Signorini's law of unilateral contact and Coulomb's friction law constitute a simple and useful framework for the analysis of unilateral frictional contact problems of a linearly elastic body with a rigid support. For quasi-static, monotone-loadings, the discrete dual formulation of this problem leads to a quasi-variational inequality, whose unknowns, after condensation, are the normal and tangential contact forces at nodes of the initial contact area. A new block-relaxation solution technique is proposed here. At the typical iteration step, shown to be a contraction for small friction coefficients, two quadratic programming problems are solved one after the other: the former is a friction problem with given normal forces, the latter is a unilateral contact problem with prescribed tangential forces. The contraction principle is used to establish the well-posedness of the discrete formulation, to prove the convergence of the algorithm, and to obtain an estimate of the convergence rate. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

Bisegna, P., Lebon, F., Maceri, F. (2001). D-PANA: a convergent block-relaxation solution method for the discretized dual formulation of the Signorini-Coulomb contact problem. COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE, 333(11), 1053-1058 [10.1016/S0764-4442(01)02153-X].

D-PANA: a convergent block-relaxation solution method for the discretized dual formulation of the Signorini-Coulomb contact problem

BISEGNA, PAOLO;MACERI, FRANCO
2001-01-01

Abstract

Signorini's law of unilateral contact and Coulomb's friction law constitute a simple and useful framework for the analysis of unilateral frictional contact problems of a linearly elastic body with a rigid support. For quasi-static, monotone-loadings, the discrete dual formulation of this problem leads to a quasi-variational inequality, whose unknowns, after condensation, are the normal and tangential contact forces at nodes of the initial contact area. A new block-relaxation solution technique is proposed here. At the typical iteration step, shown to be a contraction for small friction coefficients, two quadratic programming problems are solved one after the other: the former is a friction problem with given normal forces, the latter is a unilateral contact problem with prescribed tangential forces. The contraction principle is used to establish the well-posedness of the discrete formulation, to prove the convergence of the algorithm, and to obtain an estimate of the convergence rate. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
2001
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
English
Con Impact Factor ISI
Signorini-Coulomb contact problem; dual formulation
Erratum: published in série I, t. 333, n 11, pp. 1053–1058 comptes rendus mathematique, volume 335, issue 3, 2002, page 307, doi:10.1016/S1631-073X(02)02445-7
Bisegna, P., Lebon, F., Maceri, F. (2001). D-PANA: a convergent block-relaxation solution method for the discretized dual formulation of the Signorini-Coulomb contact problem. COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE, 333(11), 1053-1058 [10.1016/S0764-4442(01)02153-X].
Bisegna, P; Lebon, F; Maceri, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/23559
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