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Sibirskii Zhurnal Industrial'noi Matematiki, 2022, Volume 25, Number 4, Pages 107–115
DOI: https://doi.org/10.33048/SIBJIM.2021.25.409
(Mi sjim1199)
 

Uniqueness of the solution of boundary value problems of static equations of elasticity theory with an asymmetric matrix of elastic modules

N. I. Ostrosablin

Lavrentyev Institute of Hydrodynamics SB RAS, pr. Akad. Lavrentyeva 15, Novosibirsk 630090, Russia
References:
Abstract: The uniqueness of the solution of boundary value problems of static equations of elasticity theory for Cauchy elastic materials with an asymmetric matrix of elastic modules and with a symmetric matrix, but not necessarily positive definite, is proved. Using eigenstates (bases), the linear relationship of stresses and deformations is written in an invariant form. There are different ways of writing defining relations, including using symmetric matrices. The specific strain energy for all variants has the canonical form of a positive definite quadratic form.
Keywords: Cauchy elasticity, proper modules, proper basis, boundary value problems, uniqueness of the solution. .
Received: 16.06.2022
Revised: 18.08.2022
Accepted: 29.09.2022
Document Type: Article
UDC: 539.3:517.958
Language: Russian
Citation: N. I. Ostrosablin, “Uniqueness of the solution of boundary value problems of static equations of elasticity theory with an asymmetric matrix of elastic modules”, Sib. Zh. Ind. Mat., 25:4 (2022), 107–115
Citation in format AMSBIB
\Bibitem{Ost22}
\by N.~I.~Ostrosablin
\paper Uniqueness of the solution of boundary value problems of static equations of elasticity theory with an asymmetric matrix of elastic modules
\jour Sib. Zh. Ind. Mat.
\yr 2022
\vol 25
\issue 4
\pages 107--115
\mathnet{http://mi.mathnet.ru/sjim1199}
\crossref{https://doi.org/10.33048/SIBJIM.2021.25.409}
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