Buckling and free vibration of plates with different shapes subjected to in-plane loadings are analyzed using the element-free Galerkin method. The dissertation includes four main parts. Inelastic buckling of skew and rhombic thin thickness-tapered plates with and without intermediate supports, free vibration of moving laminated composite plates with and without skew roller, thermal buckling of functionally graded skew and trapezoidal plates with different boundary conditions and local buckling of moderately thick stepped skew viscoelastic composite plates are studied, respectively. The governing differential equations for a plate are 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 method is programmed, and several numerical examples are presented to demonstrate the scope and efficacy of the procedure Keywords: Inelastic buckling, Moving plate, Thermal buckling, Functionally graded plate, Viscoelastic composite plate, Element-free Galerkin method, skew plate.
