Multilayer heterostructure inhomogeneous model for the functionally graded spherical shell with rotation effect for arbitrarily varying material properties

Abstract

With the development of functionally graded materials (FGMs) composite technology, structural safety analysis related to FGMs has been widely concerned. An innovative multilayer heterostructure power-law inhomogeneous (MHPI) model is taken to solve the rotating FGMs hollow spherical shell with arbitrarily varying material properties (elastic modulus and density) along the radial direction. The basic idea of MHPI model is that the rotating FGMs spherical shell is divided into multiple sublayers, and two power functions approximate the elastic modulus and density of each sublayer respectively. For each single sublayer, the analytical solutions include two undetermined constants, which can be obtained from the boundary and continuity conditions. Many numerical examples of the rotating FGMs spherical shell are discussed, involving seven property profiles gradient laws assumptions, three boundary conditions, and nine volume fraction gradient models. Finally, this study further discusses the rotating FGMs spherical shell optimization design. The greatest advantage of this study is that the elastic response of the rotating FGMs spherical shell under various gradient assumptions is completely discussed. The numerical results show that the MHPI model can solve the problem of circumferential stress oscillation well and have good convergence and high accuracy. For many numerical examples, the error of the MHPI model results is about 5‰ when sublayer number reaches 15.