Chapter

Mechanics, Models and Methods in Civil Engineering

Volume 61 of the series Lecture Notes in Applied and Computational Mechanics pp 409-420

Discrete Models Including Non-smooth Non-linearities of Friction Type

  • Claude-Henri LamarqueAffiliated withLaboratoire GéoMatériaux, URA CNRS 1652, Ecole Nationale des Travaux Publics de l’Etat
  • , Frédéric BernardinAffiliated withLaboratoire GéoMatériaux, URA CNRS 1652, Ecole Nationale des Travaux Publics de l’Etat
  • , Matthieu HollandAffiliated withLaboratoire GéoMatériaux, URA CNRS 1652, Ecole Nationale des Travaux Publics de l’Etat
  • , Jérôme BastienAffiliated withLaboratoire de Mécatronique 3M, Université de Technologie de Belfort-Montbéliard
  • , Michelle SchatzmanAffiliated withLaboratoire de Mathématiques Appliquées de Lyon, UMR CNRS 5585, Université Claude Bernard Lyon I

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Abstract

Models with a finite number of degrees of freedom including linear terms, nonlinear smooth terms, non smooth terms of friction type and terms with delay under external deterministic or stochastic excitation are considered. Dry friction is introduced via a finite number of Saint-Venant elements. Mathematical descriptions of constitutive laws and models are given. A survey of theoretical results (existence and uniqueness) are recalled. Implicit Euler numerical scheme is then build. Convergence results with order are summarized in both deterministic and stochastic case. A few applications to mechanical systems are provided.