Nonlinear bending of third-order shear deformable carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with different edge supports

The geometrically nonlinear bending behavior of carbon nanotube/fiber/polymer multiscale laminated composite (CNT-FPMLC) rectangular plates with various edge conditions subjected to the uniform transverse mechanical loading is investigated. Based on the Reddy's third-order shear deformation plate theory and employing the von Karman hypotheses and fundamental lemma of calculus of variations, the governing equilibrium equations including the shear deformation effect and geometrical nonlinearity together with associated boundary conditions are developed. The fiber micromechanics and the Halpin-Tsai relations are employed to approximately calculate the material properties of multiscale composite. Also, the carbon nanotubes (CNTs) are assumed to be distributed uniformly and oriented arbitrarily through the epoxy resin matrix. For the large deflection analysis, first, the generalized differential quadrature (GDQ) method is used to discretize the differential governing equations and corresponding boundary conditions resulting in a set of nonlinear algebraic equations. Then, the pseudo-arclength continuation technique is utilized to numerically solve the resulting nonlinear parameterized equations and subsequently obtain the load-deflection curve of CNT-FPMLC rectangular plates with different edge supports. Several numerical results are provided to reveal the influences of the weight percentage of single-walled and multi-walled CNTs, CNT aspect ratio, volume fraction of fibers, length-to-thickness ratio of plate and boundary conditions on the nonlinear responses of the CNT-FPMLC plates.