| Title:
|
Mathematical modelling of rock bolt systems. I (English) |
| Author:
|
Malík, Josef |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
43 |
| Issue:
|
6 |
| Year:
|
1998 |
| Pages:
|
413-438 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties. (English) |
| Keyword:
|
boundary value problems for differential equations |
| Keyword:
|
variational methods |
| Keyword:
|
existence and uniqueness theorems |
| Keyword:
|
dependence of solutions of PDE on parameters |
| Keyword:
|
rock bolt systems |
| MSC:
|
35A05 |
| MSC:
|
35A15 |
| MSC:
|
35B30 |
| MSC:
|
35Q72 |
| MSC:
|
73V25 |
| MSC:
|
74L10 |
| idZBL:
|
Zbl 0940.35009 |
| idMR:
|
MR1652100 |
| DOI:
|
10.1023/A:1023217304547 |
| . |
| Date available:
|
2009-09-22T17:59:12Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133889 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/133890 |
| . |
| Reference:
|
[ISRS:1992] : Proceedings of the International Symposium on Rock Support, Sudbury, Ontario, Canada, 16–19 June 1992.Peter K. Kaiser and Dougal R. Greath, A. A. Balkema (eds.), Rotterdam, Brookfield, 1992. |
| Reference:
|
[ISATP:1995] : Proceedings of the International Symposium on Anchors in Theory and Practice, Salzburg, Austria, 9–10 October 1995.Richard Widmann, A.A. Balkema (eds.), Rotterdam, Brookfield, 1995. |
| Reference:
|
[NH:1981] J. Nečas, I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier Scientific Publishing Company, Amsterdam-Oxford-New York, 1981. MR 0600655 |
| Reference:
|
[NH:ARMA] J. Nečas, I. Hlaváček: On Inequalities of Korn’s Type.Arch. Rational Mech. Anal. 36, 305–334. MR 0252844 |
| Reference:
|
[Sobolev:1988] S. L. Sobolev: Some Applications of Functional Analysis in Mathematical Physics.Nauka, Moscow, 1988. (Russian) MR 0986735 |
| Reference:
|
[KJF:1977] A. Kufner, O. John, S. Fučík: Functional Spaces.Academia, Publishing House of the Czechoslovak Academy of Science, Prague, 1977. MR 0482102 |
| Reference:
|
[Fichera:1972] G. Fichera: Existence Theorems in Elasticity.Encyclopedia of Physics, Vol. VI a 2, S. Flüge (ed.), Springer, Berlin, 1972. |
| Reference:
|
[Cea:1971] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris, 1971. MR 0298892 |
| Reference:
|
[EkTe:1974] J. Ekland, R. Temam: Analyse convexe et problémes variationnels.Dunod, Paris, 1974. |
| . |
