The non-linear transient responses of cylindrical and doubly-curved shallow shells subjected to excited external forces are obtained and the dynamic critical buckling loads are evaluated based on the displacement responses using the criterion suggested by Budiansky and Roth. Obtained results show the essential influence of characteristics of functionally graded materials on the dynamical behaviors of shells. | Vietnam Journal of Mechanics, VAST, Vol. 32, No. 1 (2010), pp. 1 – 14 NON-LINEAR DYNAMICAL ANALYSIS OF IMPERFECT FUNCTIONALLY GRADED MATERIAL SHALLOW SHELLS Dao Huy Bich, Vu Do Long Vietnam National University, Hanoi Abstract. Dynamical behaviors of functionally graded material shallow shells with geometrical imperfections are studied in this paper. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The motion, stability and compatibility equations of these structures are derived using the classical shell theory. The non-linear equations are solved by the Newmark’s numerical integration method. The non-linear transient responses of cylindrical and doubly-curved shallow shells subjected to excited external forces are obtained and the dynamic critical buckling loads are evaluated based on the displacement responses using the criterion suggested by Budiansky and Roth. Obtained results show the essential influence of characteristics of functionally graded materials on the dynamical behaviors of shells. 1. INTRODUCTION Functionally graded materials (FGM) as a new class of advanced inhomogeneous composite materials have received considerable attention in many engineering applications for improved structural efficiency in space structures and nuclear reactors since they were first reported in Japan [1]. In recent years important studies have been researched about the stability and vibration of functionally graded plates and cylindrical shells. Birman [2] presented a formulation of the stability problem for functionally graded hybrid composite plates subjected to uniaxial compression. Elastic bifurcation of functionally graded plates acted on by compressive loading was studied by Feldman and Aboudi [3]. Reddy et al [4] gave bending solution for functionally graded circular plates and annular plates. Woo and Meguid [5] presented an analytical solution for
