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Title: Contact between elastic bodies. III. Dual finite element analysis  (English)
Author: Haslinger, Jaroslav
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 26
Issue: 5
Year: 1981
Pages: 321-344
Summary lang: English
Summary lang: Czech
Category: math
Summary: The problem of a unilateral contact between elastic bodies with an apriori bounded contact zone is formulated in terms of stresses via the principle of complementary energy. Approximations are defined by means of self-equilibriated triangular block-elements and an $L2$-error estimate is proven provided the exact solution is regular enough.
Keyword: dual finite element analysis
Keyword: unilateral contact
Keyword: elastic bodies
Keyword: apriori bounded contact zone
Keyword: terms of stresses
Keyword: principle of complementary energy
Keyword: approximations
Keyword: self-equilibriated triangular block-elements
Keyword: $L2$- error estimate
MSC: 49A29
MSC: 49S05
MSC: 65N15
MSC: 65N30
MSC: 73K25
MSC: 73T05
MSC: 74A55
MSC: 74M15
MSC: 74S05
MSC: 74S30
idZBL: Zbl 0513.73088
idMR: MR0631752
Date available: 2008-05-20T18:17:27Z
Last updated: 2015-07-09
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Reference: [1] Haslinger J., Hlaváček I.: Contact between elastic bodies.I. Continuous problems. Apl. mat. 25 (1980), 324-347. II. Finite element analysis. Apl. mat. 26. (1981), 263-290. MR 0590487
Reference: [2] Céa J.: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892
Reference: [3] Watwood V. B., Hartz B. J.: An equilibrium stress field model for finite element solution of two-dimensional elastostatic problems.Int. J. Solids Structures 4 (1968), 857-873. 10.1016/0020-7683(68)90083-8
Reference: [4] Hlaváček I.: Convergence of an equilibrium finite element model for plane elastostatics.Apl. mat. 24 (1979), 427-457. MR 0547046
Reference: [5] Johnson C., Mercier B.: Some equilibrium finite element methods for two-dimensional elasticity problems.Numer. Math. 30, (1978), 103-116. Zbl 0427.73072, MR 0483904, 10.1007/BF01403910
Reference: [6] Mosco U., Strang G.: One-sided approximations and variational inequalities.Bull. Am. Math. Soc. 80 (1974), 308-312. MR 0331818, 10.1090/S0002-9904-1974-13477-4
Reference: [7] Hlaváček I.: Dual finite element analysis for unilateral boundary value problems.Apl. mat. 22 (1977), 14-51. MR 0426453
Reference: [8] Hlaváček I.: Dual finite element analysis for semi-coercive unilateral boundary value problems.Apl. mat. 23 (1978), 52-71. MR 0480160


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