Nonlinear buckling of CNT-reinforced composite toroidal shell segment surrounded by an elastic medium and subjected to uniform external pressure

Abstract

Buckling and postbuckling behaviors of Toroidal Shell Segment (TSS) reinforced by single-walled carbon nanotubes (SWCNT), surrounded by an elastic medium and subjected to uniform external pressure are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix phase by uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Effective properties of carbon nanotube reinforced composite (CNTRC) are estimated by an extended rule of mixture through a micromechanical model. Governing equations for TSSs are based on the classical thin shell theory taking into account geometrical nonlinearity and surrounding elastic medium. Three-term solution of deflection and stress function are assumed to satisfy simply supported boundary condition, and Galerkin method is applied to obtain nonlinear load-deflection relation from which buckling loads and postbuckling equilibrium paths are determined. The effects of CNT volume fraction, distribution types, geometrical ratios and elastic foundation on the buckling and postbuckling behaviors of CNTRC TSSs are analyzed and discussed.

Buckling and postbuckling of axially-loaded CNT-reinforced composite cylindrical shell surrounded by an elastic medium in thermal environment

“…The temperature dependent properties of the (10, 10) SWCNTs are given at discrete values of temperature in works [14,19,30] and as continuous functions of temperature in the work [23] and are omitted here for sake of brevity. The CNT efficiency parameters η j (j = 1 ÷ 3) are estimated by matching the Young moduli E 11 , E 22 and shear modulus G 12 of the CNTRC determined from the extended rule of mixture to those from the molecular dynamics (MD) simulations and given in the works [14,23,30,39,40] as (η 1 , η 2 , η 3 ) = (0.137, 1.022, 0.715) for case of V * CNT = 0.12, (η 1 , η 2 , η 3 ) = (0.142, 1.626, 1.138) for case of V * CNT = 0.17 and (η 1 , η 2 , η 3 ) = (0.141, 1.585, 1.109) for case of V * CNT = 0.28.…”

“…To satisfy approximately boundary conditions (18), the following solutions of deflection and stress function are assumed [31,[37][38][39]…”

Nonlinear response of doubly curved sandwich panels with CNT-reinforced composite core and elastically restrained edges subjected to external pressure in thermal environments

“…Force and moment resultants are calculated through stress components as follows (10) where (e 11 , e 21 , e 31 , e 41 , e 51 ) = (11) and K S is shear correction coefficient.…”

“…The idea of optimal distribution of CNTs motivates the concept of functionally graded carbon nanotube reinforced composite (FG-CNTRC) [3] in which CNTs are embedded into the matrix in such a way that their volume is varied in the thickness direction of structure according to functional rules. Shen's propositional work [3] stimulated subsequent investigations on the static and dynamic responses of FG-CNTRC structures [4][5][6][7][8][9][10][11][12][13]. Based on a higher order shear deformation theory (HSDT) and a twostep perturbation approach, Shen and coworkers [14][15][16] investigated the postbuckling of pressure-loaded doubly curved panels made of functionally graded (FG) material, CNTRC and graphene-reinforced composite (GRC).…”

Thermal and thermomechanical buckling of CNT-reinforced composite sandwich cylindrical shells including elasticity of tangential edge restraint

“…Zghal et al [8] used finite element method to analyze the mechanical buckling behavior of plates and cylindrical panels made of FGM and FG-CNTRC with various boundary conditions. An analytical study of the buckling and postbuckling of simply supported FG-CNTRC toroidal shell segments under external pressure is presented by Tung and Hieu [9] making use of classical shell theory (CST) and thee-term form of deflection. A linear buckling analysis of FG-CNTRC truncated conical shells under lateral pressure was presented by Jam and Kiani [10] employing first order shear deformation theory (FSDT) and differential quadrature method (DQM).…”