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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2006, Volume 47, Issue 4, Pages 124–134
(Mi pmtf2176)
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This article is cited in 7 scientific papers (total in 7 papers)
Affine transformations of the equations of the linear theory of elasticity
N. I. Ostrosablin Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090
Abstract:
This paper deals with the general formulas of affine transformations that preserve invariance of the static equations of the linear theory of elasticity in the case of arbitrary anisotropic materials. The invariance of the equations with respect to affine transformations allows one to model a given anisotropic material by another material. All anisotropic materials are divided into classes of mutually congruent materials. The congruency conditions are obtained for orthotropic and isotropic materials and for orthotropic and transversely isotropic materials.
Keywords:
affine transformations, anisotropy, elastic moduli, congruency, invariance of equations.
Received: 11.10.2005
Citation:
N. I. Ostrosablin, “Affine transformations of the equations of the linear theory of elasticity”, Prikl. Mekh. Tekh. Fiz., 47:4 (2006), 124–134; J. Appl. Mech. Tech. Phys., 47:4 (2006), 564–572
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https://www.mathnet.ru/eng/pmtf2176 https://www.mathnet.ru/eng/pmtf/v47/i4/p124
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