Enhanced meshfree method with new correlation functions for functionally graded plates using a refined inverse sin shear deformation plate theory

This paper presents a new numerical approach based on an effective meshfree method integrated with a refined inverse sin shear deformation plate theory to perform static bending, free vibration and buckling analysis of functionally graded plates. The present formulation is based on a refined inverse sin shear deformation theory (R-ISSDT). Unlike other traditional plate theories, the theory presented gives rise to only four governing equations, does not require shear correction factor, and captures the parabolic variation of the transverse shearing stresses through the thickness of the plate. In the formulation of the meshfree method a new correlation function is proposed which effectively eliminates the correlation parameters. After proposing the formulation of the problem, numerical examples are provided and the obtained results are compared with those found in literature. •An effective meshfree method based on moving Kriging interpolation method is described.•A new correlation function for the interpolation method is proposed.•A new inverse sin distributed function through the plate thickness is proposed.•A refined inverse sin shear deformation plate theory without no correction factor is used.•Static bending, free vibration and buckling of functionally graded plates are analyzed.