On a spatial generalization of the Kolosov-Muskhelishvili formulae

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 o...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 32; no. 2; pp. 223 - 240
Main Authors: Bock, S., Gürlebeck, K.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 30.01.2009
Wiley
Subjects:
classical linear elasticity
Exact sciences and technology
functions of hypercomplex variables and generalized variables
Goursat's representation theorem
Mathematical analysis
Mathematics
monogenic functions
Potential theory
representation formulae
Sciences and techniques of general use
Three-dimensional calculations
Linear elasticity
Applied mathematics
Biharmonic equation
representation formulae
Mathematical method
monogenic functions
classical linear elasticity
Goursat's representation theorem
functions of hypercomplex variables and generalized variables
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary: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.
Bibliography:ArticleID:MMA1033
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content type line 23
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.1033