A nonlocal strain gradient analysis of laminated composites and sandwich nanoplates using meshfree approach

This paper aims to develop a nonlocal strain gradient meshfree plate approach which combines the nonlocal strain gradient theory (NSGT), higher order shear deformation theory (HSDT) and meshfree method, for the bending and free vibration analyses of laminated composite and sandwich nanoplates. Mechanical characteristics of small-scale structures can be described by using two scale parameters related to the nonlocal and strain gradient effects. The weak form of governing equations is extracted from the virtual work principle. Exploiting the higher order derivatives of moving Kriging (MK) shape functions, the present approach satisfies the requirement of the third-order derivatives of weak approximations. The displacements and natural frequencies of laminated composite and sandwich nanoplates are then determined by utilizing the MK meshfree method. Numerical results show that the deflections and natural frequencies of laminated composite and sandwich nanoplates are significantly influenced by the boundary conditions, nonlocal parameter and strain gradient parameter, geometry, length-to-thickness ratios. As observed, a large difference between NSGT and classical HSDT results is reported and discussed. It is clear that the results of both models coincide when the nonlocal and strain gradient parameters are taken as zero.