two-dimensional version of tunnel wall; isotropic elastic bodies; infinitesimal displacement; continuous; uniqueness; existence
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.
 G. Duvaut J. L. Lions: Inequalities in Mechanics and Physics
. Springer Verlag, Berlin 1976. MR 0521262
 M. Fremond: Dual formulation for potentials and complementary energies. Unilateral boundary conditions. Applications to the finite element method. In: The Mathematics of Finite Elements and Applications, J. R. Whiteman (editor). Academia Press, London 1973.
 V. Janovský: Contact problem of two elastic bodies. Technical Report BICOM 77-2, Institute of Computational Math., Brunel University, Uxbridge, England.
 J. Nečas: Les méthodes directes en théorie des équations elliptiques
. Mason, Paris, 1967. MR 0227584
 M. Cotlar R. Cignoli: An Introduction to Functional Analysis
. North-Holland Publishing Co., Amsterdam, 1974. MR 0405049