A novel meshfree radial point interpolation method with discrete shear gap for nonlinear static analysis of functionally graded plates

In this paper, the discrete shear gap (DSG) is for the first time incorporated into the meshfree radial point interpolation method (RPIM) for nonlinear static analysis of functionally graded plates based on Reissner–Mindlin theory. The technique of DSG, originally developed for finite element analysis during the last decades, is re-formulated to be adopted into a meshfree analysis to treat the well-known shear locking issue and to improve accuracy. As one of the rare meshfree scheme that possesses Kronecker delta property, the RPIM allows direct imposition of boundary conditions. Numerical integration is conducted by the Cartesian transformation method (CTM), which enables the possibility to avoid the creation of background cells during numerical integration, making one step further towards a truly meshfree approach, in the sense that there is no discretization of problem domain into sub-domains either in the form of elements or integration cells. For non-linear analysis, the iterative Newton-Raphson scheme is employed. Via various numerical examples, the accuracy and efficiency of the proposed approach (i.e. RPIM with DSG) is demonstrated and discussed. It is found that the DSG has better performance than other existing techniques used in meshfree RPIM analysis of Reissner–Mindlin plates.