Large deflection of functionally graded carbon nanotube reinforced composite cylindrical shell exposed to internal pressure and thermal gradient

Abstract

In this paper, the nonlinear bending of functionally graded carbon nanotubereinforced composite (FG-CNTRC) shell exposed to thermomechanical loading is perused. It is assumed that the composite shell is reinforced in the longitudinal axis and is also made from a polymeric matrix. Mechanical features of the constituents are obtained based on the modified rule of mixture, and they are considered to be temperature dependent (TD). Using the first-order shear deformation shell theory (FSDT) as well as von K arm an type of geometrical nonlinearity, the equilibrium mathematical relations are derived. Utilizing the dynamic relaxation (DR) procedure combined with the central finite difference method, these mathematical relations are solved in diverse boundary conditions. Finally, roles of carbon nanotube (CNT) distributions, boundary conditions, shell radius, thickness-to-radius ratios, volume fraction of CNTs, mechanical loads, thermal gradient, and temperature dependency are examined on the results. From the numerical results, it can be inferred that in the shell with the CC boundary condition, the FG-O distribution of nanotubes has the maximum deflection, and the lowest deflection belongs to the uniform distribution. However, in the SS boundary condition, the highest and lowest values of deflections are related to V and uniform distributions, respectively.

Vibration analysis of composite plates reinforced CNTs using an exponential function approach

“…Using the rule of mixture, the longitudinal and transversal elastic modulus and shear modulus for each layer, are calculated using the following equations [12,15,28,29]:…”

“…It is worth highlighting that subdividing the thickness of a plate into NL layers is a mathematical technique for numerically evaluating integrals along the thickness. This fraction can be calculated for each layer using the weight fraction wt of the reinforcement, and nanotube density ρm and ρCNT of matrix and CNTs respectively [15,26] It is assumed that the distribution of volume fraction in each layer follows both the power law and the proposed exponential law. These distribution models have the following forms: FG-X, FG-O, FG-A, and FG-V.…”

“…Using the rule of mixture, the longitudinal and transversal elastic modulus and shear modulus for each layer, are calculated using the following equations [12,15,28,29]: E11CNT, E22CNT, Em are the elastic Young modulus of CNTs and matrix, respectively. G12CNT and Gm are the shear modulus of CNT and matrix respectively.…”

“…The Poisson's ratios and density for the composite plate reinforced by CNTs are given by the standard rule of mixture [13,15,21,25]: ν12CNT and νm are the Poisson's ratios of CNTs and matrix, respectively. …”

“…In the past decade, researchers have placed significant importance on CNTs and their reinforcement due to their outstanding performance in terms of mechanical, thermal, and electrical properties, making them preferred materials in various engineering fields such as biomedical, and aerospace. In 2009, Shen [2] inspired the nonlinear distribution of single-walled CNTs from the FGM metal/ceramic concept, and since then, a significant number of papers have been published investigating various topics such as low-velocity impact analysis [3][4][5], static, vibration and free vibration [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], and dynamic analysis [21]. The vibration behaviour of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical panels was investigated by Jooybar et al [22].…”