LAUSR

This study introduces an accurate and effective mesh-free approximation based on the radial point interpolation method (RPIM) to predict the post-buckling responses of FGM plates in mechanical edge compression. In the RPIM, a new radial basis function is presented in a compactly supported form to build the shape functions without any fitting parameters. The equilibrium and governing equations for the plate are derived by using the higher-order shear deformation theory in which a new hybrid type transverse shear function is incorporated in order to better represent the displacement fields. A von Kármán type nonlinear equation which accounts for both the geometric nonlinearity and the initial geometric imperfection is constructed. A solution procedure based on the total Lagrangian formulation to trace the post-buckling path, which utilizes the modified Newton–Raphson method, is designed. The numerical results illustrate the accuracy of the proposed meshless method for predicting the post-buckling behavior of FGM plates.