×

Study of a rheological model with a friction term and a cubic term: deterministic and stochastic cases. (English) Zbl 1073.74006

Summary: First, results on existence of solutions and their numerical approximations are given for the studied models. Some results of the identification of hysteretic discrete mechanical systems with damping submitted to deterministic or stochastic forcing are given. The identification is obtained thanks to hysteresis cycles which are convex or nonconvex.

MSC:

74A20 Theory of constitutive functions in solid mechanics
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bastien, J., 2000. Etude théorique et numérique d’inclusions différentielles maximales monotones. Applications à des modèles élastoplastiques, PhD Thesis, Université Lyon I, Numéro d’ordre: 96-2000; Bastien, J., 2000. Etude théorique et numérique d’inclusions différentielles maximales monotones. Applications à des modèles élastoplastiques, PhD Thesis, Université Lyon I, Numéro d’ordre: 96-2000
[2] Bastien, J.; Schatzman, M., Schéma numérique pour des inclusions différentielles avec terme maximal monotone, C. R. Acad. Sci. Paris Sér. I Math., 330, 611-615 (2000) · Zbl 0951.65059
[3] Bastien, J.; Schatzman, M.; Lamarque, C.-H., Study of some rheological models with a finite number of degrees of freedom, Eur. J. Mech. A Solids, 19, 2, 277-307 (2000) · Zbl 0954.74011
[4] Bastien, J.; Schatzman, M.; Lamarque, C.-H., Study of an elastoplastic model with an infinite number of internal degrees of freedom, Eur. J. Mech. A Solids, 21, 2, 199-222 (2002) · Zbl 1023.74009
[5] Bernardin, F., Multivalued stochastic differential equations: convergence of a numerical scheme, Set-Valued Anal., 11, 4, 393-415 (2004) · Zbl 1031.60050
[6] Brézis, H., Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Notas de Matemática (50), North-Holland Math. Stud., vol. 5 (1973), North-Holland: North-Holland Amsterdam · Zbl 0252.47055
[7] Cépa, E., Equations différentielles stochastiques multivoques, (Séminaire de Probabilités XXIX. Séminaire de Probabilités XXIX, Lectures Notes in Math. (1995)), 86-107 · Zbl 0833.60079
[8] Coutel, S., 2005. Wavelets based Methods for piecewise linear systems identification. PhD Thesis, École doctorale MEGA, ENTPE, Lyon, in preparation; Coutel, S., 2005. Wavelets based Methods for piecewise linear systems identification. PhD Thesis, École doctorale MEGA, ENTPE, Lyon, in preparation
[9] Karatzas, I.; Shreve, E., Brownian Motion and Stochastic Calculus (1991), Springer: Springer New York · Zbl 0734.60060
[10] Pernot, S., 2000. Méthodes ‘Ondelettes’ pour l’Etude des Vibrations et de la Stabilité des Systèmes Dynamiques. PhD Thesis, École doctorale MEGA, ENTPE, Lyon; Pernot, S., 2000. Méthodes ‘Ondelettes’ pour l’Etude des Vibrations et de la Stabilité des Systèmes Dynamiques. PhD Thesis, École doctorale MEGA, ENTPE, Lyon
[11] Slominski, L., On approximations of solutions of multidimensional SDE’s with reflecting boundary conditions, Stochastic Process. Appl., 50, 197-219 (1994) · Zbl 0799.60055
[12] Schatzman, M.; Bastien, J.; Lamarque, C.-H., An ill-posed mechanical problem with friction, Eur. J. Mech. A Solids, 18, 3, 415-420 (1999) · Zbl 0940.74040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.