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Quaternionic representation of the 3D elastic and thermoelastic boundary problems
Author(s) -
Tsalik Alexander
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180904
Subject(s) - thermoelastic damping , mathematics , quaternion , boundary (topology) , representation (politics) , elasticity (physics) , mathematical analysis , boundary value problem , boundary element method , finite element method , algebra over a field , pure mathematics , geometry , thermal , physics , materials science , politics , meteorology , law , political science , composite material , thermodynamics
This paper contains new representations of the 3D elasticity and thermoelasticity problems, expressed in terms of regular quaternion functions, which in 3D and 4D have properties analogous to those of complex analytical functions in 2D. The known and some new results, described in the paper, are used to formulate boundary 3D problems, related to the theory. The formulae obtained are very similar to those given by Muskhelishvili for 2D boundary problems. The obtained representations can be used for development of a 3D boundary element method in numerical analysis.