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Research Papers

Axisymmetric Stresses in an Elastic Radially Inhomogeneous Cylinder Under Length-Varying Loadings

[+] Author and Article Information
Yuriy Tokovyy

Pidstryhach Institute for Applied Problems of
Mechanics and Mathematics,
National Academy of Sciences of Ukraine,
3-B Naukova Street,
Lviv 79060, Ukraine
e-mail: tokovyy@gmail.com

Chien-Ching Ma

Fellow ASME
Department of Mechanical Engineering,
National Taiwan University,
No. 1 Roosevelt Road, Sec. 4
Taipei 10617, Taiwan
e-mail: ccma@ntu.edu.tw

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 1, 2016; final manuscript received August 13, 2016; published online September 8, 2016. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 83(11), 111007 (Sep 08, 2016) (7 pages) Paper No: JAM-16-1277; doi: 10.1115/1.4034459 History: Received June 01, 2016; Revised August 13, 2016

In this paper, we present an analytical solution to the axisymmetric elasticity problem for an inhomogeneous solid cylinder subjected to external force loadings, which vary within the axial coordinate. The material properties of the cylinder are assumed to be arbitrary functions of the radial coordinate. By making use of the direct integration method, the problem is reduced to coupled integral equations for the shearing stress and the total stress (given by the superposition of the normal ones). By making use of the resolvent-kernel solution, the latter equations were uncoupled and then solved in a closed analytical form. On this basis, the effect of variable material moduli in the stress distribution has been examined with special attention given to the negative Poisson's ratio.

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Figures

Grahic Jump Location
Fig. 2

Full-field distributions of the radial, circumferential, axial, and shearing stresses for the homogeneous material, normalized by p0, with n=0 and ν0=0.3 in Eq. (31) due to the loading profile (Eq. (30)) with λ=1

Grahic Jump Location
Fig. 3

Distribution of the radial stress in an elastic cylinder with material properties (Eq. (31)), where n=1 and m=0 (solid line) and m=2 (dashed line), in cross section z=0 due to force loading (Eq. (30)) with λ=1

Grahic Jump Location
Fig. 4

The axial stress in cross section z=0 of an elastic cylinder with properties (Eq. (31)), where n=1 and m=0 (solid line) and m=2 (dashed line), due to force loading (Eq. (30)) with λ=1

Grahic Jump Location
Fig. 5

The shearing stress in cross sections z=2/2 and z=2 of an elastic cylinder with properties (Eq. (31)), where n=1 and m=0 (solid line) and m=2 (dashed line), due to force loading (Eq. (30)) with λ=1

Grahic Jump Location
Fig. 6

The radial stress in cross section z=0 for: ν=0.5, n=1, and m=0 (curve 1); ν=0, n=1, and m=0 (curve 2); ν=−0.3, n=1, and m=0 (curve 3); ν=−0.5, n=1, and m=0 (curve 4); ν=−0.3, n=1 and m=2 (curve 5); and ν0=2,ν1=−1/2,κ=1,τ=2, n=1, and m=2 (curve 6)

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