The use of complex valued functions for the solution of three-dimensional elasticity problems
type: Item
instance of: scholarly article
title: The use of complex valued functions for the solution of three-dimensional elasticity problems
zbMATH Open document ID: 0619.73004
DOI: 10.1007/BF00044194
author: Reinhard Piltner
published in: Journal of Elasticity
publication date: 1987-01-01T00:00:00Z
review text: For the treatment of plane elasticity problems the use of complex functions has turned out to be an elegant and effective method. The complex formulation of stresses and displacements resulted from the introduction of a real stress function which has to satisfy the 2- dimensional biharmonic equation. It can be expressed therefore with the aid of complex functions. In this paper the fundamental idea of characterizing the elasticity problem in the case of zero body forces by a biharmonic stress function represented by complex valued functions is extended to 3-dimensional problems. The complex formulas are derived in such a way that the Muskhelishvili formulation for plane strain is included as a special case. As in the plane case, arbitrary complex valued functions can be used to ensure the satisfaction of the governing equations. Within the solution of an analytical example some advantages of the presented method are illustrated.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 31B30
Mathematics Subject Classification ID: 74B10
zbMATH DE Number: 4005682
zbMATH Keywords: zero body forces
zbMATH Keywords: biharmonic stress function
zbMATH Keywords: complex valued functions
zbMATH Keywords: 3-dimensional problems
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00044194
OpenAlex ID: W2051986492
description: scientific article; zbMATH DE number 4005682