Article
MSC:
49J40,
73T05,
74A55,
74B99,
74G30,
74H25,
74H99,
74K15,
74M15,
74S05,
74S30 | MR 0723202 | Zbl 0534.73091 | DOI: 10.21136/AM.1983.104054
Full entry |
PDF
(2.6 MB)
Feedback
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
Summary:
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.
References:
[1] J. Céa: Optimisation, Théorie et Algorithrnes. Dunod Paris, 1971. MR 0298892
[2] P. G. Ciarlet: The finite element method for elliptic problems. North-Holland 1978. MR 0520174 | Zbl 0383.65058
[3] G. Duvaut J. L. Lions: Inequalities in mechanics and physics. Berlin, Springer Verlag 1975. MR 0521262
[4] R. Glowinski J. L. Lions R. Trémolieres: Numerical analysis of variational inequalities. North-Holland, Amsterdam, New York 1981. MR 0635927
[5] I. Ekeland R. Temam: Analyse convexe et problèmes variationnels. Dunod, Paris 1974. MR 0463993
[6] J. Haslinger I. Hlaváček: Contact between elastic bodies II. Finite element analysis. Apl. mat. 26, 1981, p. 263-290. MR 0623506
[7] I. Hlaváček J. Haslinger J. Nečas J. Lovíšek: Solution of variational inequalities in mechanics. (Slovak). ALFA-SNTL, 1982. MR 0755152
[8] I. Hlaváček J. Nečas: On inequalities of Korn's type. Arch. Rat. Mech. Anal., 36, 1970, 305-334. DOI 10.1007/BF00249518 | MR 0252844
[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.
[10] N. Kikuchi T. Oden: Contact problems in elasticity. SIAM, Philadelphia, 1981.
[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. MR 0613950
[12] D. Kinderlehrer G. Stampacchia: An introduction to variational inequalities and their applications. Academic Press, 1980. MR 0567696
[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. MR 0464840
[14] J. L. Lions: Quelques méthodes de résolution děs problèmes aux limites non linéaires. Dunod, Paris, 1969. MR 0259693 | Zbl 0189.40603
[15] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia Praha, 1967. MR 0227584
[16] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies: An introduction. Elsevier 1981. MR 0600655
[17] B. L. Pelech: Generalized theory of shells. (Russian). Lvov 1978.
Search
Partner of