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Mathematical modelling of rock bolt systems. II. (English) Zbl 1058.74036
The author continues Part I [Appl. Math., Praha 43, 413–438 (1998; Zbl 0940.35009)]. A reinforcement consisting of fully grouted elastic bolts is modelled by an elliptic system stemming from linear elasticity applied to both the bolts and the rock mass. The existence and uniqueness of solution is proved. Some asymptotic results enable to replace the real bolt system with a continuous one more suitable for discretization.
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
35Q72 Other PDE from mechanics (MSC2000)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74K99 Thin bodies, structures
74L05 Geophysical solid mechanics
Full Text: DOI EuDML
[1] J. Malík: Mathematical modelling of rock bolt systems I . Appl. Math. 43 (1998), 413-438. · Zbl 0940.35009 · doi:10.1023/A:1023217304547 · eudml:32521
[2] J. Nečas, I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier Scientific Publishing Company, Amsterdam-Oxford-New York, 1981.
[3] J. Nečas, I. Hlaváček: On inequalities of Korn’s type. Arch. Rational Mech. Anal. 36 (1970), 305-334. · Zbl 0193.39001 · doi:10.1007/BF00249518
[4] A. Kufner, O. John, S. Fučík: Functional Spaces. Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1977.
[5] A. L. Sobolev: Some Applications of Functional Analysis in Mathematical Physics. Nauka, Moscow, 1988.
[6] J. Céa: Optimisation, Théorie et Algorithmes. Dunod, Paris, 1971. · Zbl 0211.17402
[7] J. Ekland, R. Temam: Analyse Convexe et Problémes Variationnels. Dunod, Paris, 1974.
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