Calculation of displacements in a viscoelastic square plate with a round cut

Abstract

Calculation of the strained state of structures made of anisotropic viscoelastic materials under the influence of temperatures is reduced to the calculation of the strained state of structures made of elastic materials on the basis of the conformity principle developed earlier.  A method of calculating the strained state of non-uniform anisotropic structures of an arbitrary shape in the case of their static loading under the influence of temperatures has been developed on the basis of this principle. Displacements caused by the influence of external variable pressure and variable temperature field inside a steel square plate with a round cut are calculated. The problem of linear incoherent thermoviscoelasticity selected as a model provides a strict analytical solution, convenient for the analysis of steel parts in different operation modes. 

About the authors

E. Yu. Ivanov

Samara State Transport University

Author for correspondence.
Email: planeta@samaramail.ru

Postgraduate student

Russian Federation

References

  1. Ermolenko G.Yu., Ivanov E.Yu. The principles of correlation between statical boundary value problems of thermoviscoelasticity and thermoelasticity. Journal of Applied Mathematics and Mechanics. 2014. V. 78, Iss. 6. P. 613-616. doi: 10.1016/j.jappmathmech.2015.04.008
  2. Gorlach B.A., Ermolenko G.Yu. Method of basic functions for the solution problems of mathematics and mechanics. Vestnik SamGTU. Seriya: Fiziko-matematicheskie nauki. No 26. 2004. P. 122-126. (In Russ)
  3. Il'yushin A.A., Pobedrya B.E. Osnovy matematicheskoj teorii termovyazkouprugosti [Foundations of the mathematical theory of thermoviscoelasticity]. Moscow: Nauka Publ., 1970. 280 p.

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