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Iteration method for solving linear viscoelasticity problems

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Abstract

Substantiation is given for a new iteration method that makes it possible to solve, with prescribed accuracy, boundary-value problems of quasistatics of a linearly viscoelastic body. A theorem is proved about the convergence of the iteration processes introduced. An approximate correspondence principle, making it possible to construct a solution for viscoelastic problems from known elastic problems, is obtained as a consequence of the theorem. Examples are given of an approximate determination of the connected-creep function, in terms of which numerous analytical solutions to viscoelasticity problems can be expressed.

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Authors
  1. S. M. Pavlov
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  2. A. A. Svetashkov
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Additional information

Deceased.

Scientific-Research Institute of Applied Mathematics and Mechanics at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 129–136, April, 1993.

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Pavlov, S.M., Svetashkov, A.A. Iteration method for solving linear viscoelasticity problems. Russ Phys J 36, 400–406 (1993). https://doi.org/10.1007/BF00570749

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