Mesh-free radial basis function method for static, free vibration and buckling analysis of shear deformable composite laminates

A mesh-free radial basis function method is presented to analyze the static deflection, free vibration and buckling analysis of laminated composite plates using third-order shear deformation plate theory. The problem domain represented by a set of scattered nodes in its support domain based on the radial basis functions with polynomial reproduction. Based on the third-order shear deformation plate theory, variation forms of the static, free vibration and buckling system equations are formulated in terms of displacements and are discretized. The shape function thus constructed possesses a delta function property, and hence the essential boundary conditions can be implemented with ease as in the conventional finite element method. Several numerical examples are presented to demonstrate the convergence, accuracy and validity of the proposed method. Comparison of results with the exact solution as well as finite element method in the literature suggests that the mesh free radial basis function method yields an effective solution method for laminated composite plates. The effects of the modulus ratio, side-to-thickness ratio, shear correction factor and boundary conditions are discussed.