Variable separation method for solving boundary value problems of isotropic linearly viscoelastic bodies

Research output: Contribution to journalArticle

Abstract

The availability of accurate methods to mathematically model and predict the behavior of viscoelastic structures under mechanical, thermal and other loads remains a critical issue in different fields ranging from construction engineering to aerospace. Methods to calculate elastic structures are well developed; however, considering that viscoelastic properties require significant effort, we have developed and tested a new analytical method to solve boundary problems of isotropic linearly viscoelastic bodies. According to the proposed algorithm, to find the solution for a linear viscoelasticity boundary problem, we must replace the elastic constants with some functions of time and then numerically or analytically calculate the stress–strain state of the structure at any moment of its loading history. As a result of the theoretical justification of the proposed method, carried out in three independent ways, identical expressions of effective modules are obtained. The obtained results, as well as testing on solutions to several problems, allow us to conclude that the new analytical method is applicable to the calculation of the stress–strain state of viscoelastic bodies.

Original languageEnglish
Pages (from-to)3583-3606
Number of pages24
JournalActa Mechanica
Volume231
Issue number9
DOIs
Publication statusPublished - 1 Sep 2020

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering

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