Easy Adaptation of a Commercial Fem Code for Self-Similarity
(1995) In Communications in Numerical Methods in Engineering 11(2). p.117-125- Abstract
- Self‐similar situations are idealized states often referred to in continuum mechanics. Such a situation is generally expected when the formulated problem only involves one significant length parameter. The state at a stationary or at a steadily moving concentrated load may be self‐similar. In heat conductivity, the progressive phase transformation near a point‐shaped heat source results in a self‐similar situation. The problem may be non‐linear and history‐dependent. Thus, an incremental theory is needed, generally implying that the load has to be applied in small increments. However, at self‐similarity the solutions for different loads are similar. The final solution therefore includes its own history, which may be... (More)
- Self‐similar situations are idealized states often referred to in continuum mechanics. Such a situation is generally expected when the formulated problem only involves one significant length parameter. The state at a stationary or at a steadily moving concentrated load may be self‐similar. In heat conductivity, the progressive phase transformation near a point‐shaped heat source results in a self‐similar situation. The problem may be non‐linear and history‐dependent. Thus, an incremental theory is needed, generally implying that the load has to be applied in small increments. However, at self‐similarity the solutions for different loads are similar. The final solution therefore includes its own history, which may be exploited.
This short communication demonstrates how an available FEM code (including many commercial codes) may be conveniently used for investigations of self‐similar situations in solid mechanics. Quasistatic elastic‐plastic problems are considered. The theory covers a general material behaviour including large strains and large deformations. The FEM code must allow for a user‐defined material. The technique is demonstrated on a problem for an edge crack growing while the scale of yielding is large. The result is compared with calculations using a node relaxation technique.
(Less) - Abstract (Swedish)
- Self-similar situations are idealized states often referred to in continuum mechanics. Such a situation is generally expected when the formulated problem only involves one significant length parameter. The state at a stationary or at a steadily moving concentrated load may be self-similar. In heat conductivity, the progressive phase transformation near a point-shaped heat source results in a self-similar situation. The problem may be non-linear and history-dependent. Thus, an incremental theory is needed, generally implying that the load has to be applied in small increments. However, at self-similarity the solutions for different loads are similar. The final solution therefore includes its own history, which may be exploited. This short... (More)
- Self-similar situations are idealized states often referred to in continuum mechanics. Such a situation is generally expected when the formulated problem only involves one significant length parameter. The state at a stationary or at a steadily moving concentrated load may be self-similar. In heat conductivity, the progressive phase transformation near a point-shaped heat source results in a self-similar situation. The problem may be non-linear and history-dependent. Thus, an incremental theory is needed, generally implying that the load has to be applied in small increments. However, at self-similarity the solutions for different loads are similar. The final solution therefore includes its own history, which may be exploited. This short communication demonstrates how an available FEM code (including many commercial codes) may be conveniently used for investigations of self-similar situations in solid mechanics. Quasistatic elastic-plastic problems are considered. The theory covers a general material behaviour including large strains and large deformations. The FEM code must allow for a user-defined material. The technique is demonstrated on a problem for an edge crack growing while the scale of yielding is large. The result is compared with calculations using a node relaxation technique. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/fad83b76-4ea1-4c28-b439-e84cc8d668e2
- author
- Ståhle, P. LU
- publishing date
- 1995
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Communications in Numerical Methods in Engineering
- volume
- 11
- issue
- 2
- pages
- 9 pages
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- wos:A1995QJ72800003
- scopus:84989491938
- ISSN
- 1069-8299
- DOI
- 10.1002/cnm.1640110205
- language
- English
- LU publication?
- no
- additional info
- Stahle, p Stahle, Per/J-3590-2014
- id
- fad83b76-4ea1-4c28-b439-e84cc8d668e2
- date added to LUP
- 2019-06-26 00:47:17
- date last changed
- 2021-01-03 05:18:37
@article{fad83b76-4ea1-4c28-b439-e84cc8d668e2,
abstract = {{Self‐similar situations are idealized states often referred to in continuum mechanics. Such a situation is generally expected when the formulated problem only involves one significant length parameter. The state at a stationary or at a steadily moving concentrated load may be self‐similar. In heat conductivity, the progressive phase transformation near a point‐shaped heat source results in a self‐similar situation. The problem may be non‐linear and history‐dependent. Thus, an incremental theory is needed, generally implying that the load has to be applied in small increments. However, at self‐similarity the solutions for different loads are similar. The final solution therefore includes its own history, which may be exploited.<br/><br/>This short communication demonstrates how an available FEM code (including many commercial codes) may be conveniently used for investigations of self‐similar situations in solid mechanics. Quasistatic elastic‐plastic problems are considered. The theory covers a general material behaviour including large strains and large deformations. The FEM code must allow for a user‐defined material. The technique is demonstrated on a problem for an edge crack growing while the scale of yielding is large. The result is compared with calculations using a node relaxation technique.<br/><br/>}},
author = {{Ståhle, P.}},
issn = {{1069-8299}},
language = {{eng}},
number = {{2}},
pages = {{117--125}},
publisher = {{John Wiley & Sons Inc.}},
series = {{Communications in Numerical Methods in Engineering}},
title = {{Easy Adaptation of a Commercial Fem Code for Self-Similarity}},
url = {{http://dx.doi.org/10.1002/cnm.1640110205}},
doi = {{10.1002/cnm.1640110205}},
volume = {{11}},
year = {{1995}},
}