A meshless collocation method for the plane problems of functionally graded material beams and plates using the DRK interpolation

A meshless collocation method is developed for the static analysis of plane problems of functionally graded (FG) elastic beams and plates under transverse mechanical loads using the differential reproducing kernel (DRK) interpolation, in which the DRK interpolant is constructed by the randomly distributed nodes. A point collocation method based on this DRK interpolation is developed for the plane stress and strain problems of homogeneous and FG elastic beams and plates. It is shown that the present DRK interpolation-based collocation method is indeed a truly meshless approach with excellent accuracy and has a fast convergence rate.

► A DRK interpolation-based collocation method is developed.
► The shape functions of the DRK interpolant satisfy nodal interpolation properties, and these for derivatives of the DRK interpolant are obtained using a set of differential reproducing conditions without directly differentiating the DRK interpolant.
► The accuracy and convergence rate of this DRK interpolation is validated using two benchmark problems of plane elasticity.
► The through-thickness distributions of normal stress components induced in FG plates, which appear higher-order polynomials, are different from those in homogeneous plates, which appear linear function.