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ψ ‐Hyperholomorphic functions and a Kolosov–Muskhelishvili formula
Author(s) -
Bock S.,
Gürlebeck K.,
Legatiuk D.,
Nguyen H. M.
Publication year - 2015
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.3431
Subject(s) - holomorphic function , mathematics , generalization , algebra over a field , pure mathematics , function (biology) , mathematical analysis , evolutionary biology , biology
Holomorphic function theory is an effective tool for solving linear elasticity problems in the complex plane. The displacement and stress field are represented in terms of holomorphic functions, well known as Kolosov–Muskhelishvili formulae. InR 3 , similar formulae were already developed in recent papers, using quaternionic monogenic functions as a generalization of holomorphic functions. However, the existing representations use functions fromR 3toR 4 , embedded in H . It is not completely appropriate for applications inR 3 . In particular, one has to remove many redundancies while constructing basis solutions. To overcome that problem, we propose an alternative Kolosov–Muskhelishvili formula for the displacement field by means of a (paravector‐valued) monogenic, an anti‐monogenic and a ψ ‐hyperholomorphic function. Copyright © 2015 John Wiley & Sons, Ltd.