Vietnam Journal of Mechanics, VAST, Vol. 41, No. 1 (2019), pp. 31 – 49 DOI: https://doi.org/10.15625/0866-7136/12602 BUCKLING AND POSTBUCKLING OF AXIALLY-LOADED CNT-REINFORCED COMPOSITE CYLINDRICAL SHELL SURROUNDED BY AN ELASTIC MEDIUM IN THERMAL ENVIRONMENT Hoang Van Tung 1,∗ , Pham Thanh Hieu 2 1 Hanoi Architectural University, Vietnam 2 University of Transport Technology, Hanoi, Vietnam ∗ E-mail: hoangtung0105@gmail.com Received: 31 May 2018 / Published online: 09 October 2018 Abstract. Buckling and postbuckling behaviors of nanocomposite cylindrical shells rein- forced by single walled carbon nanotubes (SWCNTs), surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform axial compression are inves- tigated in this paper. Material properties of carbon nanotubes (CNTs) and isotropic matrix are assumed to be temperature dependent, and effective properties of nanocomposite are estimated by extended rule of mixture. The CNTs are embedded into matrix via uni- form distribution (UD) or functionally graded (FG) distribution along the thickness direc- tion. Governing equations are based on Donnell classical shell theory taking into account von Karman-Donnell nonlinear terms and interaction between the shell and surround- ing elastic medium. Three-term form of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain load-deflection relation from which buckling and postbuckling behaviors are analyzed. Numerical examples are carried out to analyze the effects of CNT volume fraction and distribution types, geometrical ratios, environment temperature and surrounding elastic foundation on the buckling loads and postbuckling strength of nanocomposite cylindrical shells. Keywords: CNT-reinforced composite; nanocomposite cylindrical shell; nonlinear stability; axial compression; elastic foundation. 1. INTRODUCTION Carbon nanotubes (CNTs) have attracted huge attention in most areas of science and engineering due to their exceptional physical and mechanical properties. Single walled carbon nanotube (SWCNT) is a cylinder with diameter of order of 1 nm and length of up to centimeters and formed by seamless rolling a single sheet of graphene. No previ- ous material has displayed extraordinary mechanical, thermal and electrical properties as CNTs. For example, the elastic modulus of SWCNT is approximately 1 TPa, the strength c  2019 Vietnam Academy of Science and Technology