An enrichment of Q4γs plate finite element using incomplete quadratic functions, an assumed energy orthogonality of Bergan’s free formulation, and mixed transverse shear strains

Abstract

This paper introduces a new quadrilateral plate element named DSPM4, which improves upon the previous Q4γ_s element. The DSPM4 element has twelve DOFs and four temporary DOFs at the mid-sides of the element. The rotation functions βs are modified by adding an incomplete quadratic function to improve the bending performance. An orthogonality condition between the lower and higher-order bending energy is assumed to satisfy the constant bending patch test. The element development involves kinematic and mixed transverse shear strains. In the local normal-tangential (n-s) coordinate system of each side, the mixed transverse shear strains are obtained by combining the constitutive law for shear forces, equilibrium equations, the constitutive law for bending, and curvatures. The relationship between the temporary DOFs and the final DOFs at the corner nodes is established by equating the constant kinematic and mixed transverse shear strains in the direction cosines of each side of the element. As in the Q4γ_s element, the discrete shear projection method is applied to avoid the shear-locking effect. Numerical analyses are conducted for thin and thick isotropic plates, and the results are compared with those of the DKMQ and MITC4 elements. Numerical results prove that the DSPM4 element is free of shear locking in thin and thick plates, has a proper rank, and provides better convergence behaviour than the Q4γ_s element. Its performance in static and free vibration analyses of isotropic plates is highly comparable to the DKMQ element.