Bending and Buckling of FG-GRNC Laminated Plates via Quasi-3D Nonlocal Strain Gradient Theory

Abstract

To improve the structural stiffness, strength and reduce the weight of nanoplate structure, functionally graded (FG) graphene-reinforced nanocomposite (GRNC) laminated plates are exploited in this paper. The bending and buckling behaviors of FG-GRNC laminated nanoplates are investigated by using novel quasi-3D hyperbolic higher order shear deformation plate theory in conjunction with modified continuum nonlocal strain gradient theory, which considered both length and material scale parameters. The modified model of Halpin–Tsai is employed to calculate the effective Young’s modulus of the GRNC plate along the thickness direction, and Poisson’s ratio and mass density are computed by using the rule of mixture. An analytical approach of the Galerkin method is developed to solve governing equilibrium equations of the GRNC nanoplate and obtain closed-form solutions for bending deflection, stress distributions and critical buckling loads. A detailed parametric analysis is carried out to highlight influences of length scale parameter (nonlocal), material scale parameter (gradient), distribution pattern, the GPL weight fraction, thickness stretching, geometry and size of GPLs, geometry of the plate and the total number of layers on the stresses, deformation and critical buckling loads. Some details are studied exclusively for the first time, such as stresses and nonlocality effect.

Effects of graphene-platelets reinforcement on the free vibration, bending, and buckling of porous functionally-graded metal-ceramic plates

“…Table 8 shows the results validation of uni-axial buckling parameter N^=((1−ν2)/Eh)N of a GPls-reinforced epoxy plate. Our results are given next to the quasi-3D solution of Ghandourah et al 55 that considers stretching effects, and the solution of Gholami et al 56 The plate is made of a single-component matrix with E = 3 GPa and ν = 0.34. We can validate from Table 8 the accuracy of our solution using the hyperbolic plate theory in predicting the critical buckling loads of GPls-reinforced plates.…”

A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

“…By considering the four unknowns of displacements and examining various boundary conditions, the Galerkin approach is employed. Galerkin expressions of displacements can be provided as [42][43][44]:…”

Thermal buckling and postbuckling of functionally graded multilayer GPL-reinforced composite beams on nonlinear elastic foundations

“…The nonlinear vibration of functionally graded GPLRC cylindrical plates under transverse excitation was studied by Niu et al [ 31 ] using the Navier method. To examine the impact of microstructure and length scale on the buckling and bending of functionally graded multilayer GPLRC plates, Ghandourah et al [ 32 ] combined the continuous nonlocal strain graded theory with the quasi-3D hyperbolic higher order shear deformation plate theory. Daikh et al [ 33 ] first proposed the static bending response and stress distribution of functionally graded multilayer sandwich nanoplates under the variable Winkler foundation model.…”