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

Abstract

Nonlinear buckling and postbuckling of longitudinally compressed carbon nanotube-reinforced (CNTR) cylindrical shells stiffened by longitudinal or circumferential CNTR stiffeners in thermal environments surrounded by elastic medium are presented in the present study. Five linear distributions of CNT are considered for the shell-stiffener structure system and they are modeled by innovation homogenization technique for CNTR stiffeners. Based on the classical Donnell thin shell theory with von Karman's nonlinearities and the Galerkin procedure, the governing equations can be built to analyze the critical buckling compression and postbuckling compression-deflection and compression-shortening behavior. The noticeable effects of volume fraction of CNTs, shell-foundation interaction stiffnesses, uniformly distributed temperature, and geometric properties of stiffened cylindrical shells on the critical buckling compression and compression-deflection and compression-shortening postbuckling behaviors of stiffened CNTR cylindrical shells are obtained and remarked in numerical examinations. INTRODUCTIONCarbon Nanotube (CNT) reinforced composite is known to be an advanced composite with high-performance material. The CNTs with the high aspect ratio, low density, exceptional, electro-thermo-mechanical properties can be used to enhance the electrical thermal, and mechanical properties of basic materials. 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. An ideal for a CNTR composite material with the two-directional reinforcements of CNTs was presented [15,16] and nonlinear buckling of cylindrical

An investigation on the torsional vibration of a FG strain gradient nanotube

“…Unless otherwise stated, the geometrical properties used for functionally graded composite nanotubes are as follows: 𝑟 2 = 1 nm, 𝑟 1 = 2 nm and L = 10 𝑟 1 = 20 nm. The properties of zirconia (outer material) and aluminium (inner material) are defined via: 𝐸 1 = 151 𝐺𝑃𝑎, 𝐸 2 = 70 𝐺𝑃𝑎, 𝜌 1 = 3000 𝑘 𝑔 ∕𝑚 3 , 𝜌 2 = 2707 𝑘 𝑔 ∕𝑚 3 , 𝜐 1 = 𝜐 2 = 0.3. In addition, some dimensionless parameters for the functionally graded composite nanotubes are used in the study.…”

“…The above frequency equation is used to analyze homogeneous materials. In order to make a consistent comparison with the above equation, we consider a nanotube consisting only of ceramic material with the properties 𝐸 = 151 𝐺𝑃𝑎, 𝜌 = 3000 𝑘 𝑔 ∕𝑚 3 , 𝜐 = 0.3. It should also be noted that J and μ are calculated, respectively, as follows:…”

“…Carbon nanotubes have many application areas on their own. Also, their superior mechanical properties have made them attractive for use as reinforcement elements of composites [2][3][4][5][6][7][8][9][10][11][12] too.…”

Nonlinear thermo-elastic stability of corrugated-core toroidal shell segments with carbon nanotube-reinforced face sheets under radial pressure

“…An anisotropic smeared stiffener technique was developed for the CNT-reinforced stiffeners to analyze the buckling behavior of the CNT-reinforced cylindrical shells with suitable designs of CNT distributions in the stiffeners and in the shells. 38,39 In addition, CNTreinforced composites can also be designed as face sheets and combined with auxetic cores to increase the bearing capacity of the cylindrical shells and toroidal shell segments. [40][41][42] Some works on the viscoelastic behavior of CNT-reinforced cylindrical shells subjected to earthquake loads were also performed taking into account the thermal and moisture effects.…”