| Title:
|
On general boundary value problems and duality in linear elasticity. I (English) |
| Author:
|
Hünlich, Rolf |
| Author:
|
Naumann, Joachim |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
23 |
| Issue:
|
3 |
| Year:
|
1978 |
| Pages:
|
208-230 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The equilibrium state of a deformable body under the action of body forces is described by the well known conditions of equilibrium, the straindisplacement relations, the constitutive law of the linear theory and the boundary conditions. The authors discuss in detail the boundary conditions. The starting point is the general relation between the vectors of stress and displacement on the boundary which can be expressed in terms of a subgradient relation. It is shown that this relation includes as special cases all known classical, bilateral and unilateral boundary conditions. Further, the principle of virtual displacements and the principle of minimum of the potential energy are established and it is shown that these principles are equivalent to the original boundary condition problem. (English) |
| Keyword:
|
boundary value problems |
| Keyword:
|
linear elasticity |
| Keyword:
|
law of interaction |
| Keyword:
|
principle of virtual displacements |
| Keyword:
|
principal of minimum potential energy |
| MSC:
|
35Q20 |
| MSC:
|
46N05 |
| MSC:
|
73C35 |
| MSC:
|
74B99 |
| MSC:
|
74H99 |
| idZBL:
|
Zbl 0401.73025 |
| idMR:
|
MR0489538 |
| DOI:
|
10.21136/AM.1978.103746 |
| . |
| Date available:
|
2008-05-20T18:09:33Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103746 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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[9] F. Lené: Sur les matériaux élastiques à énergie de déformation non quadratique.J. Méc., 13 (1974), 499-534. MR 0375890 |
| Reference:
|
[10] J. J. Moreau: Fonctionelles convexes.College de France, 1966- 1967. MR 0390443 |
| Reference:
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| Reference:
|
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| Reference:
|
[13] J. J. Moreau: La notion de sur-potentiel et les liasions unilaterales en élastostatique.12th Intern. Congr. Appl. Mech. |
| Reference:
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[14] B. Nayroles: Quelques applications variationnelles de la théorie des functions duales à la mécanique de solides.J. Méc., 10 (1971), 263-289. MR 0280053 |
| Reference:
|
[15] B. Nayroles: Duality and convexity in solid equilibrium problems.Laboratoire Méc. et d'Acoustique, C. N. R. S., Marseille 1974. |
| Reference:
|
[16] B. Nayroles: Point de vue algebrique. Convexité et integrandes convexes en mécanique des solides.In: New variational techniques in mathematical physics. C. T. M. E., Ed. Cremonese, Roma 1974, 325-404. |
| Reference:
|
[17] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
|
[18] R. T. Rockafellar: Extension of Fenchel's duality theorem for convex functions.Duke Math. J., 33 (1966), 81-90. Zbl 0138.09301, MR 0187062, 10.1215/S0012-7094-66-03312-6 |
| . |
