A high-performance four-node flat shell element with drilling degrees of freedom

This paper presents a new four-node quadrilateral flat shell element, named QFSUQ, for analysis of shell structures. The element is formed by assemblage of a new membrane element and a plate-bending element. The membrane component is an unsymmetric quadrilateral element with drilling degrees of freedom. The trial functions of the membrane element are determined using the element stress fields formulated based on the analytical solutions of the Airy stress function in global Cartesian coordinate system. The corresponding test functions are obtained through the four-node isoparametric-based displacement fields which are enhanced by drilling rotations. The bending component is based on the Hellinger-Reissner variational principle for analysis of Reissner-Mindlin plates. To validate the performance of the proposed element several numerical benchmark problems are employed and the obtained results are compared with other shell elements. The results prove that the QFSUQ element preserves the advantages of the parent element formulation namely explicit stiffness matrix, free of membrane locking, shear locking and singularity problems and is also appropriate in analysis of shell structures with complex geometry, loading and boundary conditions.