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On a spatial generalization of the Kolosov–Muskhelishvili formulae
Author(s) -
Bock S.,
Gürlebeck K.
Publication year - 2008
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.1033
Subject(s) - mathematics , generalization , biharmonic equation , hypercomplex number , representation (politics) , algebra over a field , construct (python library) , basis (linear algebra) , pure mathematics , mathematical analysis , quaternion , geometry , politics , political science , computer science , law , programming language , boundary value problem
The main goal of this paper is to construct a spatial analog to the Kolosov–Muskhelishvili formulae using the framework of the hypercomplex function theory. We prove a generalization of Goursat's representation theorem for solutions of the biharmonic equation in three dimensions. On the basis of this result, we construct explicitly hypercomplex displacement and stress formulae in terms of two monogenic functions. Copyright © 2008 John Wiley & Sons, Ltd.