Auxetic materials are usually designed as cores for structures subject to high impulse loads. Furthermore, the lightweight and high load capacity of the auxetic core construction is also an important advantage even for structures subjected to static loads. The combination of auxetic core and face sheets made by the advanced composite materials is a solution to dramatically increase the load-carrying capacity of the structure. In this paper, a new design of auxetic-core cylindrical shells with carbon nanotube-reinforced coatings is presented. Additionally, the nonlinear buckling behaviors of auxetic-core cylindrical shells with carbon nanotube-reinforced coatings under axially compressive loads are investigated. Three distributed types of functionally graded carbon nanotube-reinforced coatings and the honeycomb lattice form of the auxetic core are investigated. The homogenization model for auxetic lattice structures is considered to constitute the formulations of stiffnesses of the core layer. The nonlinear basic formulations are formulated by using the geometrically nonlinear Donnell shell theory considering Pasternak’s foundation. The Galerkin procedure can be applied three times for three states of buckling behaviors, and the expressions of the compressive load-maximal deflection and compressive load-average end shortening postbuckling curves are achieved. The numerically obtained investigations present the significant effects of auxetic core, volume fraction, direction arrangement and distributed law of carbon nanotube, foundation stiffnesses, geometrical parameters of auxetic core and shell on the critical buckling load and postbuckling behavior of structures.
This paper presents a semi-analytical approach for investigating the nonlinear buckling and postbuckling of spiral corrugated sandwich functionally graded (FGM) cylindrical shells under external pressure and surrounded by a two-parameter elastic foundation based on Donnell shell theory. The improved homogenization theory for the spiral corrugated FGM structure is applied and the geometrical nonlinearity in a von Karman sense is taken into account. The nonlinear equilibrium equation system can be solved by using the Galerkin method with the three-term solution form of deflection. An explicit solution form for the nonlinear buckling behavior of shells is obtained. The critical buckling pressure and the postbuckling strength of shells are numerically investigated. Additionally, the effects of spiral corrugation in enhancing the nonlinear buckling behavior of spiral corrugated sandwich FGM cylindrical shells are validated and discussed.
This paper deals with the nonlinear large deflection torsional buckling of functionally graded carbon nanotube (CNT) orthogonally reinforced composite cylindrical shells surrounded by Pasternak’s elastic foundations with the thermal effect. The shell is made by two layers where the polymeric matrix is reinforced by the CNTs in longitudinal and circumferential directions for outer and inner layers, respectively. The stability equation system is obtained by combining the Donnell’s shell theory, von Kármán nonlinearity terms, the circumferential condition in average sense and three-state solution form of deflection. The critical torsional buckling load, postbuckling load-deflection and the load-end shortening expressions are obtained by applying the Galerkin procedure. The effects of temperature change, foundation parameters, geometrical properties and CNT distribution law on the nonlinear behavior of cylindrical shell are numerically predicted. Especially, the effect of orthogonal reinforcement in comparison with longitudinal and circumferential reinforcement on the torsional buckling behavior of shells is observed.
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
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