GENERAL SOLUTION FOR THE TWO-DIMENSIONAL SYSTEM OF STATIC LAME’S EQUATIONS WITH AN ASYMMETRIC ELASTICITY MATRIX Full article
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Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 |
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| Output data | Year: 2018, Volume: 12, Number: 1, Pages: 126-135 Pages count : 10 DOI: 10.1134/S1990478918010118 | ||
| Tags | Cauchy elasticity; eigenbasis; eigenmodule; general solution; quasielasticity; transversal isotropy; two-dimensional isotropy | ||
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Abstract:
We study a two-dimensional system of equations of linear elasticity theory in the case when the symmetric stress and strain tensors are related by an asymmetric matrix of elasticity moduli or elastic compliances. The linear relation between stresses and strains is written in an invariant form which contains three positive eigenmodules in the two-dimensional case. Using a special eigenbasis in the strain space, it is possible to write the constitutive equations with a symmetric matrix, i.e., in the same way as in the case of hyperelasticity. We obtain a representation of the general solution of two-dimensional equations in displacements as a linear combination of the first derivatives of two functions which satisfy two independent harmonic equations. The obtained representation directly implies a generalization of the Kolosov–Muskhelishvili representation of displacements and stresses in terms of two analytic functions of complex variable. We consider all admissible values of elastic parameters, including the case when the system of differential equations may become singular. We provide an example of solving the problem for a plane with a circular hole loaded by constant stresses.
Cite:
OSTROSABLIN N.I.
GENERAL SOLUTION FOR THE TWO-DIMENSIONAL SYSTEM OF STATIC LAME’S EQUATIONS WITH AN ASYMMETRIC ELASTICITY MATRIX
Journal of Applied and Industrial Mathematics. 2018. V.12. N1. P.126-135. DOI: 10.1134/S1990478918010118 Scopus РИНЦ OpenAlex
GENERAL SOLUTION FOR THE TWO-DIMENSIONAL SYSTEM OF STATIC LAME’S EQUATIONS WITH AN ASYMMETRIC ELASTICITY MATRIX
Journal of Applied and Industrial Mathematics. 2018. V.12. N1. P.126-135. DOI: 10.1134/S1990478918010118 Scopus РИНЦ OpenAlex
Original:
Остросаблин Н.И.
ОБЩЕЕ РЕШЕНИЕ ДВУМЕРНОЙ СИСТЕМЫ СТАТИЧЕСКИХ УРАВНЕНИЙ ЛАМЕ ЛИНЕЙНОЙ УПРУГОСТИ С НЕСИММЕТРИЧНОЙ МАТРИЦЕЙ МОДУЛЕЙ УПРУГОСТИ
Сибирский журнал индустриальной математики. 2018. Т.21. №1 (73). С.61-71. РИНЦ
ОБЩЕЕ РЕШЕНИЕ ДВУМЕРНОЙ СИСТЕМЫ СТАТИЧЕСКИХ УРАВНЕНИЙ ЛАМЕ ЛИНЕЙНОЙ УПРУГОСТИ С НЕСИММЕТРИЧНОЙ МАТРИЦЕЙ МОДУЛЕЙ УПРУГОСТИ
Сибирский журнал индустриальной математики. 2018. Т.21. №1 (73). С.61-71. РИНЦ
Identifiers:
| Scopus: | 2-s2.0-85043252646 |
| Elibrary: | 35537639 |
| OpenAlex: | W2793179347 |