Contact problem of two elastic bodies. I

Vladimír Janovský; Petr Procházka

Aplikace matematiky (1980)

  • Volume: 25, Issue: 2, page 87-109
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Janovský, Vladimír, and Procházka, Petr. "Contact problem of two elastic bodies. I." Aplikace matematiky 25.2 (1980): 87-109. <http://eudml.org/doc/15135>.

@article{Janovský1980,
abstract = {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.},
author = {Janovský, Vladimír, Procházka, Petr},
journal = {Aplikace matematiky},
keywords = {two-dimensional version of tunnel wall; isotropic elastic bodies; infinitesimal displacement; continuous; uniqueness; existence; two-dimensional version of tunnel wall; isotropic elastic bodies; infinitesimal displacement; continuous; uniqueness; existence},
language = {eng},
number = {2},
pages = {87-109},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Contact problem of two elastic bodies. I},
url = {http://eudml.org/doc/15135},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Janovský, Vladimír
AU - Procházka, Petr
TI - Contact problem of two elastic bodies. I
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 2
SP - 87
EP - 109
AB - 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.
LA - eng
KW - two-dimensional version of tunnel wall; isotropic elastic bodies; infinitesimal displacement; continuous; uniqueness; existence; two-dimensional version of tunnel wall; isotropic elastic bodies; infinitesimal displacement; continuous; uniqueness; existence
UR - http://eudml.org/doc/15135
ER -

References

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  1. G. Duvaut J. L. Lions, Inequalities in Mechanics and Physics, Springer Verlag, Berlin 1976. (1976) MR0521262
  2. 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. (1973) 
  3. I. Hlaváček J. Nečas, 10.1007/BF00249519, Arch. Rat. Mech. Anal., 36, 312 - 334, 1970. (1970) MR0252845DOI10.1007/BF00249519
  4. V. Janovský, Contact problem of two elastic bodies, Technical Report BICOM 77-2, Institute of Computational Math., Brunel University, Uxbridge, England. 
  5. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Mason, Paris, 1967. (1967) MR0227584
  6. M. Cotlar R. Cignoli, An Introduction to Functional Analysis, North-Holland Publishing Co., Amsterdam, 1974. (1974) MR0405049

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