This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection. | Vietnam Journal of Mechanics, VAST, Vol. 34, No. 3 (2012), pp. 139 – 156 SOLVING NONLINEAR STABILITY PROBLEM OF IMPERFECT FUNCTIONALLY GRADED CIRCULAR CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION BY GALERKIN’S METHOD Dao Van Dung, Le Kha Hoa University of Science, VNU Abstract. This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection. Equations to find the critical load and the load-deflection curve are established by Galerkin’s method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper [13] which were solved by Ritz energy method. Key words: imperfect. Cylindrical shells, non - linear stability, functionally graded materials, 1. INTRODUCTION The structures made of functionally graded materials (FGMs) including cylindrical shell structure play an important role in modern industries [1]. Therefore, the research on strength and stability of FGM cylindrical shells are interested very much by scientists. In 2002, Shen [2] solved the postbuckling problem of axially - loaded FGM cylindrical shells in the thermal environments by perturbation technique. By the same method, Shen and Noda [3] analyzed the postbuckling of FGM cylindrical shells under combined axial and radial mechanical loads in the thermal environments. Shahsiah and Eslami [4] based on improved Donnell equations considered FG cylindrical shell themal instability. Wu et al. [5] studied the .
