A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates

•We present an effective meshfree method based on moving Kriging interpolation for analysis of through-thickness FG plates.•We integrate a novel simple TSDT with four variables into our meshfree method, without shear-locking effect.•We analyze static bending, free vibration and buckling of through-thickness FG plates.•We validate the obtained mechanical results with reference existing solutions, showing a very good agreement. In this paper a novel numerical method based on the Moving Kriging (MK) interpolation meshfree method, integrated with a simple higher-order shear deformation plate theory for analysis of static bending, free vibration and buckling of functionally graded (FG) plates is presented. In the proposed technique, the shape functions are built by the Kriging technique which possesses the property of Kronecker delta function which makes it easy to enforce essential boundary conditions. The present formulation is based on a refined simple third-order shear deformation theory (R-STSDT), which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the plate present in the original simple third-order shear deformation theory (STSDT). In this theory, instead of assuming a specific distribution for the displacement field, the theory of elasticity is used for obtaining the kinematics of the plate deformation. We first propose the formulation, and then several numerical examples are provided to show the merits of the proposed approach.