Polymer Mechanics

, Volume 7, Issue 6, pp 952–956 | Cite as

Solution of the problems of a perforated disk, a conical bar, and a flat wedge of nonlinear viscoelastic material in pure shear, torsion, and bending, respectively

  • V. V. Kolokol'chikov


Exact solutions and approximations have been obtained for the problems of a disk with an opening twisted by opposite moments uniformly distributed over the inner and outer surfaces and of a conical bar twisted by a moment applied at the vertex of the cone. An approximate solution has been found for the problem of a flat wedge bent by pressure uniformly distributed along one of its sides. The disk is made of nonlinear viscoelastic material. In [1] it was proposed that problems for such a material be solved by the method of approximations. The rheological law of the nonlinear viscoelastic material of the cone and the wedge in Laplace—Carson transforms is the relation of the theory of small elastoplastic deformations with a power law of strain hardening.


Exact Solution Approximate Solution Outer Surface Strain Hardening Viscoelastic Material 
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Literature cited

  1. 1.
    V. V. Kolokol'chikov, Mekhan. Polim., No. 1, 66 (1971).Google Scholar
  2. 2.
    G. Kauderer, Nonlinear Mechanics, Springer Verlag (1958).Google Scholar
  3. 3.
    A. A. Il'yushin, Plasticity [in Russian], Moscow (1948).Google Scholar
  4. 4.
    V. V. Sokolovskii, Theory of Plasticity [in Russian], Moscow (1969).Google Scholar

Copyright information

© Consultants Bureau, a division of Plenum Publishing Corporation 1974

Authors and Affiliations

  • V. V. Kolokol'chikov

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