 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
|
| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 80, Issue 6 / 2016 | Next article >> |
| L.M. Zubov and A.N. Rudev, "Criterion for the strong ellipticity of the equations of motion of an anisotropic linear-elastic material," J. Appl. Math. Mech. 80 (6), 485-509 (2016) |
| Year |
2016 |
Volume |
80 |
Issue |
6 |
Pages |
485-509 |
| DOI |
10.1016/j.jappmathmech.2017.06.007 |
| Title |
Criterion for the strong ellipticity of the equations of motion of an anisotropic linear-elastic material |
| Author(s) |
L.M. Zubov (The Southern Federal University, Rostov-on-Don, Russia, zubovl@yandex.ru)
A.N. Rudev (The Southern Federal University, Rostov-on-Don, Russia) |
| Abstract |
Two methods of verifying the strong ellipticity of the equations of motion (the SE-condition) for an arbitrary anisotropic linear-elastic material are proposed. A mechanical interpretation of a number of the corollaries of the SE-condition is given. Effective sufficient criteria for the realizability of the SE-condition and the weak version of it, the so-called Hadamard inequality, are found for materials of the monoclinic and 6-constant hexagonal systems. The case of a two-dimensional space is considered. Finite sets of elementary inequalities that are equivalent to the SE-condition and the Hadamard inequality are presented for materials of a 7-constant tetragonal system as well as a simple sufficient criterion for the ellipticity of the equilibrium equations of a uniform medium. Numerical examples are analysed and a comparison of the different methods of verifying the SE-condition is presented. |
| Received |
02 June 2015 |
| Link to Fulltext |
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