Previous |  Up |  Next


boundary value problems for differential equations; variational methods; existence and uniqueness theorems; dependence of solutions of PDE on parameters; rock bolt systems
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.
[Malik:1997] J. Malík: Mathematical modelling of rock bolt systems I . Appl. Math. 43 (1998), 413–438. DOI 10.1023/A:1023217304547 | MR 1652100
[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
[NH:ARMA] J. Nečas, I. Hlaváček: On inequalities of Korn’s type. Arch. Rational Mech. Anal. 36 (1970), 305–334. DOI 10.1007/BF00249518 | MR 0252844
[KJF:1977] A. Kufner, O. John, S. Fučík: Functional Spaces. Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1977. MR 0482102
[Sobolev:1988] A. L. Sobolev: Some Applications of Functional Analysis in Mathematical Physics. Nauka, Moscow, 1988. (Russian)
[Cea:1971] J. Céa: Optimisation, Théorie et Algorithmes. Dunod, Paris, 1971. MR 0298892
[EkTe:1974] J. Ekland, R. Temam: Analyse Convexe et Problémes Variationnels. Dunod, Paris, 1974.
Partner of
EuDML logo