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Variational and Quasi-Variational Inequalities in Mechanics [electronic resource] /by Alexander S. Kravchuk, Pekka J. Neittaanmäki.

by Kravchuk, Alexander S [author.]; Neittaanmäki, Pekka J [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Solid Mechanics and Its Applications: 147Publisher: Dordrecht : Springer Netherlands, 2007.Description: online resource.ISBN: 9781402063770.Subject(s): Engineering | Materials | Engineering | Continuum Mechanics and Mechanics of Materials | Computational IntelligenceDDC classification: 620.1 Online resources: Click here to access online
Contents:
Notations and Basics -- Variational Setting of Linear Steady-state Problems -- Variational Theory for Nonlinear Smooth Systems -- Unilateral Constraints and Nondifferentiable Functionals -- Transformation of Variational Principles -- Nonstationary Problems and Thermodynamics -- Solution Methods and Numerical Implementation -- Concluding Remarks.
In: Springer eBooksSummary: The essential aim of the present book is to consider a wide set of problems arising in the mathematical modelling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities, and the transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems. Important new results concern contact problems with friction. The Coulomb friction law and some others are considered, in which relative sliding velocities appear. The corresponding quasi-variational inequality is constructed, as well as the appropriate iterative method for its solution. Outlines of the variational approach to non-stationary and dissipative systems and to the construction of the governing equations are also given. Examples of analytical and numerical solutions are presented. Numerical solutions were obtained with the finite element and boundary element methods, including new 3D problems solutions.
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Notations and Basics -- Variational Setting of Linear Steady-state Problems -- Variational Theory for Nonlinear Smooth Systems -- Unilateral Constraints and Nondifferentiable Functionals -- Transformation of Variational Principles -- Nonstationary Problems and Thermodynamics -- Solution Methods and Numerical Implementation -- Concluding Remarks.

The essential aim of the present book is to consider a wide set of problems arising in the mathematical modelling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities, and the transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems. Important new results concern contact problems with friction. The Coulomb friction law and some others are considered, in which relative sliding velocities appear. The corresponding quasi-variational inequality is constructed, as well as the appropriate iterative method for its solution. Outlines of the variational approach to non-stationary and dissipative systems and to the construction of the governing equations are also given. Examples of analytical and numerical solutions are presented. Numerical solutions were obtained with the finite element and boundary element methods, including new 3D problems solutions.

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