Inelastic buckling of skew and rhombic thin thickness-tapered plates with and without intermediate supports using the element-free Galerkin method

In this paper, skew and rhombic isotropic plates subjected to in-plane loadings are analyzed using the element-free Galerkin method. Inelasticity effect is included in the buckling analysis while plates are thin thickness-tapered type. The governing differential equation for a plate in plastic range of response is numerically solved using the Galerkin method. The shape functions are constructed using the moving least squares (MLS) approximation and the essential boundary conditions are introduced into the formulation through the use of the Lagrange multiplier method and the orthogonal transformation techniques. The Stowell theory for the plastic buckling of flat skew plates with variable thicknesses is used. The inelastic analysis is based on the Ramberg–Osgood representation of the stress–strain curve which is used in the deformation theory of plasticity. Using this method the initial inelastic local buckling of skew plates with or without intermediate line supports is studied. Stiffness and geometric matrices are formulated by weak form of the Galerkin method. Finally, the inelastic local buckling loads of these plates are obtained and the results are compared with known solutions in the literature.