On necessary and sufficient conditions of strong ellipticity of equilibrium equations for certain classes of anisotropic linearly elastic materials

Within the framework of linear elasticity of anisotropic solids, the strong ellipticity (SE) condition is discussing. In this paper, the SE‐condition is deriving for 19 classes of 32 known ones of anisotropy. For each class SE‐condition reduces to a finite set of elementary inequalities. As a specia...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik 2016-09, Vol.96 (9), p.1096-1102
Main Authors: Zubov, Leonid M., Rudev, Alexander N.
Format: Article
Language:English
Subjects:
Anisotropy
Computational fluid dynamics
Economic models
Elastic anisotropy
Elasticity
Ellipticity
Equilibrium equations
Hadamard's inequality
incompressibility
Inequalities
linear elasticity
Mathematical analysis
Strong ellipticity
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Summary:Within the framework of linear elasticity of anisotropic solids, the strong ellipticity (SE) condition is discussing. In this paper, the SE‐condition is deriving for 19 classes of 32 known ones of anisotropy. For each class SE‐condition reduces to a finite set of elementary inequalities. As a special case, incompressible materials are also considered. Within the framework of linear elasticity of anisotropic solids, the strong ellipticity (SE) condition is discussing. In this paper, the SE‐condition is deriving for 19 classes of 32 known ones of anisotropy. For each class SE‐condition reduces to a finite set of elementary inequalities. As a special case, incompressible materials are also considered.
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.201500167