A higher-order isoparametric superelement for free vibration analysis of functionally graded shells of revolution

A higher-order isoparametric superelement is developed to study the vibration of functionally graded shells of revolution. The effective material properties of functionally graded materials (FGMs) vary continuously along the thickness direction of the shell in accordance with the power law distribution. The governing equations are presented based on the three-dimensional elasticity theory using Hamilton's principle. Since the isoparametric formulation is considered, a unified formulation is presented for all types of shells of revolution. The properties of the FG shells are graded through the thickness direction, and consequently, the analysis of such structures is quite difficult using conventional three-dimensional finite elements. The proposed superelement facilitates the analysis of FG shell structures. Different types of circular shell structures including cylindrical, conical, spherical and circular toroid are considered in this study. To show the accuracy and efficiency of the proposed superelement, different comparative studies are presented.