Journal of Mathematical Sciences

, Volume 90, Issue 1, pp 1856–1862 | Cite as

On a method of solving two-dimensional problems of the linear theory of viscoelasticity

  • A. A. Kaminskii
  • I. Yu. Podil’chuk


We describe the basic propositions of the linear theory of viscoelasticity. We give transformation formulas for the resolvent integral operators of viscoelasticity with an arbitrary analytic kernel of difference type. The method of computing the irrational operator functions is illustrated by determining the real parameters of the two-dimensional stressed state of an orthotropic plate. Three figures. Bibliography: 7 titles.


Linear Theory Continue Fraction Resolvent Operator Elliptic Hole Difference Type 
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Literature Cited

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    A. A. Kaminskii,Rupture of Viscoelastic Bodies with Cracks [in Russian], Kiev (1990).Google Scholar
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    A. A. Kaminskii and D. A. Gavrilov,Prolonged Rupture of Polymer and Composite Materials with Cracks [in Russian], Kiev (1992).Google Scholar
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    A. A. Kaminskii and S. A. Kekukh, “On a method of solving problems of the linear theory of viscoelasticity for anisotropic materials (taking account of the presence of cracks)’,Prikl. Mekh., No. 4, 82–91 (1994).MathSciNetGoogle Scholar
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    Mathematical Analysis. Functions, Limits, Series, Continued Fractions [in Russian], Moscow (1961).Google Scholar
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    S. G. Lekhnitskii,Theory of Elasticity of an Anisotropic Body [in Russian], Moscow (1977).Google Scholar
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    V. G. Gromov, “On the question of solving boundary-value problems of linear viscoelasticity,”Mekh. Polym. No. 6, 999–1012 (1967).MathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. A. Kaminskii
  • I. Yu. Podil’chuk

There are no affiliations available

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