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Research Papers

Radial Deformation of Cylinders Due to Torsion

[+] Author and Article Information
Srikant Sekhar Padhee1

NMCAD Lab., Department of Aerospace Engineering,  Indian Institute of Science, Bangalore - 560012, Indiasspadhee@gmail.com

Dineshkumar Harursampath

NMCAD Lab., Department of Aerospace Engineering,  Indian Institute of Science, Bangalore - 560012, Indiadinesh@aero.iisc.ernet.in

Latin indices run from 1 to 3 while Greek indices run from 2 to 3.

Repeated indices are summed over their ranges.

1

Corresponding author.

J. Appl. Mech 79(6), 061013 (Sep 21, 2012) (6 pages) doi:10.1115/1.4006803 History: Received February 03, 2011; Posted April 02, 2012; Revised April 22, 2012; Published September 21, 2012; Online September 21, 2012

Classical literature on solid mechanics claims existence of radial deformation due to torsion but there is hardly any literature on analytic solutions capturing this phenomenon. This paper tries to solve this problem in an asymptotic sense using the variational asymptotic method (VAM). The method makes no ad hoc assumptions and hence asymptotic correctness is assured. The VAM splits the 3D elasticity problem into two parts: A 1D problem along the length of the cylinder which gives the twist and a 2D cross-sectional problem which gives the radial deformation. This enables closed form solutions, even for some complex problems. Starting with a hollow cylinder, made up of orthotropic but transversely isotropic material, the 3D problem has been formulated and solved analytically despite the presence of geometric nonlinearity. The general results have been specialized for particularly useful cases, such as solid cylinders and/or cylinders with isotropic material.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Thick cylinder and coordinate system

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Figure 2

Variation of radial deformation with radius and Poisson’s ratio for solid cylinder (Y = 70 GPa)

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Figure 3

Variation of radial deformation with radius for solid cylinder (material: aluminum)

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Figure 4

Variation of radial deformation with radius for hollow cylinder (material: aluminum)

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Figure 5

Variation of radial deformation with Poisson’s ratio for hollow cylinder (material: aluminum)

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Figure 6

Variation of radial deformation with radius for solid cylinder made up of transversely isotropic material

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Figure 7

Variation of radial deformation with radius for hollow cylinder made up of transversely isotropic material

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