A CLASS OF SUFFICIENTLY SMALL FRICTION COEFFICIENTS FOR THE UNIQUENESS OF THE SOLUTION OF THE QUASI-STATIC CONTACT PROBLEM

Citation
In. Doudoumis et En. Mitsopoulou, A CLASS OF SUFFICIENTLY SMALL FRICTION COEFFICIENTS FOR THE UNIQUENESS OF THE SOLUTION OF THE QUASI-STATIC CONTACT PROBLEM, Mathematical and computer modelling, 28(4-8), 1998, pp. 309-321
Citations number
22
Categorie Soggetti
Mathematics,"Computer Science Interdisciplinary Applications","Computer Science Software Graphycs Programming",Mathematics,"Computer Science Interdisciplinary Applications","Computer Science Software Graphycs Programming
ISSN journal
08957177
Volume
28
Issue
4-8
Year of publication
1998
Pages
309 - 321
Database
ISI
SICI code
0895-7177(1998)28:4-8<309:ACOSSF>2.0.ZU;2-E
Abstract
The present work is concerned with the quasistatic 2D frictional conta ct problem between discretized elastic bodies. The problem is formulat ed as a Linear Complementarity Problem. The basic scope of the paper i s to give some simple quantitative criteria which define a range of '' sufficiently small'' coefficients of friction for which it is assured that the problem has a unique solution. The range of the ''sufficientl y small'' friction coefficients depends on the initial contact state o f the nodal pairs. At the beginning of the loading history, a special case may sometimes happen for which these nodal pairs are in geometric contact without reactions. For this case, it is proved that the minim um eigenvalue of a sequence of eigenvalue problems gives the demanded range of ''sufficiently small'' coefficients. During the loading proce ss, generally, it is possible to reduce the problem to the determinati on of the minimum eigenvalue of just one eigenvalue problem. (C) 1998 Elsevier Science Ltd. All rights reserved.