Solutions of Lamé–Navier System in Ball Shell Domain

Solutions of the Lamé–Navier system in R 3 have been represented in quaternion analysis by several generalized Kolosov–Muskhelishvili formulae. These representations depend on the shape of the domains such as star-like domain, normal domain with respect to one direction and complement of a star-like...

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Bibliographic Details
Published in:Journal of elasticity 2022, Vol.150 (2), p.327-339
Main Author: Dinh, Doan Cong
Format: Article
Language:English
Subjects:
Biomechanics
Classical and Continuum Physics
Classical Mechanics
Domains
Engineering
Fluid flow
Materials Science
Mathematical Applications in the Physical Sciences
Quaternions
Series expansion
Theoretical and Applied Mechanics
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Summary:Solutions of the Lamé–Navier system in R 3 have been represented in quaternion analysis by several generalized Kolosov–Muskhelishvili formulae. These representations depend on the shape of the domains such as star-like domain, normal domain with respect to one direction and complement of a star-like domain. In this paper, we consider the Lamé–Navier system in a ball shell domain Ω = { x ∈ R 3 | r 1 < | x | < r 2 } . Using the Laurent series expansion of monogenic functions, we prove a generalized Kolosov–Muskhelishvili formula in Ω .
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-022-09915-2