An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core

. The main aim of this paper is to present an analytical approach on the postbuckling for torsionally loaded sandwich carbon nanotube (CNT) reinforced cylindrical shells with the auxetic core. The considered shells consist of three layers, external and internal CNT reinforced layers, and the auxetic lattice core made by isotropic material. The homogenization model for honeycomb auxetic lattice core is utilized, and the equilibrium equations are formulated based on the nonlinear Donnell’s thin shell theory with von K´arm´an geometrical nonlinearities. The three terms of deﬂection are considered, the Airy’s stress function and Galerkin’s method are utilized, the explicit expression of critical buckling of torsionally loaded shells and load-deﬂection expression of postbuckling states are achieved. The effects of two carbon nanotube reinforced layers, the auxetic core layer, the volume fraction of carbon nanotube on the torsional buckling behavior are examined and remarked.