Buckling analysis of isotropic skew plates under general in-plane loads by the modified differential quadrature method

Abstract

• Buckling analysis of thin skew plates using modified DQM is presented. • A complete set of differential equations in oblique coordinate system is established. • Accurate buckling loads are presented and verified by the FEM data. • Effects of boundary conditions, loadings, skew angles and aspect ratios are discussed. Perhaps due to the bending moment singularity at the obtuse plate corners, the existing buckling loads vary appreciably even for simply supported rhombic plate under uniaxial loading. In this paper, the buckling analysis of skew plates under various loadings is presented using the modified differential quadrature method (DQM). A complete set of equations of equilibrium, bending and twisting moments, equivalent shear forces and corner force in oblique coordinate system is given. Eight combinations of simply supported, clamped and free boundary conditions, four skew angles, and five aspect ratios are considered. Convergence studies are made for rhombic plates with the largest skew angle subjected to uniaxial and equal biaxial compressive loads. The solution accuracy is further verified by comparing the results with data obtained by the finite element method using very fine meshes. New data are tabulated and plotted for skew plates with different edge conditions, aspect ratios and skew angles, subjected to uniaxial, biaxial, as well as combined shear with uniaxial loads. Most of the data, not available thus far, may be useful for other researches in testing the validity of their numerical techniques for thin plate analysis.