Nonlinear analyses of FGM plates in bending by using a modified radial point interpolation mesh-free method

A modified mesh-free radial point interpolation method (RPIM) which employs a new radial basis function capable of building the shape functions without any supporting fixing parameters is developed for the nonlinear bending analyses of functionally graded material (FGM) plates. The shape functions constructed by the RPIM possess Kronecker delta function property and thus special schemes for imposing boundary conditions are not needed. The nonlinear bending formulations of FGM plates are based on a higher-order shear deformation plate theory considering the von Kármán large deflection assumption. The nonlinear equations are solved by the modified Newton-Raphson iterative technique. The computed results by the modified RPIM are compared with the other numerical solutions reported in the literature to verify the effectiveness and accuracy of the proposed mesh-free method. Detailed parametric studies are then carried out to scrutinize the effects that the volume fraction, plate length-to-thickness ratio, boundary condition and initial deflection have on the nonlinear flexural responses of FGM plates. Results illustrate that the modified mesh-free RPIM can effectively predict the nonlinear bending behavior of FGM plates.