Naturally stabilized nodal integration meshfree formulations for analysis of laminated composite and sandwich plates

This article addresses a naturally stabilized nodal integration (NSNI) meshfree formulation for static, free vibration and buckling analyses of laminated composite and sandwich plates based on the higher order shear deformation theory (HSDT). The crucial idea is to directly compute integrations at nodes similar to the direct nodal integration (DNI) but the instability existing in DNI is avoided and the computational cost is significantly reduced when compared to traditional high-order Gauss quadrature schemes. Due to the displacements, strains and stresses directly computed at nodes, the computing time of the present approach is equivalent with the DNI. Being different from the stabilized conforming nodal integration technique using a divergence theorem to evaluate gradient strains by the surface-to-boundary integration, NSNI is a naturally implicit gradient expansion. Variational consistency in Galerkin weak form is explicitly described. Thanks to the satisfied Kronecker delta function property, the moving Kriging integration (MKI) shape function is used to impose directly essential boundary conditions as same as the finite element method (FEM). A variety of numerical examples with various complex geometries, aspect ratios, stiffness ratios and boundary conditions are studied. Numerical results show the effectiveness of the present method in comparison with some existing ones in the literature.