Quaternionic functions approach to the transversely isotropic elasticity

The quaternionic functions method is an analytical tool used in elasticity theory. For isotropic elasticity, there are known a few variants of three-dimensional analogues of the Kolosov-Muskhelishvili formulae. In this case, a general solution of the Lamé equation for the spatial theory of elasticit...

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Bibliographic Details
Main Authors: Grigor’ev, Yuri M., Yakovlev, Andrei M.
Format: Conference Proceeding
Language:English
Subjects:
Elastic media
Elastic properties
Elasticity
Lame functions
Mathematical analysis
Matrix algebra
Permafrost
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Summary:The quaternionic functions method is an analytical tool used in elasticity theory. For isotropic elasticity, there are known a few variants of three-dimensional analogues of the Kolosov-Muskhelishvili formulae. In this case, a general solution of the Lamé equation for the spatial theory of elasticity is expressed in terms of two regular quaternionic or monogenic Clifford functions. For the anisotropic elasticity, a close approach exists when equations of equilibrium are factorized by means of matrix algebra. In this report, we will discuss the quaternionic factorization method in the transversely isotropic theory of elasticity. The model of an elastic media with such symmetry is described by five elastic constants, and for example, can be used in the mechanics of rocks in permafrost conditions.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0106216