Structural Engineering and Mechanics, Vol. 60, No. 4 (2016) 615-631 DOI: http://dx.doi.org/10.12989/sem.2016.60.4.615 615 Copyright © 2016 Techno-Press, Ltd. http://www.techno-press.org/?journal=sem&subpage=8 ISSN: 1225-4568 (Print), 1598-6217 (Online) Post-buckling of cylindrical shells with spiral stiffeners under elastic foundation Alireza Shaterzadeh  and Kamran Foroutan a Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran (Received February 11, 2016, Revised July 22, 2016, Accepted August 3, 2016) Abstract. In this paper, an analytical method for the Post-buckling response of cylindrical shells with spiral stiffeners surrounded by an elastic medium subjected to external pressure is presented. The proposed model is based on two parameters elastic foundation Winkler and Pasternak. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. According to the Von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method is used to solve the nonlinear problem. To valid the formulations, comparisons are made with the available solutions for nonlinear static buckling of stiffened homogeneous and un-stiffened FGM cylindrical shells. The obtained results show the elastic foundation Winkler on the response of buckling is more effective than the elastic foundation Pasternak. Also the ceramic shells buckling strength higher than the metal shells and minimum critical buckling load is occurred, when both of the stiffeners have angle of thirty degrees. Keywords: FGM cylindrical shells; nonlinear analysis; spiral stiffener; post-buckling 1. Introduction The eccentrically stiffened FGM cylindrical shells have more application in modern Engineering. In many application, the shell under pressure and may be buckling. Therefore, research on nonlinear stability of these structures has been of interest to scientists. In fact, used to stiffeners with low weight to support the structures for bearing Load. Study on nonlinear behavior of these structures is important of the practical. Van der Neut (1947) showed the importance of stiffeners in the buckling of isotropic cylindrical shell under axial load. A careful analysis of post-buckling behavior of eccentrically stiffened FGM thin circular cylindrical shells is surrounded by an elastic foundation and external pressure was presented by Shaterzadeh and Foroutan (2015). Dung and Nga (2013) studied the Post-buckling of eccentrically stiffened FGM cylindrical shells with elastic foundation under uniform external pressure. Shen, Zhou et al. (1993) studied the Buckling and post-buckling behavior of complete and incomplete eccentrically stiffened cylindrical shell under external pressure and axial compression by using boundary layer theory. The mechanical buckling of Corresponding author, Ph.D., E-mail: a_shaterzadeh@shahroodut.ac.ir