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IssuesArchive of Issues2016-6pp.485-509

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

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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 2 June 2015
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892817300345
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