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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
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.
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Received: 16.06.2022 Revised: 18.08.2022 Accepted: 29.09.2022
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
Linking options:
https://www.mathnet.ru/eng/sjim1199 https://www.mathnet.ru/eng/sjim/v25/i4/p107
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