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Title: Contact between elastic bodies. I. Continuous problems (English)
Author: Haslinger, Jaroslav
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 25
Issue: 5
Year: 1980
Pages: 324-347
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: Problems of a unilateral contact between bounded bodies without friction are considered within the range of two-dimensional linear elastostatics. Two classes of problems are distinguished: those with a bounded contact zone and with an enlargign contact zone. Both classes can be formulated in terms of displacements by means of a variational inequality. The proofs of existence of a solution are presented and the uniqueness discussed. (English)
Keyword: zero friction
Keyword: small deformations
Keyword: basic relations
Keyword: minimum principles for potential energy
Keyword: conditions which guarantee existence and uniqueness of weak solutions
Keyword: one-dimensional spaces of rigid virtual displacements
MSC: 35P99
MSC: 49J40
MSC: 73T05
MSC: 74A55
MSC: 74M15
idZBL: Zbl 0449.73117
idMR: MR0590487
DOI: 10.21136/AM.1980.103868
Date available: 2008-05-20T18:14:58Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] H. Hertz: Miscellaneous Papers.Mc Millan, London 1896.
Reference: [2] S. H. Chan, I. S. Tuba: A finite element method for contact problems of solid bodies.Intern. J. Mech. Sci, 13, (1971), 615-639. Zbl 0226.73052, 10.1016/0020-7403(71)90032-4
Reference: [3] T. F. Conry, A. Seireg: A mathematical programming method for design of elastic bodies in contact.J.A.M. ASME, 2 (1971), 387-392. 10.1115/1.3408787
Reference: [4] A. Francavilla, O. C. Zienkiewicz: A note on numerical computation of elastic contact problems.Intern. J. Numer. Meth. Eng. 9 (1975), 913 - 924. 10.1002/nme.1620090410
Reference: [5] B. Fredriksson: Finite element solution of surface nonlinearities in structural mechanics.Соmр. & Struct. 6 (1976), 281 - 290. Zbl 0349.73036, 10.1016/0045-7949(76)90003-1
Reference: [6] P. D. Panagiotopoulos: A nonlinear programming approach to the unilateral contact - and friction - boundary value problem in the theory of elasticity.Ing. Archiv 44 (1975), 421 to 432. Zbl 0332.73018, MR 0426584, 10.1007/BF00534623
Reference: [7] G. Duvaut: Problèmes de contact entre corps solides deformables.Appl. Meth. Fund. Anal. to Problems in Mechanics, (317 - 327), ed. by P. Germain and B. Nayroles, Lecture Notes in Math., Springer-Verlag 1976. Zbl 0359.73017, MR 0669228
Reference: [8] G. Duvaut, J. L. Lions: Les inéquations en mécanique et en physique.Paris, Dunod 1972. Zbl 0298.73001, MR 0464857
Reference: [9] A. Signorini: Questioni di elasticità non linearizzata o serni-linearizzata.Rend. di Matem. e delle sue appl. 18 (1959). MR 0118021
Reference: [10] G. Fichera: Boundary value problems of elasticity with unilateral constraints.Encycl. of Physics (ed. by S. Flugge), vol. VIa/2, Springer-Verlag, Berlin 1972.
Reference: [11] I. Hlaváček, J. Nečas: On inequalities of Korn's type.Arch. Ratl. Mech. Anal., 36 (1970), 305-334. Zbl 0193.39002, MR 0252844, 10.1007/BF00249518
Reference: [12] J. Nečas: On regularity of solutions to nonlinear variational inequalities for second-order elliptic systems.Rend. di Matematica 2, (1975), vol. 8, Ser. Vl, 481 - 498. MR 0382827
Reference: [13] J. Nečas, I. Hlaváček: Matematická teorie pružných a pružně plastických těles.SNTL Praha (to appear). English translation: Mathematical theory of elastic and elastoplastic bodies. Elsevier, Amsterdam 1980. MR 0600655


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