Mathematical modelling of rock bolt systems. I

Josef Malík

Applications of Mathematics (1998)

  • Volume: 43, Issue: 6, page 413-438
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Malík, Josef. "Mathematical modelling of rock bolt systems. I." Applications of Mathematics 43.6 (1998): 413-438. <http://eudml.org/doc/32521>.

@article{Malík1998,
abstract = {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.},
author = {Malík, Josef},
journal = {Applications of Mathematics},
keywords = {boundary value problems for differential equations; variational methods; existence and uniqueness theorems; dependence of solutions of PDE on parameters; rock bolt systems; non-homogeneous elasticity; quasistatic problems; continuous dependence},
language = {eng},
number = {6},
pages = {413-438},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Mathematical modelling of rock bolt systems. I},
url = {http://eudml.org/doc/32521},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Malík, Josef
TI - Mathematical modelling of rock bolt systems. I
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 6
SP - 413
EP - 438
AB - 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.
LA - eng
KW - boundary value problems for differential equations; variational methods; existence and uniqueness theorems; dependence of solutions of PDE on parameters; rock bolt systems; non-homogeneous elasticity; quasistatic problems; continuous dependence
UR - http://eudml.org/doc/32521
ER -

References

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  1. 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. (1992) 
  2. 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. (1995) 
  3. Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier Scientific Publishing Company, Amsterdam-Oxford-New York, 1981. (1981) MR0600655
  4. On Inequalities of Korn’s Type, Arch. Rational Mech. Anal. 36, 305–334. MR0252844
  5. Some Applications of Functional Analysis in Mathematical Physics, Nauka, Moscow, 1988. (Russian) (1988) MR0986735
  6. Functional Spaces, Academia, Publishing House of the Czechoslovak Academy of Science, Prague, 1977. (1977) MR0482102
  7. Existence Theorems in Elasticity, Encyclopedia of Physics, Vol. VI a 2, S.  Flüge (ed.), Springer, Berlin, 1972. (1972) 
  8. Optimisation, théorie et algorithmes, Dunod, Paris, 1971. (1971) MR0298892
  9. Analyse convexe et problémes variationnels, Dunod, Paris, 1974. (1974) 

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