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Uniqueness of the Solution of Boundary Value Problems for the Static Equations of Elasticity Theory with a Nonsymmetric Matrix of Elastic Moduli

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Abstract

We prove the uniqueness of a solution of boundary value problems for the static equations of elasticity theory for Cauchy elastic materials with a nonsymmetric (or symmetric but not necessarily positive definite) matrix of elastic moduli. Using eigenstates (eigenbases), we write the linear stress-strain relation in invariant form. There are various ways of writing the constitutive relations, including those using symmetric matrices. The specific strain energy for all cases is represented canonically as a positive definite quadratic form.

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ACKNOWLEDGMENTS

The article was written at the suggestion of Acad. B.D. Annin. The author thanks B.D. Annin and R.I. Ugryumov for useful discussions.

Funding

The work was carried out within the framework of the Program of Fundamental Research of the Siberian Branch of the Russian Academy of Sciences, project no. 2.3.1.3.1.

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    N. I. Ostrosablin

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  1. N. I. Ostrosablin
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Correspondence to N. I. Ostrosablin.

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Translated by V. Potapchouck

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Ostrosablin, N.I. Uniqueness of the Solution of Boundary Value Problems for the Static Equations of Elasticity Theory with a Nonsymmetric Matrix of Elastic Moduli. J. Appl. Ind. Math. 16, 713–719 (2022). https://doi.org/10.1134/S1990478922040123

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  • DOI: https://doi.org/10.1134/S1990478922040123

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