Iterative method for solving quasistatic nonlinear viscoelastic problems

Authors

  • Roman Georgievich Kulikov Perm State Technical University
  • Nikolay Alexandrovich Trufanov Perm State Technical University

DOI:

https://doi.org/10.7242/1999-6691/2009.2.3.22

Keywords:

nonlinear viscoelasticity, boundary-value problem, numerical methods, iterative algorithm

Abstract

Construction of an iterative procedure for nonlinear viscoelastic boundary-value problems is considered. The proposed approach allows us to obtain the solution of the problem by solving the sequence of simpler linear elastic problems. Substantiation of the convergence of iterations is given, and the main merits of the developed method are formulated. Two model problems are solved to illustrate the construction of iterative schemes by different approximate methods and to assess the practical convergence of the iterative procedure.

Downloads

Download data is not yet available.

References

Pavlov S.M., Svetaskov A.A. Iteracionnyj metod resenia zadac linejnoj vazkouprugosti // Izv. VUZov. Fizika. - 1993. - T. 36, vyp.4. - S.129-136.
Il’usin A.A., Pobedra B.E. Osnovy matematiceskoj teorii termovazkouprugosti - M.: Nauka, 1970. - 280s.
Arutunan N.H., Kolmanovskij V.V. Teoria polzucesti neodnorodnyh tel. - M.: Nauka, 1983. - 336s.
Bugakov I.I. Polzucest’ polimernyh materialov (teoria i prilozenia). - M.: Nauka, 1973. - 288s.
Pobedra B.E. Mehanika kompozicionnyh materialov - M.: Izd-vo MGU, 1984 - 336s.
Pobedra B.E. Matematiceskaa teoria nelinejnoj vazkouprugosti // V kn.: Uprugost’ i neuprugost’. Vyp. 3. - M.: Izd-vo Mosk. un-ta, 1973. - S.95-173.
Sardakov I.N., Troanovskij I.E., Trufanov N.A. Metod geometriceskogo pogruzenia dla resenia kraevyh zadac teorii uprugosti. - Sverdlovsk: UNC AN SSSR,1984. - 66s.
Sardakov I.N., Trufanov N.A., Matveenko V.P. Metod geometriceskogo pogruzenia v teorii uprugosti. - Ekaterinburg: UrO RAN, 1999. - 298s.
Demidov S.P. Teoria uprugosti. - M.: Vyss. skola, 1979. - 432s.
Zenkevic O., Morgan K. Konecnye elementy i approksimacia: - M.: Mir, 1986. - 318s.

Downloads

Published

2009-07-01

Issue

Vol. 2 No. 3 (2009)

Section

Articles

License

Copyright (c) 2009 Computational Continuum Mechanics

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Kulikov, R. G., & Trufanov, N. A. (2009). Iterative method for solving quasistatic nonlinear viscoelastic problems. Computational Continuum Mechanics, 2(3), 44-56. https://doi.org/10.7242/1999-6691/2009.2.3.22