Analysis of the Stress–Strain State of Inhomogeneous Hollow Cylinders

Abstract

The stress-strain state of an inhomogeneous hollow cylinder with different boundary conditions at the ends is analyzed using the three-dimensional theory of elasticity. Spline collocation is used to reduce the two-dimensional boundary-value problem to a boundary-value problem for a system of ordinary differential equations of high order with respect to the radial coordinate, which is solved with the stable discrete-orthogonalization method. The results obtained using the spline-collocation, Fourier-series, and finite-element methods are compared materials, and the consideration of three-dimensional effects in thick-walled structural members necessitate studying hollow cylindrical structures in three dimensions. The stress-strain analysis of thick-walled structures based on the three-dimensional theory of elasticity involves severe difficulties associated with the complexity of the starting systems of partial differential equations and the necessity to satisfy boundary conditions on the surface of an elastic body. These difficulties are even more severe when designing cylindrical elements made of anisotropic and inhomogeneous materials, such as functionally graded materials (FGM) with variable elastic characteristics. Modern technologies make it possible to produce structures with required smoothly varying elastic moduli. The physical and mechanical properties of FGMs based on various compositions are addressed in (3, 11-13). Of great practical interest and importance for fundamental research is the analysis of the stress-strain state of various structural members made of FGMs, including finite-length cylinders. In view of the above, it is necessary to determine the dynamic characteristics of such structural members in three dimensions. Due to great computational difficulties, there are only few publications on the