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Title: History-Dependent Problems with Applications to Contact Models for Elastic Beams

We prove an existence and uniqueness result for a class of subdifferential inclusions which involve a history-dependent operator. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Problems of such kind arise in a large number of mathematical models which describe quasistatic processes of contact. To provide an example we consider an elastic beam in contact with a reactive obstacle. The contact is modeled with a new and nonstandard condition which involves both the subdifferential of a nonconvex and nonsmooth function and a Volterra-type integral term. We derive a variational formulation of the problem which is in the form of a history-dependent hemivariational inequality for the displacement field. Then, we use our abstract result to prove its unique weak solvability. Finally, we consider a numerical approximation of the model, solve effectively the approximate problems and provide numerical simulations.
Authors:
; ; ;  [1] ;  [2]
  1. Jagiellonian University, Faculty of Mathematics and Computer Science (Poland)
  2. Université de Perpignan Via Domitia, Laboratoire de Mathématiques et Physique (France)
Publication Date:
OSTI Identifier:
22469615
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 73; Journal Issue: 1; Other Information: Copyright (c) 2016 Springer Science+Business Media New York; Article Copyright (c) 2015 The Author(s); http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BEAMS; COMPUTERIZED SIMULATION; ELASTICITY; FUNCTIONS; INTEGRALS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; VARIATIONAL METHODS; VOLTERRA INTEGRAL EQUATIONS