Buckling of shear deformable FG‐CNTRC cylindrical shells and toroidal shell segments under mechanical loads in thermal environments

Abstract

An analytical study on buckling of carbon nanotube reinforced composite (CNTRC) circular cylindrical shells and toroidal shell segments surrounded by elastic media, exposed to thermal environments and subjected to axial compression and combined mechanical loads is presented in this paper. Carbon nanotubes (CNTs) are reinforced into isotropic matrix through uniform and functionally graded distributions. Material properties of constituents are assumed to be temperature dependent and effective elastic moduli of CNTRC are estimated by an extended rule of mixture. Formulations are based on first order shear deformation theory taking into account interaction between the shell and surrounding medium. Two‐term solution of deflection is assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain closed‐form expressions of buckling loads. Numerical illustrations are given to analyze the effects of CNT volume fraction and distribution patterns, preexisting loads, surrounding elastic media and geometrical parameters on the stability of CNTRC shells. The proposed approach is simple and effective to evaluate buckling loads of moderately thick closed nanocomposite shells under different types of mechanical loads.

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

“…Beside the commonly used value K S = 5/6 [10,13,14,16,24,26,33,34], the shear correction coefficient was also suggested to be a value depending on Poisson's ratios of constituent materials in work of Efraim and Eisenberger [35] for functionally graded material (FGM). This suggestion of variable Poisson's rations was also developed in work of Lei et al [36] for FG-CNTRC.…”

“…Above boundary conditions are approximately satisfied by assuming the following analytical solutions [33,34]…”

“…Recently, Hieu and Tung [33,34] suggested an effective analytical approach using two-term form of deflection for linear buckling analysis of shear deformable FG-CNTRC cylindrical shells and toroidal shell segments. As an extension of previous work [33], this paper adopts an analytical approach to investigate the buckling behavior of sandwich cylindrical shells comprising CNTRC and homogeneous layers subjected to uniform temperature rise and external lateral pressure.…”

An analytical approach of nonlinear buckling behavior of longitudinally compressed carbon nanotube‐reinforced (CNTR) cylindrical shells with CNTR stiffeners in thermal environment

“…By reinforcing the CNTs for the same directions into the isotropic material, Shen [1, 2], created the special type of CNT-reinforced (CNTR) composite with the functionally graded (FD) volume fraction of CNT in the thickness direction of shells. The longitudinally compressed CNTR cylindrical shells are the outstanding structures that were studied with different thermo-mechanically linear and nonlinear problems such as static buckling and postbuckling behaviors [1-3], combined loads of axial compression and external pressure [4], free and forced vibration responses [5][6][7], and dynamic stability [8][9][10][11][12]. The more complex load types as dynamical seismic loads applied for CNTR cylindrical shells were also considered and analyzed [13,14] taking into account the moisture and hygrothermal effects.…”

“…𝜓 1 𝜓 2 + 𝑚 4 𝑛 4 𝜋 4 𝜆 4 𝜋 2 𝐿 2 ℎ𝑝𝜓 1 − 𝜎 0𝑦 ℎ𝑛 2 𝐿 2 𝜆 2 𝜓 1 + 𝐿4 𝐾 1 𝜓 1 + 𝐿 2 𝐾 2 𝜓 1 The closed condition in the circumferential direction can be added for the cylindrical shell, as…”