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
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.