An improved four-node hybrid-mixed element based upon Mindlinʹs plate theory

Based on the mixed shear projected (MiSP) approach (Reference [54]: Int. J. Numer. Meth. Engng 1998; 42:1149–1179), an enhanced bending approximation for homogeneous isotropic plates is presented. Some hard benchmark tests, such as the skew plate (30◦) problem, have often shown poor convergence when low-order elements (3- or 4-node element) are developed using linear approximations for kinematic variables. To put right this weakness, we propose a high-order interpolation for rotational dofs which results in more rich bending curvatures. The mid-side rotational nodes are eliminated using a combination of local discrete kinematic and constitutive Mindlin hypotheses. The derived 4-node quadrilateral element, called MiSP4+, is free of shear locking and passes all patch tests for thick and thin plates in an arbitrary mesh