Mechanics of Solids (about journal) Mechanics of Solids
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IssuesArchive of Issues2005-2pp.113-120

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K. I. Romanov, "The shapes of a rheonomic bar in a gravity field," Mech. Solids. 40 (2), 113-120 (2005)
Year 2005 Volume 40 Number 2 Pages 113-120
Title The shapes of a rheonomic bar in a gravity field
Author(s) K. I. Romanov (Moscow)
Abstract On the basis of the hypothesis of plane sections, a new solution is obtained for the problem of relating the Lagrange and Euler coordinates in the creep of a bar stretched by the forces of its own weight. A version of the method of successive approximations is proposed. It is shown that the homogeneous strain state can be adopted as the initial approximation which ensures the convergence of the successive approximations. As a result, the time dependence of the bar shape is determined and the fracture time is obtained in accordance with the Hoff scheme corresponding to infinite elongation. The bar shape is studied for large creep strains as a function of the exponent in the constitutive relation for a nonlinearly viscous body.

Two different problems of the bar shape are solved, namely, the direct one, in which the current shape at an arbitrary instant of time is determined for a given initial shape, and the inverse one, in which the lateral bar surface at the initial instant of time is determined for the shape given at a certain instant. The solutions can be applied to the design of new technologies of making elongated crystals and nibs of complicated shapes formed due to a natural source of geomechanical energy.
References
1.  P. F. Papkovich, Theory of Elasticity [in Russian], Oborongiz, Moscow, 1939.
2.  Yu. N. Rabotnov, Creep of Structural Members [in Russian], Nauka, Moscow, 1966.
3.  Rayleigh Lord, The Theory of Sound, MacMillan, Liverpool, 1929.
4.  V. F. Zaytsev and A. D. Polyanin, Handbook on Nonlinear Ordinary Differential Equations [in Russian], Factorial, Moscow, 1977.
5.  E. Kamke, Handbook on Ordinary Differential Equations [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1950.
Received 08 April 2003
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