A naturally stabilized nodal integration meshfree formulation for carbon nanotube-reinforced composite plate analysis

Naturally stabilized nodal integration (NSNI) meshfree formulations associated with the higher-order shear deformation plate theory (HSDT) are proposed to analyze bending and free vibration behaviors of carbon nanotube-reinforced composite (CNTRC) plates. An extended rule of mixture is used to compute the effective material properties of CNTRC plates. The uniform and functionally graded distributions of carbon nanotube (CNTs) via the plate thickness are studied. In the present approach, gradient strains are directly computed at nodes similar to the direct nodal integration (DNI). Outstanding features of the current approach are to alleviate instability solutions in the DNI and to significantly decrease computational cost as compared to the traditional high-order Gauss quadrature scheme. Discrete equations for bending and free vibration analyses are obtained by variational consistency in the Galerkin weak form. Enforcing essential boundary conditions is completely similar to the finite element method (FEM) due to satisfying the Kronecker delta function property of moving Kriging integration shape functions. Numerical validations with various complex geometries, stiffness ratios, volume fraction of CNTs and boundary conditions are given to show the efficiency of the present approach.