Mesh-Free Method for Static Analyses of Carbon Nanotube-Reinforced Composite Plates

A mesh-free method is presented to investigate the static bending properties of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The curvature of the plate is directly interpolated with the nodal deflections due to the higher-order continuity property of the moving least-squares approximation, establishing a mesh-free computational scheme where the nodal deflections are the only unknowns. The convergence and efficiency of the proposed method are studied based on a homogeneous square plate. The FG-CNTRC plates are modeled with continuously varying Young's moduli along the I thickness direction according to the volume fraction of the carbon nanotubes (CNTs). Detailed studies have been conducted on the effects of different boundary conditions, CNT volume fractions, geometric shapes, and width-to-thickness ratios on bending behavior. CNT efficiency parameters are introduced to account for load transfer between the nanotubes and the matrix, treating the nanocomposites as orthotopic materials. However, in the actual structure, arranging the CNTs in the desired direction is more difficult compared to other fibers. Therefore, in the present study, CNTs in the composites are considered to be arranged randomly, resulting in the composite properties being treated as isotropic. The study includes second-order derivatives of deflections, and the finite element method typically requires C1 continuity for interpolation, which introduces challenges in building elements and constructing interpolation functions. The distinct advantage of the mesh-free method is that it requires only C0 weight functions. A mesh-free computational scheme based on moving least-squares approximations for composite plates using Kirchhoff plate theory is established. Bending analyses of homogeneous and FG-CNTRC plates are conducted using the proposed method. Aspects such as boundary conditions, CNT volume fractions, geometric shapes, and width-to-thickness ratios are also discussed. Regular node arrangements and background meshes are adopted in the present study. Results are computed using different scalar parameters and numbers of nodes. Convergence properties for the central deflection of isotropic plates are analyzed in terms of the number of nodes and different scalar parameters. The normalized central deflection is defined and examined under various boundary conditions.