Article
MSC:
35J65,
49A29,
49D15,
65N15,
73T05,
74A55,
74M15,
74S05 | MR 0560325 | Zbl 0442.73116 | DOI: 10.21136/AM.1980.103844
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Keywords:
two elastic bodies; convergence; continuous model; tunnel problem
two elastic bodies; convergence; continuous model; tunnel problem
Summary:
The goal of the paper is the study of the contact problem of two elastic bodies which is applicable to the solution of displacements and stresses of the earth continuum and the tunnel wall. In this first part the variational formulation of the continuous and discrete model is stated. The second part covers the proof of convergence of finite element method to the solution of continuous problem while in the third part some practical applications are illustrated.
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References:
[1] J. H. Bramble S. Hilbert: Bounds for a class of linear functional with applications to Hermite interpolation. Numer. Math., 16, 1971, 362-369. DOI 10.1007/BF02165007 | MR 0290524
[2] P. K. Ciarlet P. A. Raviart: General Lagrange and Hermite interpolation in $R_m$ with application to finite element methods. Arch. Rat. Mech. Anal. 46, 1972, 172 - 199.
[3] V. Janovský: Contact problem of two elastic bodies. Technical Report BICOM 77-2, Institute of Computational Math., Brunel Univ., England.
[4] V. Janovský P. Procházka: Contact problem of two elastic bodies-Part I. Aplikace matematiky 25 (1980), 87-109. MR 0560325
[5] A. Kufner O. John S. Fučík: Function Spaces. Academia, Prague 1977. MR 0482102
[6] J. Nečas: Les Méthodes directes en théorie des équations elliptiques. Mason, Paris, 1967. MR 0227584
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