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Finite cylindrical deformation of a cord-reinforced rubber belt

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Abstract

The deformations and stresses in an initially straight belt, bent and sheared around a rigid cylindrical drum, are theoretically investigated. The belt is made of a Mooney-type material and reinforced by a cord layer, assumed thin and inextensible. Three types of solutions are obtained, where the actual type is shown to depend on the conditions of the initial application of the belt to the drum.

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Abbreviations

a i :

Cartesian material coordinates of the undeformed body

α :

Arc angle of the deformed body

C 1, C 2 :

Constants in the Mooney strain energy function

f 1, f 2 :

Radial-dependent functions defined by (7)

g ij, gij :

Convariant and contravariant metric tensor components of the undeformed body

G ij, Gij :

Covariant and contravariant metric tensor components of the deformed body

H, H 1 :

Relative shear displacement of the cord

I 1, I 2 :

Strain invariants

λ :

Axial extension ratio

M :

Applied torque per unit width

μ :

Coefficient of friction between belt and drum

p :

Pressure function

R 0, R 1, R 2 :

Inner, cord, resp. outer radii in the deformed state

r, θ, z :

Cylindrical spatial coordinates of the deformed body

σ ij :

Physical stress components of the deformed body

τ ij :

Stress tensor components of the deformed body

T :

Cord tension per unit width

W :

Strain energy function

q :

denotes partial differentiation with respect to q

References

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  4. Treloar, L. R. G., The Physics of Rubber Elasticity, 2nd ed. Oxford Univ. Press, London, 1958.

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  6. Meier, J. H., H. C. Lee, J. W. Raider, and H. D. Conway, J. Appl. Mech. 39 (1972) 767.

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  7. Spencer, A. J. M., Deformations of Fibre-reinforced Materials, Oxford Univ. Press, London, 1972.

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Authors and Affiliations

  1. Div. of Mech., Chalmers Univ. of Technology, Gothenburg, Sweden

    H. Torstensson

Authors
  1. H. Torstensson
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Torstensson, H. Finite cylindrical deformation of a cord-reinforced rubber belt. Appl. Sci. Res. 33, 225–241 (1977). https://doi.org/10.1007/BF00383953

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  • DOI: https://doi.org/10.1007/BF00383953

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