History-Dependent Problems with Applications to Contact Models for Elastic Beams
- Jagiellonian University, Faculty of Mathematics and Computer Science (Poland)
- Université de Perpignan Via Domitia, Laboratoire de Mathématiques et Physique (France)
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.
- OSTI ID:
- 22469615
- Journal Information:
- Applied Mathematics and Optimization, Vol. 73, 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); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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