Geometrically nonlinear analysis of functionally graded material plates using an improved moving Kriging meshfree method based on a refined plate theory

This paper presents a novel formulation based on an improved moving Kriging (iMK) meshfree method and a refined plate theory (RPT) for geometrically nonlinear static and dynamic analyses of functionally graded material (FGM) plates. The nonlinearity of plates is formed in the total Lagrangian approach based on the von Karman strain assumptions. The present plate formulation has the following advantages: only four variables for each node, the tangential stress-zero boundary condition at the top and bottom surfaces of plates, and the stringent continuity requirement of the generalized displacements being simply treated without any additional variables. The novelty of the iMK meshfree method is to propose a quartic spline correlation function for establishment of basic shape functions. Thanks to this improvement, the solution of the iMK meshfree method is stable and no longer depends on an uncertain adjustment of correlation parameter θ. In addition, a simple rotation-free technique originated from isogeometric analysis (IGA) is successfully applied to the iMK meshfree method for enforcing the slopes of clamped boundary condition. Several numerical examples are provided to demonstrate high performance of the present method in comparison with other numerical methods.