tailieunhanh - Postbuckling of functionally graded cylindrical shells based on improved donnell equations

This paper presents an analytical approach to investigate the buckling and postbuckling of functionally graded cylindrical shells subjected to axial and transverse mechanical loads incorporating the effects of temperature. Material properties are assumed to be temperature independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. | Vietnam Journal of Mechanics, VAST, Vol. 35, No. 1 (2013), pp. 1 – 15 POSTBUCKLING OF FUNCTIONALLY GRADED CYLINDRICAL SHELLS BASED ON IMPROVED DONNELL EQUATIONS Dao Huy Bich1 , Nguyen Xuan Nguyen1 , Hoang Van Tung2 1 Hanoi University of Science, VNU, Vietnam 2 Hanoi Architectural University, Vietnam Abstract. This paper presents an analytical approach to investigate the buckling and postbuckling of functionally graded cylindrical shells subjected to axial and transverse mechanical loads incorporating the effects of temperature. Material properties are assumed to be temperature independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium equations for perfect cylindrical shells are derived by using improved Donnell shell theory taking into account geometrical nonlinearity. One-term approximate solution is assumed to satisfy simply supported boundary conditions and closed-form expressions of buckling loads and load-deflection curves are determined by Galerkin method. Analysis shows the effects of material and the geometric parameters, buckling mode, pre-existent axial compressive and thermal loads on the nonlinear response of the shells. Keywords: Postbuckling, functionally graded materials, cylindrical shells, improved Donnell theory, temperature effects. 1. INTRODUCTION Cylindrical shell is one of the most common structures found in many applications of various industries. As a result, problems relating to the stability including buckling and postbuckling behaviors of this type of shell have a major importance for safe and reliable design and attract attention of many researchers. Brush and Almroth [1] introduced an excellent work on buckling of bars, plates and shells in which linear stability of cylindrical shell structures under basic types of loading has been analyzed. However, the results were mainly presented for isotropic shallow cylindrical shells. Birman .