| Title:
|
Mathematical modelling of rock bolt systems. II (English) |
| Author:
|
Malík, Josef |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
177-203 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main goal of the paper is to describe a reinforcement consisting of fully grouted bolts, which is applied to stabilizing underground openings and tunnels. After a variational formulation is given, the existence and uniqueness is proved. Some asymptotic results that make it possible to replace the real system with a continuous one more suitable for discretization are presented. Some other types of reinforcements and properties are studied. (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:
|
74G25 |
| idZBL:
|
Zbl 1058.74036 |
| idMR:
|
MR1757240 |
| DOI:
|
10.1023/A:1023066827495 |
| . |
| Date available:
|
2009-09-22T18:03:21Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133890 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/133889 |
| . |
| Reference:
|
[Malik:1997] J. Malík: Mathematical modelling of rock bolt systems I .Appl. Math. 43 (1998), 413–438. MR 1652100, 10.1023/A:1023217304547 |
| 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 (1970), 305–334. MR 0252844, 10.1007/BF00249518 |
| Reference:
|
[KJF:1977] A. Kufner, O. John, S. Fučík: Functional Spaces.Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1977. MR 0482102 |
| Reference:
|
[Sobolev:1988] A. L. Sobolev: Some Applications of Functional Analysis in Mathematical Physics.Nauka, Moscow, 1988. (Russian) |
| 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. |
| . |
