Proceedings of the International Symposium of Mechanism and Machine Science, 2017 AzC IFToMM – Azerbaijan Technical University 11-14 September 2017, Baku, Azerbaijan 164 Stability Analysis of Orthotropic Conical Shells Resting On Winkler Elastic Foundation Based on the FOSDST Abdullah SOFIYEV 1* , Ali NAJAFOV 2 1* Department of Civil Engineering of Engineering Faculty of Suleyman Demirel University, 32600, Isparta, Turkey, E-mail: abdullahavey@sdu.edu.tr 2* Institute for Machine Elements of Azerbaijan Technical University, E-mail: ali.najafov@rohe.az Abstract In this study, the stability of freely supported orthotropic conical shells (OCS) resting on Winkler elastic foundation (WEF) on the basis of the first order shear deformation shell theory (FOSDST) is analyzed by using Donnell-type shell theory and Galerkin method. KEYWORDS: Stability, Orthotropic Material, Elastic foundation, FOSDST, Critical pressure. 1. INTRODUCTION The anisotropic constructions are widely used in automotive, marine and aerospace industries, which require a strong, rigid and lightweight construction. The possibility of predicting the reaction of composite orthotropic shells subjected to lateral pressure is of particular interest to researchers in the field of continuous mechanics. Previously, numerous studies have been carried out on the loss of stability of orthotropic conical shells using the classical theory of shells (CST) [1-3]. The development of the theory of shells made it possible to know the important role of shear stresses (or deformations) in the behavior of structures consisting of composite materials. Due to the increasing importance of orthotropic materials in the design of composite structures and their characteristics, the loss of stability, taking into account the effect of transverse shear strains or using shear deformations shell theory (SDST), is vital. In this context, the researchers have published some publications, taking into account the influence of shear deformations on the bending of structural elements [4-6]. In the above studies, the effect of continuous environments on the stability of the orthotropic conical shells is not taken into consideration. In recent years, orthotropic conical shells have been used in various elastic media. The effects of such environments on the stability behavior of the anisotropic conical shells have not yet been investigated based on the SDST [7, 8]. The purpose of this study is to solve the problem of loss of stability of orthotropic conical shells resting on WEF by using FOSDST. 2. METHOD OF SOLUTION Consider orthotropic truncated conical shell subjected to the uniform lateral pressure, P, resting on the WEF in which the notations are presented in Fig. 1. Let the coordinate system ( r Oz ) be chosen such that, the origin O is at the vertex of the whole cone. Figure 1. Orthotropic truncated conical shells on the WEF with the coordinate systems and notations The effect of WEF is modeled as w K R w  (1) where R is the force per unit area, ) m / N ( K 3 w is the Winkler foundation stiffness (spring stiffness) and w is the small deflection. The stress-strain relationships of orthotropic conical shells within the first order shear deformations theory (FOSDST) are obtained as [9]: