Variable separation method for solving boundary value problems of isotropic linearly viscoelastic bodies
| Autor: | A. A. Vakurov, M. S. Pavlov, A A Svetashkov, N. A. Kupriyanov |
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| Rok vydání: | 2020 |
| Předmět: |
Mechanical Engineering
Mathematical analysis Boundary problem Isotropy Computational Mechanics Boundary (topology) 02 engineering and technology 01 natural sciences Viscoelasticity 010305 fluids & plasmas Moment (mathematics) 020303 mechanical engineering & transports 0203 mechanical engineering 0103 physical sciences Solid mechanics Boundary value problem Variable (mathematics) Mathematics |
| Zdroj: | Acta Mechanica. 231:3583-3606 |
| ISSN: | 1619-6937 0001-5970 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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