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

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

Journal

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789

Output data

Year: 2022, Volume: 16, Number: 4, Pages: 713-719 Pages count : 7 DOI: 10.1134/S1990478922040123

Tags

Cauchy elasticity, eigenmoduli, eigenbasis, boundary value problem, uniqueness of solution

Authors

Ostrosablin N.I. ¹

Affiliations

1	Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences

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.

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
Journal of Applied and Industrial Mathematics. 2022. V.16. N4. P.713-719. DOI: 10.1134/S1990478922040123 Scopus РИНЦ OpenAlex

Остросаблин Н.И.
Единственность решения граничных задач статических уравнений теории упругости с несимметричной матрицей модулей упругости
Сибирский журнал индустриальной математики. 2022. Т.25. №4. С.107-115. DOI: 10.33048/SIBJIM.2022.25.409 РИНЦ

Scopus:	2-s2.0-85149997471
Elibrary:	59605671
OpenAlex:	W4323344532

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