Abstract
In this paper, an analytical and numerical study of strain fields, stress fields and displacements in a rotating hollow cylinder, whose walls were completely made in Functionally Graded Materials (FGM), was conducted. We have considered the rotating hollow cylinder submitted to an asymmetric radial loading. It is assumed that, because of the functional graduation of the material, the mechanical properties such as Young elastic modulus and the density varies in the radial direction, in accordance with a the power law function. The inhomogeneity parameter was selected between -1 and 1. On the basis of the second law of Newton, Hooke’s law and the strain-stress relationship, we established the differential equation which governs the equilibrium for a rotating hollow cylinder. We found the analytical solution and compared to the numerical solution obtained by using the shooting method and the fourth order Runge-Kutta algorithm. The analytical and numerical results lead to the conclusion that the magnitude of the tangential stresses is greater than that of the radial stresses. The changes due to the graduation of FGM does not produce consistent variations in the distribution of radial stresses, but strongly affects the distribution of tangential stresses. The tangential stresses, tangential strains and displacements are much higher at the inner surface of the cylinder wall. The internal radial pressure intensely affects the radial stresses and the radial strain.
Highlights
Rotary devices such as disks, cylinders and even spheres have been widely used in mechanical applications and engineering including steam turbines and gas rotors, turbine generators and jet engines, internal combustion engines, boat propellers or even reciprocating and centrifugal compressors [1]-[15]
An analytical and numerical study of strain fields, stress fields and displacements in a rotating hollow cylinder, whose walls were completely made in Functionally Graded Materials (FGM), was conducted
We have considered the rotating hollow cylinder submitted to an asymmetric radial loading
Summary
Rotary devices such as disks, cylinders and even spheres have been widely used in mechanical applications and engineering including steam turbines and gas rotors, turbine generators and jet engines, internal combustion engines, boat propellers or even reciprocating and centrifugal compressors [1]-[15] In such mechanical applications, the rotating hollow cylinder is often subject to different requirements with diverse characteristics. The optimization of the modeling and design of homogeneous hollow cylinder, for example to reduce the risk of accidents and disfunctioning of systems in which they are been integrated, require the understanding of their elasto-plastic regime. This topic has been so far extensively treated. The estimation of strain and stress fields and displacement in the rotating hollow cylinders constructed on the basis of the FGM is an important and actual topic in engineering, but remains poorly investigated
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