot of numerical tests were carried out for the validation of the present 4-node shell element and the results are in good agreement with references.