# Nonlinear postbuckling of eccentrically stiffened functionally graded plates and shallow shells

## The paper deals with the formulation of governing equations of eccentrically stiffened functionally graded plates and shallow shells based uppon the classical shell theory and the smeared stiffeners technique taking into account geometrical nonlinearity in Von Karman-Donnell sense. | Vietnam Journal of Mechanics, VAST, Vol. 33, No. 3 (2011), pp. 131 – 147 NONLINEAR POSTBUCKLING OF ECCENTRICALLY STIFFENED FUNCTIONALLY GRADED PLATES AND SHALLOW SHELLS Dao Huy Bich1 , Vu Hoai Nam2 , Nguyen Thi Phuong2 1 Hanoi University of Science, VNU 2 University of Transport Technology, Hanoi, Vietnam Abstract. The paper deals with the formulation of governing equations of eccentrically stiffened functionally graded plates and shallow shells based uppon the classical shell theory and the smeared stiffeners technique taking into account geometrical nonlinearity in Von Karman-Donnell sense. Material properties are assumed to be temperatureindependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of constituents. The shells are reinforced by eccentrically longitudinal and transversal stiffeners made of full metal or full ceramic depending on situation of stiffeners at metal-rich side or ceramic-rich side of the shell respectively. Obtained governing equations can be used in research on nonlinear postbuckling of mentioned above structures. By use of the Galerkin method an approximated analytical solution to the nonlinear stability problem of reinforced FGM plates and shallow shells is performed. The postbuckling load-deflection curves of the shells are investigated and analytical expressions of the upper and lower buckling loads are presented. A comparison of the effectiveness of stiffeners in enhancing the stability of FGM plates and shallow shells is given. Key words: Functionally graded material, plates, shallow shells, stiffeners, upper and lower buckling loads, nonlinear postbuckling. 1. INTRODUCTION Functionally graded materials (FGMs) have properties varying smoothly through the thickness by changing continuously in the volume fractions of their constituents. Reinforced FGM structures like plates and shallow shells may be used in aerospace vehicles and nuclear reactors. They can be found

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