Engineering Transactions,
9, 4, pp. 725-741, 1961
Zastosowanie Nieliniowej Teorii Sprężystości do Obliczania Pewnych Typów Łączników Gumowych
This is a continuation of the author's papers [1] and [2] devoted to the application of the methods of (geometrically and physically) non-linear theory of elasticity to the computation of rubber connecting pieces.
The problem under consideration in the present paper is that of circularly symmetric shearing of cylindrical connecting pieces in which a cylindrical rubber part has been pressed between two metal tubes and the problem of axial torsion of cylindrical connecting pieces in which the cylindrical rubber part has been joined to the metal tubes during the vulcanization process. Both problems are solved assuming that rubber is incompressible, the elastic potential being assumed in a form characterized by three material constants (cf. [1]). Particular attention is devoted to the obtainment of the relations between the unit-shear force and the corresponding axial displacement in the first problem and between the unit torque and the corresponding angle of twist in the second problem.
The case of the Mooney material is considered. It is shown that the present author's solutions constitute a generalization of the results obtained by R. S. RIVLIN, A. E. GREEN, W. L. BIDERMAN and others assuming that the properties of the material are in agreement with the Mooney model.
The problem under consideration in the present paper is that of circularly symmetric shearing of cylindrical connecting pieces in which a cylindrical rubber part has been pressed between two metal tubes and the problem of axial torsion of cylindrical connecting pieces in which the cylindrical rubber part has been joined to the metal tubes during the vulcanization process. Both problems are solved assuming that rubber is incompressible, the elastic potential being assumed in a form characterized by three material constants (cf. [1]). Particular attention is devoted to the obtainment of the relations between the unit-shear force and the corresponding axial displacement in the first problem and between the unit torque and the corresponding angle of twist in the second problem.
The case of the Mooney material is considered. It is shown that the present author's solutions constitute a generalization of the results obtained by R. S. RIVLIN, A. E. GREEN, W. L. BIDERMAN and others assuming that the properties of the material are in agreement with the Mooney model.
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References
S. ZAHORSKI, A Form of Elastic Potential for Rubber-Like Materials, Arch. Mech. Stos.; 5, 10 (1959).
S. ZAHORSKT, Kołowo-symetryczne i płaskie ścinanie liczników gumowych w świetle nieliniowej teorii sprężystości, Rozpr. Inzyn., 2, 8 (1960).
L. TRELOAR, The Physics of Rubber Elasticity, Oxford 1949.
A. E. GREEN, W. ZERNA, Theoretical Elasticity, Oxford 1954.
R. S. RIVLIN, Torsion of Rubber Cylinder, J. Appl. Phys., 18 (1947), 444-449.
R. S. RIVLIN, A Note on the Torsion of an Incompressible Highly Elastic Cylinder, Proc. Cambr. Phil. Soc., 45 (1949), 485-487.
[in Russian]
S. ZAHORSKI, Doświadczalne badania niektórych własności mechanicznych gumy, Rozpr. Inzyn., 1, 10 (1962).