Non-linear dynamical analysis of imperfect functionally graded material shallow shells

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.