Two 8-node quadrilateral unsymmetric elements with different incompatible modes immune to severe distortion

Most unsymmetric quadrilateral elements have demonstrated a high tolerance to mesh distortion in pure bending problems involving coarse meshes. However, they have difficulty achieving acceptable results in shearing-dominated problems, and the element's performance is affected by the degree of mesh distortion. In this paper, two 8-node quadrilateral elements are developed by introducing two different incompatible modes into the unsymmetric formulation. The unsymmetric framework with two different sets of interpolation functions for displacement fields provides the basis for the immunity property. The incompatible displacement mode and the enhanced assumed strain guarantee the completeness of the displacement field interpolation polynomials, and the satisfaction of L2$$ {L}_2 $$-orthogonality condition ensures the accuracy of the simulations. The resulting elements, respectively, denoted as UQ10 and UQ10/E4, can provide exact solutions for both pure and linear bending problems and exhibit excellent insensitivity in shear-dominated tests. Furthermore, they are invariant, rapidly converging, and free of various locking problems.