An analysis of a contact problem for a cylindrical shell: A primary and dual formulation

Igor Bock; Ján Lovíšek

Aplikace matematiky (1983)

  • Volume: 28, Issue: 6, page 408-429
  • ISSN: 0862-7940

Abstract

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In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.

How to cite

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Bock, Igor, and Lovíšek, Ján. "An analysis of a contact problem for a cylindrical shell: A primary and dual formulation." Aplikace matematiky 28.6 (1983): 408-429. <http://eudml.org/doc/15321>.

@article{Bock1983,
abstract = {In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.},
author = {Bock, Igor, Lovíšek, Ján},
journal = {Aplikace matematiky},
keywords = {sequence converges strongly to solution; existence; frictionless; linear elastic cylindrical shell; rigid stamp; no numerical applications; governing relations; weak form of the problem; dual formulation; saddle functional; unique solution of the FE approximation exists; sequence converges strongly to solution; existence; frictionless; linear elastic cylindrical shell; rigid stamp; no numerical applications; governing relations; weak form of the problem; dual formulation; saddle functional; unique solution of the FE approximation exists},
language = {eng},
number = {6},
pages = {408-429},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An analysis of a contact problem for a cylindrical shell: A primary and dual formulation},
url = {http://eudml.org/doc/15321},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Bock, Igor
AU - Lovíšek, Ján
TI - An analysis of a contact problem for a cylindrical shell: A primary and dual formulation
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 6
SP - 408
EP - 429
AB - In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.
LA - eng
KW - sequence converges strongly to solution; existence; frictionless; linear elastic cylindrical shell; rigid stamp; no numerical applications; governing relations; weak form of the problem; dual formulation; saddle functional; unique solution of the FE approximation exists; sequence converges strongly to solution; existence; frictionless; linear elastic cylindrical shell; rigid stamp; no numerical applications; governing relations; weak form of the problem; dual formulation; saddle functional; unique solution of the FE approximation exists
UR - http://eudml.org/doc/15321
ER -

References

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  2. P. G. Ciarlet, The finite element method for elliptic problems, North-Holland 1978. (1978) Zbl0383.65058MR0520174
  3. G. Duvaut J. L. Lions, Inequalities in mechanics and physics, Berlin, Springer Verlag 1975. (1975) Zbl0331.35002MR0521262
  4. R. Glowinski J. L. Lions R. Trémolieres, Numerical analysis of variational inequalities, North-Holland, Amsterdam, New York 1981. (1981) Zbl0463.65046MR0635927
  5. I. Ekeland R. Temam, Analyse convexe et problèmes variationnels, Dunod, Paris 1974. (1974) MR0463993
  6. J. Haslinger I. Hlaváček, Contact between elastic bodies II. Finite element analysis, Apl. mat. 26, 1981, p. 263-290. (1981) Zbl0465.73144MR0623506
  7. I. Hlaváček J. Haslinger J. Nečas J. Lovíšek, Solution of variational inequalities in mechanics, (Slovak). ALFA-SNTL, 1982. (1982) Zbl0654.73019MR0755152
  8. I. Hlaváček J. Nečas, 10.1007/BF00249518, Arch. Rat. Mech. Anal., 36, 1970, 305-334. (1970) Zbl0193.39002MR0252844DOI10.1007/BF00249518
  9. N. D. Hung G. de Saxcé, Finite element analysis of contact problems based on the unilateral constraints formulation, Structural Control. H.H.E. Leipholz (ed) IUTAM, 1980, p. 341-373. (1980) Zbl0435.73119
  10. N. Kikuchi T. Oden, Contact problems in elasticity, SIAM, Philadelphia, 1981. (1981) Zbl0685.73002
  11. N. Kikuchi Y. Joon Song, Penalty, finite-element approximations of a class of unilateral problems in linear elasticity, Quarterly of Appl. Math. Vol. XXXVIV No 1. April 1981. (1981) Zbl0457.73097MR0613950
  12. D. Kinderlehrer G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, 1980. (1980) Zbl0457.35001MR0567696
  13. A. C. Kravčuk, On Hertz's problem for linearly and nonlinearly elastic bodies of finite dimensions, (Russian). Prikladnaja matematika i mechanika, 1977, t. 41, No 2, s. 28-30. (1977) MR0464840
  14. J. L. Lions, Quelques méthodes de résolution děs problèmes aux limites non linéaires, Dunod, Paris, 1969. (1969) Zbl0189.40603MR0259693
  15. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia Praha, 1967. (1967) MR0227584
  16. J. Nečas I. Hlaváček, Mathematical theory of elastic and elasto-plastic bodies: An introduction, Elsevier 1981. (1981) Zbl0448.73009MR0600655
  17. B. L. Pelech, Generalized theory of shells, (Russian). Lvov 1978. (1978) 

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