The method of fundamental solutions for axisymmetric elasticity problems
type: Item
instance of: scholarly article
title: The method of fundamental solutions for axisymmetric elasticity problems
zbMATH Open document ID: 1011.74005
published in: Computational Mechanics
publication date: 2003-06-02T00:00:00Z
review text: A method of fundamental solutions is proposed to obtain approximate solutions for axisymmetric boundary value problems of linear homogeneous isotropic elastostatics. The axially symmetric fundamental solutions for infinite body are represented in terms of complete elliptic integrals, and an approximate solution is expressed as a linear combination of fundamental solutions with singularities outside the domain of the problem, e.g., with singularities placed uniformly around the domain at a fixed distance along the normal to the boundary. The locations of these singularities and the coefficients of fundamental solutions in the linear combination are determined by a least square fit of boundary data. The method is illustrated by numerical solution of the problem for a finite cylinder under uniform axial tension and by numerical solution to the problem of torsion of a hollow finite cylinder subject to mixed boundary conditions. The authors also propose an extension of the method to examine axisymmetric bodies with non-axisymmetric boundary conditions.
reviewed by: Józef Ignaczak
Mathematics Subject Classification ID: 74B05
zbMATH DE Number: 1491157
zbMATH Keywords: method of fundamental solutions
zbMATH Keywords: approximate solutions
zbMATH Keywords: axisymmetric boundary value problems
zbMATH Keywords: linear homogeneous isotropic elastostatics
zbMATH Keywords: elliptic integrals
zbMATH Keywords: singularities
zbMATH Keywords: finite cylinder
zbMATH Keywords: uniform axial tension
zbMATH Keywords: torsion
zbMATH Keywords: hollow finite cylinder
author: A. Karageorghis
author: Graeme Fairweather
MaRDI profile type: Publication
full work available at URL: s004660050500
OpenAlex ID: W2029214048
DOI: 10.1007/S004660050500
description: scientific article; zbMATH DE number 1491157