An exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young’s modulus and constant Poisson’s ratio. In the solution, the cylinder is first approximated by a piecewise homogeneous one, of the same overall dimension and composed of perfectly bonded constituent homogeneous hollow circular cylinders. For each of the constituent cylinders, the solution can be obtained from the theory of homogeneous elasticity in terms of several constants. In the limit case when the number of the constituent cylinders becomes unboundedly large and their thickness tends to infinitesimally small, the piecewise homogeneous hollow circular cylinder reverts to the original nonhomogeneous one, and the constants contained in the solutions for the constituent cylinders turn into continuous functions. These functions, governed by some systems of first-order ordinary differential equations with variable coefficients, stand for the exact elasticity solution of the nonhomogeneous cylinder. Rigorous and explicit solutions are worked out for the ordinary differential equation systems, and used to generate a number of numerical results. It is indicated in the discussion that the developed method can also be applied to hollow circular cylinders with arbitrary, continuous radial nonhomogeneity.
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September 1999
Technical Papers
Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder
Xiangzhou Zhang,
Xiangzhou Zhang
Department of Civil Engineering, Shanghai Tiedao University, Shanghai 200333, P. R. China
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Norio Hasebe
Norio Hasebe
Department of Civil Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan
Search for other works by this author on:
Xiangzhou Zhang
Department of Civil Engineering, Shanghai Tiedao University, Shanghai 200333, P. R. China
Norio Hasebe
Department of Civil Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan
J. Appl. Mech. Sep 1999, 66(3): 598-606 (9 pages)
Published Online: September 1, 1999
Article history
Received:
April 28, 1998
Revised:
February 25, 1999
Online:
October 25, 2007
Citation
Zhang, X., and Hasebe, N. (September 1, 1999). "Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder." ASME. J. Appl. Mech. September 1999; 66(3): 598–606. https://doi.org/10.1115/1.2791477
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