A formulation of the linear discrete Coulomb friction problem via convex optimization

被引：32

作者：

Acary, Vincent ^{[1
]}

Cadoux, Florent ^{[1
]}

Lemarechal, Claude ^{[1
]}

Malick, Jerome ^{[1
]}

机构：

[1] Inria Rhone Alpes, F-38330 Montbonnot St Martin, France

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2011年 / 91卷 / 02期

关键词：

Nonsmooth mechanics; contact mechanics; Coulomb friction; Painleve's problem; fixed-point theorem; convex analysis; convex optimization; second-order cone programming; MATHEMATICAL-PROGRAMMING APPROACH; GENERALIZED NEWTON METHOD; CONTACT PROBLEMS; UNILATERAL CONTACT; BOUNDED FRICTION; EXISTENCE; ALGORITHMS; UNIQUENESS; BODIES;

D O I：

10.1002/zamm.201000073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new formulation of the dynamical Coulomb friction problem in finite dimension with discretized time. The novelty of our approach is to capture and treat directly the friction model as a parametric quadratic optimization problem with second-order cone constraints coupled with a fixed point equation. This intrinsic formulation allows a simple existence proof under reasonable assumptions, as well as a variety of solution algorithms. We study mechanical interpretations of these assumptions, showing in particular that they are actually necessary and sufficient for a basic example similar to the so-called "paradox of Painleve". Finally, we present some implementations and experiments to illustrate the practical aspect of our work. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：155 / 175

页数：21

共 75 条

[1] Abadie M, 2000, LECT NOTES PHYS, V551, P61
[2] ACARY, 2008, LECT NOTES APPL COMP, V35
[3] ACARY V, 2010, CMIS 2009 C IN PRESS
[4] Generalized Newton method in contact mechanics
Alart, P
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (01): : 83 - 108
[5] A MIXED FORMULATION FOR FRICTIONAL CONTACT PROBLEMS PRONE TO NEWTON LIKE SOLUTION METHODS
ALART, P
CURNIER, A
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1991, 92 (03) : 353 - 375
[6] CRITERIA OF INJECTIVITY AND SUBJECTIVITY FOR CERTAIN MAPPINGS OF R(N) INTO ITSELF - APPLICATION TO CONTACT MECHANICS
ALART, P
[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1993, 27 (02): : 203 - 222
[7] HARD AND SOFT FINGERED ROBOT GRIPPERS - THE LINEAR COMPLEMENTARITY APPROACH
ALFAHED, AM
STAVROULAKIS, GE
PANAGIOTOPOULOS, PD
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1991, 71 (7-8): : 257 - 265
[8] Second-order cone programming
Alizadeh, F
Goldfarb, D
[J]. MATHEMATICAL PROGRAMMING, 2003, 95 (01) : 3 - 51
[9] Existence results for quasistatic contact problems with Coulomb friction
Andersson, LE
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2000, 42 (02) : 169 - 202
[10] Time-stepping for three-dimensional rigid body dynamics
Anitescu, M
Potra, FA
Stewart, DE
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1999, 177 (3-4) : 183 - 197

← 1 2 3 4 5 6 7 8 →