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On the Interior Stress Problem for Elastic Bodies

Helsing, Johan LU (2000) In Journal of Applied Mechanics 67(4). p.658-662
Abstract
The classic Sherman-Lauricella integral equation and an integral equation due to Muskhelishvili for the interior stress problem are modified. The modified formulations differ from the classic ones in several respects: Both modifications are based on uniqueness conditions with clear physical interpretations and, more importantly, they do not require the arbitrary placement of a point inside the computational domain. Furthermore, in the modified Muskhelishvili equation the unknown quantity, which is solved for, is simply related to the stress. In Muskhelishvili’s original formulation the unknown quantity is related to the displacement. Numerical examples demonstrate the greater stability of the modified schemes.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Applied Mechanics
volume
67
issue
4
pages
658 - 662
publisher
American Society Of Mechanical Engineers (ASME)
external identifiers
  • scopus:0000256744
ISSN
0021-8936
DOI
10.1115/1.1327251
language
English
LU publication?
no
id
4e0cf6f5-a489-44d8-8b5e-e29d1880bdb3 (old id 4254282)
alternative location
http://www.maths.lth.se/na/staff/helsing/ASME00.pdf
date added to LUP
2014-02-03 12:35:28
date last changed
2017-01-01 04:38:07
@article{4e0cf6f5-a489-44d8-8b5e-e29d1880bdb3,
  abstract     = {The classic Sherman-Lauricella integral equation and an integral equation due to Muskhelishvili for the interior stress problem are modified. The modified formulations differ from the classic ones in several respects: Both modifications are based on uniqueness conditions with clear physical interpretations and, more importantly, they do not require the arbitrary placement of a point inside the computational domain. Furthermore, in the modified Muskhelishvili equation the unknown quantity, which is solved for, is simply related to the stress. In Muskhelishvili’s original formulation the unknown quantity is related to the displacement. Numerical examples demonstrate the greater stability of the modified schemes.},
  author       = {Helsing, Johan},
  issn         = {0021-8936},
  language     = {eng},
  number       = {4},
  pages        = {658--662},
  publisher    = {American Society Of Mechanical Engineers (ASME)},
  series       = {Journal of Applied Mechanics},
  title        = {On the Interior Stress Problem for Elastic Bodies},
  url          = {http://dx.doi.org/10.1115/1.1327251},
  volume       = {67},
  year         = {2000},
}