Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates

Abstract

Highlights Buckling and postbuckling of biaxially compressed functionally graded multilayer GPLRC plates are investigated. The material properties of the GPL-reinforced composite (GPLRC) are evaluated through a micromechanics model. Theoretical formulations based on the first-order shear deformation plate theory and von Kármántype nonlinear kinematics are developed. A two step perturbation technique is employed to determine the asymptotic postbuckling solutions of both perfect and imperfect plates. The effects of GPL weight fraction, distribution pattern, geometry on buckling and postbuckling behaviors of GPLRC plates are examined.

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

“…For overcoming this problem, the functionally graded GPL reinforced multilayer structures are introduced, because a functionally graded GPL reinforced multilayer nanocomposite structure in which each individual layer is made from a mixture of uniformly distributed GPL reinforcements and polymer matrix with GPL concentration incrementally varying layer by layer is much easier to fabricate. The published results have provided authentic evidence that such a multilayer structure is an excellent approximation to the ideal functionally graded structure with a continuous and smooth variation of GPLs across the thickness direction when the total number of layers is sufficiently large [18,31,32,[49][50][51].…”

“…The Halpin-Tsai model was used to calculate the effective Young's modulus of a polymer nanocomposite reinforced by graphene nanoplatelets (GPLs), and the comparisons between the theoretical predictions and experimental results were also performed [47,48]. Due to the simple form in mathematics, the Halpin-Tsai micromechanics model has been widely employed to estimate the effective Young's modulus of functionally graded graphene nanoplatelets reinforced composites [27][28][29][30][31][32][33][34][35][36][37]. The main objective of the current work is to propose an adjustable distribution law to find a more effective way to use the GPL reinforcements.…”

“…A polymer with a low concentration of GPLs exhibits distinct improvement in mechanical properties. Yang and his coauthors devoted great efforts to the bending, buckling, and vibration behaviors of FG-GPLRC structures [30][31][32]. Shen et al [33,34] discussed various results of the nonlinear bending, vibration, and buckling behaviors of FG-GPLRC plates, panels, and shells.…”

Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations

“…Based on a large numerical investigation, an effective increase of the stiffness was reached for a uniform distribution of the porosity and GPL within the matrix. A different approach based on the first order shear deformation theory and von-Karman nonlinear strain theory was applied by Song et al [13] for the nonlinear analysis of the buckling and post buckling response of FG multilayer composite plates reinforced with GPLs. Thus, an eigenvalue problem was solved by the authors using a two-step perturbation technique.…”

“…Based on the available literature on the vibration and bending response of beams and plates reinforced with GPLs at the macroscale [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], as well as on the curved beams at the macroand nano-scales [18][19][20][21][22][23][24][25][26][27], here we propose a combined study of curved nanobeams reinforced with nanoplatelets. In mechanical problems of technical interest, the elastic equilibrium is generally defined in bounded structural domains, so that suitable constitutive boundary conditions have to be prescribed to ensure the equivalence between integral and differential equations [33].…”