Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder

[+] Author and Article Information
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 66(3), 598-606 (Sep 01, 1999) (9 pages) doi:10.1115/1.2791477 History: Received April 28, 1998; Revised February 25, 1999; Online October 25, 2007


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.

Copyright © 1999 by The American Society of Mechanical Engineers
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