In the present paper the non-linear buckling analysis of functionally graded spherical shells subj ected to external pressure is investigated. The material properties are graded in the t hickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In t he formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. | Vietnam Journal of Mechanics, VAST, , No. l (2009), pp. 17 - 30 NON-LINEAR BUCKLING ANALYSIS OF FUNCTIONALLY GRADED SHALLOW SPHERICAL SHELLS Dao Huy Bich Vietnam National University, Hanoi Abstract. In the present paper the non-linear buckling analysis of functionally graded spherical shells subj ected to external pressure is investigated. The material properties are graded in the t hickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In t he formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained , that allows easily to investigate stability behaviors of the shell. 1. INTRODUCTION A new class of materials, called functionally graded materials (FGMs), has received considerable attention for improved structural efficiency in space structures and nuclear reactors. FGMs are microscopically inhomogeneous, in which the material properties vary smoothly and continuously from one surface of the material to the other surface. This is achieved by gradually varying the volume fractions of the constituent materials. These materials are made from a mixture of ceramic and metal, or combination of different materials [l]. In recent years, important studies have been researched about t he stability and vibration of functionally graded plates and cylindrical shells. Birman [2] presented a formulation of the slitability problem for functionally graded hybrid composite plates subjected to uniaxial compression. Feldman and Aboudi [3] studied elastic bifurcation of functionally graded plates acted on by compressive loading. Reddy et al [4] gave bending solution for FGM circular plates and annular plates. In the works [5, 6] a free vib-ration analysis of FGM cylindrical
