Higher-order assumed stress quadrilateral element for the Mindlin plate bending problem

In this paper an 8-node quadrilateral assumed stress hybrid Mindlin plate element with $39{\beta}$ is presented. The formulation is based on complementary energy principle. The proposed element is free of shear locking and is capable of passing all the patch tests, especially the non-zero constant shear enhanced patch test. To accomplish this purpose, special attention is devoted to selecting boundary displacement interpolation and stress approximation in domain. The arbitrary order Timoshenko beam function is successfully used to derive the boundary displacement interpolation. According to the equilibrium equations, an appropriate stress approximation is rationally derived. Particularly, in order to improve element's accuracy, the assumed stress field is derived by employing $39{\beta}$ rather than conventional $21{\beta}$. The resulting element can be adopted to analyze both moderately thick and thin plates, and the convergence for the very thin case can be ensured theoretically. Excellent element performance is demonstrated by a wide of experimental evaluations.