An unsymmetric 4-node quadrilateral Reissner–Mindlin plate element using radial–polynomial interpolation for linear and nonlinear analyses

Traditional Reissner–Mindlin plate elements often encounter considerable challenges, particularly their sensitivity to mesh distortion and limited accuracy in stress prediction. This study introduces a novel unsymmetric quadrilateral plate element formulation, extending its application to doubly-curved shells and geometrically nonlinear analysis. The formulation differentiates between test and trial functions to independently construct virtual and real displacement fields, respectively. The virtual displacement field is constructed using standard isoparametric interpolation combined with the mixed interpolation of tensorial components method, effectively suppressing shear locking whilst maintaining inter-element displacement continuity. This construction technique also retains the advantages of isoparametric elements in applying boundary conditions and calculating equivalent nodal external force. Meanwhile, the real displacement field is generated through a radial–polynomial interpolation strategy, using element supports to substantially improve inter-element stress continuity. Numerical examples confirm that the new element successfully eliminates shear locking, exhibits high resistance to mesh distortion, achieves high stress accuracy and ensures excellent inter-element stress continuity.