Abstract
The present work is part of a research effort devoted to the study of bifurcation and instability phenomena in frictional contact problems. Several situations have been considered in these studies:
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(i)
the occurrence of bifurcations in quasi-static paths; this is a stiffness and friction induced phenomenon of non-uniqueness of quasi-static solutions;
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(ii)
the initiation of dynamic solutions at equilibrium positions, with no initial perturbations, but with initial acceleration and reaction discontinuities; this is a mass and friction induced phenomenon of non-uniqueness of dynamic solutions;
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(iii)
the existence of smooth non-oscillatory growing dynamic solutions with perturbed initial conditions arbitrarily close to equilibrium configurations, i.e. the divergence instability of equilibrium states;
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(iv)
the existence of non-oscillatory or oscillatory growing dynamic solutions with perturbed initial conditions arbitrarily close to portions of quasi-static paths;
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(v)
the occurrence of non-oscillatory (divergence) or oscillatory (flutter) instabilities of steady sliding equilibrium states.
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References
Björkman, G., (1992) Path following and critical points for contact problems, Computational Mechanics, Vol. no. 10, pp 231–246.
Chateau, X. and Nguyen, Q.S., (1991) Buckling of elastic structures in unilateral contact with or without friction, Eur. J. Mech., A/Solids, Vol. no. 10, no 1, pp 71–89.
De Moor, B., Vandenberghe, L. and Vandewalle, J., (1992) The generalized linear complementarity problem and an algorithm to find all its solutions, Mathematical Programming, Series A, Vol. no. 57, no. 3, pp 415–426.
Klarbring, A., (1988) On discrete and discretized non-linear elastic structures in unilateral contact (stability, uniqueness and variational principles), Int. J. Solids Structures, Vol. no. 24, no. 5, pp 459–479.
Klarbring, A., (1990) Derivation and analysis of rate boundary-value problems of frictional contact, Eur. J. Mech., A/Solids, Vol. no. 9, no. 1, pp 53–85.
Klarbring, A., (1997) Contact, friction, discrete mechanical structures and mathematical programming, Lecture notes for the CISM course Contact Problems: Theory, Methods, Applications.
Klarbring, A., (1997) Steady Sliding and Linear Complementarity, in Complementarity and Variational problems, Ferris-Pang (eds), SIAM publ., Philadelphia, pp. 132–147.
Martins, J.A.C. and Pinto da Costa, A., (1998) Stability of finite dimensional systems with unilateral contact and friction: non-linear elastic behaviour and obstacle curvature, Relatorio ICIST AI no. 9/98.
Martins, J.A.C. and Pinto da Costa, A., (1998) Dynamic stability of frictional contact systems: complementarity formulations, International Symposium on Impact and Friction of Solids, Structures and Intelligent Machines: Theory and Applications in Engineering and Science, Ottawa, June 1998.
Martins, J.A.C, Barbarin, S., Raous, M. and Pinto da Costa, A. (to appear) Dynamic Stability of Finite Dimensional Linearly Elastic Systems with Unilateral Contact and Coulomb Friction, Comp. Meth. Appl. Mech. Engng..
Pires, E.B. and Trabucho, L. (1990) The Steady Sliding Problem with Nonlocal Friction, Int. J. Engng. Sci., Vol. no. 28, no. 7, pp. 631–641
Rabier, P., Martins, J.A.C, Oden, J.T. and Campos, L. (1986) Existence and local uniqueness of solutions for contact problems with non-linear friction laws. Int. J. Engng. Sci., Vol. no. 24, no. 11, pp. 1755–1768.
Raous, M., Chabrand, P., and Lebon, F., (1988) Numerical Methods for Frictional Contact Problems and Applications, Journal de Mécanique Théorique et Appliquée, sup. no. 1 to Vol. no. 7, pp. 111–128.
Trinkle, J.C., Pang, J.-S., Sudarsky, S. and Lo, G., (1997) On dynamic multi-rigid-body contact problems with Coulomb friction. ZAMM, Vol. no. 77, no. 4, pp 267–279.
Vola, D., Pratt, E., Jean, M., and Raous, M., (to appear) Consistent Time Discretization for a Dynamic Frictional Contact Problem and Complementarity Techniques, Revue Européenne des Eléments Finis.
Zeghloul, T., and Villechaise, B., 1996, Stress waves in a sliding contact. Part 1: experimental study, in Proceedings of the 22nd Leeds Lyon Symposium on Tribology, Dowson et al. (eds.), Elsevier Science, pp. 33–37.
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Vola, D., da Costa, A.P., Barbarin, S., Martins, J.A.C., Raous, M. (1999). Bifurcations and Instabilities in Some Finite Dimensional Frictional Contact Problems. In: Pfeiffer, F., Glocker, C. (eds) IUTAM Symposium on Unilateral Multibody Contacts. Solid Mechanics and its Applications, vol 72. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4275-5_18
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