Reduction of the Lamé Tensor Equations to the System of Non-Coupled Tetraharmonic Equations

Автор: Georgievskii D.V.
Сборник: Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics
Серия: Understanding Complex Systems
Год издания: 2021
Издательство: Springer Nature
Местоположение издательства: Switzerland
Первая страница: 27
Последняя страница: 33
DOI: 10.1007/978-3-030-50302-4_2
Аннотация: Reductions of the systems of equations in terms of displacements in 3Delasticity to the systems of higher orders based on the operators which are suitablefor both numerical and analytical investigation better than the Lamé operator, arecalled representations of the solution. The Galerkin representation is one of suchtypical procedures in classical theory of elasticity. Below the Galerkin procedure isgeneralized in conformity to the systems generated by linear symmetric tensor (of thesecond rank) differential operator of the forth order acting on symmetric tensor field.Reduction of such systems to the systems of non-coupled tetraharmonic equationsis realized. The fundamental solutions of the derived tetraharmonic equations inmany-dimensional spaces are given.
Добавил в систему: Георгиевский Дмитрий Владимирович

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