Elastic and Viscoelastic Solutions for Rotating Functionally Graded Hollow and Solid Cylinders

A. M. Zenkour; K. A. Elsibai; D. S. Mashat

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(12): 1457-1471

A. M. Zenkour, K. A. Elsibai, D. S. Mashat. Elastic and Viscoelastic Solutions for Rotating Functionally Graded Hollow and Solid Cylinders[J]. Applied Mathematics and Mechanics, 2008, 29(12): 1457-1471.

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Elastic and Viscoelastic Solutions for Rotating Functionally Graded Hollow and Solid Cylinders

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21859, Saudi Arabia;Permanemtn address: Department of Mathematics, Faculty of Education, Kafr El-sheikh University, Kafr El-Sheikh 33516, Egypt;

Received Date: 2008-05-14
Rev Recd Date: 2008-07-15
Publish Date: 2008-12-15

Abstract

Abstract

Analytical solutions for rotating functionally graded hollow and solid long cylinders are developed. Young's modulus and material density of the cylinder are assumed to vary exponentially through the radial direction and Poisson's ratio was assumed to be constant.A unified governing equation was derived from the equilibrium equations,compatibility equation,deformation theory of elasticity and the stress-strain relationships.The governing second-order differential equation was solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders.Dependence of stresses in the cylinder on the inhomogeneous parameters,geometry and boundary conditions was examined and discussed.Proposed solution was validated by comparing the results for rotating functionally graded hollow and solid cylinders to the results for rotating homogeneous isotropic cylinders.In addition,a viscoelastic solution for the rotating viscoelastic cylinder was presented.Moreover,the dependence of stresses in hollow and solid cylinders on the time parameter was examined.
- rotating,
- hollow cylinder,
- solid shaft,
- functionally graded materials

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References(25)

References

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