A mesh-free method for static and free vibration analysis of shear deformable laminated composite plates

A mesh-free method is presented to analyze the static deflection and natural frequencies of thin and thick laminated composite plates using high order shear deformation theory. In the present method, the problem domain is represented by a set of properly scattered nodes and no element conformability is required. Moving least-squares method is applied to construct the shape functions. Variational principle is used to derive the discrete system equations based on the third order shear deformation theory (TSDT) of Reddy. Essential boundary conditions are efficiently implemented by a penalty technique for both the static deflection and natural frequency analysis. Several examples are solved to demonstrate the convergence, accuracy and validity of the proposed method. The present solutions are verified with those available values by analytical as well as finite element method. The results from classical plate theory and first order shear deformation theory are also computed and compared with those of TSDT. The effects of the material coefficients, side-to-thickness ratio, nodal distribution and shear correction factor are discussed.