ψ‐Hyperholomorphic functions and a Kolosov–Muskhelishvili formula |
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| Authors: | S Bock K Gürlebeck D Legatiuk H M Nguyen |
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| Affiliation: | 1. Chair of Applied Mathematics, Bauhaus‐Universit?t Weimar, Germany;2. Research Training Group 1462, Bauhaus‐Universit?t Weimar, Germany |
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| Abstract: | 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. In  , similar formulae were already developed in recent papers, using quaternionic monogenic functions as a generalization of holomorphic functions. However, the existing representations use functions from  to  , embedded in  . It is not completely appropriate for applications in  . 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. |
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| Keywords: | harmonic functions hyperholomorphic functions linear elasticity quaternion analysis representation formulae uniqueness problem |
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