Contact between elastic bodies. II. Finite element analysis

Jaroslav Haslinger; Ivan Hlaváček

Aplikace matematiky (1981)

  • Volume: 26, Issue: 4, page 263-290
  • ISSN: 0862-7940

Abstract

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The paper deals with the approximation of contact problems of two elastic bodies by finite element method. Using piecewise linear finite elements, some error estimates are derived, assuming that the exact solution is sufficiently smooth. If the solution is not regular, the convergence itself is proven. This analysis is given for two types of contact problems: with a bounded contact zone and with enlarging contact zone.

How to cite

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Haslinger, Jaroslav, and Hlaváček, Ivan. "Contact between elastic bodies. II. Finite element analysis." Aplikace matematiky 26.4 (1981): 263-290. <http://eudml.org/doc/15200>.

@article{Haslinger1981,
abstract = {The paper deals with the approximation of contact problems of two elastic bodies by finite element method. Using piecewise linear finite elements, some error estimates are derived, assuming that the exact solution is sufficiently smooth. If the solution is not regular, the convergence itself is proven. This analysis is given for two types of contact problems: with a bounded contact zone and with enlarging contact zone.},
author = {Haslinger, Jaroslav, Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {piecewise linear elements; error estimate; exact solution sufficiently smooth; solution not regular; convergence; piecewise linear elements; error estimate; exact solution sufficiently smooth; solution not regular; convergence},
language = {eng},
number = {4},
pages = {263-290},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Contact between elastic bodies. II. Finite element analysis},
url = {http://eudml.org/doc/15200},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Hlaváček, Ivan
TI - Contact between elastic bodies. II. Finite element analysis
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 4
SP - 263
EP - 290
AB - The paper deals with the approximation of contact problems of two elastic bodies by finite element method. Using piecewise linear finite elements, some error estimates are derived, assuming that the exact solution is sufficiently smooth. If the solution is not regular, the convergence itself is proven. This analysis is given for two types of contact problems: with a bounded contact zone and with enlarging contact zone.
LA - eng
KW - piecewise linear elements; error estimate; exact solution sufficiently smooth; solution not regular; convergence; piecewise linear elements; error estimate; exact solution sufficiently smooth; solution not regular; convergence
UR - http://eudml.org/doc/15200
ER -

References

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  1. J. Haslinger I. Hlaváček, Contact between elastic bodies. Part I. Continuous problems, Apl. Mat. 25 (1980), 324-348. (1980) MR0590487
  2. J. Céa, Optimisation, théorie et algorithmes, Dunod, Paris 1971. (1971) MR0298892
  3. M. Zlámal, 10.1137/0710022, SIAM J. Numer. Anal. 10, (1973), 229-240. (1973) MR0395263DOI10.1137/0710022
  4. G. Strang G. Fix, An analysis of the finite element method, Prentice-Hall, 1973. (1973) MR0443377
  5. J. Nitsche, 10.1007/BF02995904, Abh. Math. Sem. Univ. Hamburg, 36 (1971), 9-15. (1971) MR0341903DOI10.1007/BF02995904
  6. I. Hlaváček J. Lovíšek, Finite element analysis of the Signorini problem in semi-coercive cases, Apl. Mat. 25 (1980), 274-285. (1980) MR0583588
  7. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  8. J. Haslinger, Finite element analysis for unilateral problems with obstacles on the boundary, Apl. Mat. 22(1977), 180-187. (1977) Zbl0434.65083MR0440956
  9. F. Brezzi W. W. Hager P. A. Raviart, 10.1007/BF01404345, Numer. Math. 28 (1977), 431 - 443. (1977) MR0448949DOI10.1007/BF01404345

Citations in EuDML Documents

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  1. Igor Bock, Ján Lovíšek, An analysis of a contact problem for a cylindrical shell: A primary and dual formulation
  2. Jaroslav Haslinger, Ivan Hlaváček, Contact between elastic perfectly plastic bodies
  3. Jaroslav Haslinger, Ivan Hlaváček, Contact between elastic bodies. III. Dual finite element analysis
  4. Van Bon Tran, Dual finite element analysis for contact problem of elastic bodies with an enlarging contact zone
  5. Z. Belhachmi, J.-M. Sac-Epée, S. Tahir, Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity

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