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Mathematical Models in Contact Mechanics.
A complete introduction to the modelling and mathematical analysis of contact processes with deformable solids.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
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| Colección: | London Mathematical Society lecture note series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Series; Title; Copyright; Dedication; Contents; Preface; Part I Introduction to variational inequalities; 1 Preliminaries on functional analysis; 1.1 Normed spaces; 1.1.1 Basic definitions; 1.1.2 Linear continuous operators; 1.1.3 Fixed point theorems; 1.2 Hilbert spaces; 1.2.1 Projection operators; 1.2.2 Orthogonality; 1.2.3 Duality and weak convergence; 1.3 Elements of nonlinear analysis; 1.3.1 Monotone operators; 1.3.2 Convex lower semicontinuous functions; 1.3.3 Minimization problems; 2 Elliptic variational inequalities; 2.1 Variational inequalities of the first kind.
- 2.1.1 Existence and uniqueness2.1.2 Penalization; 2.2 Variational inequalities of the second kind; 2.2.1 Existence and uniqueness; 2.2.2 A convergence result; 2.2.3 Regularization; 2.3 Quasivariational inequalities; 2.3.1 The Banach fixed point argument; 2.3.2 The Schauder fixed point argument; 2.3.3 A convergence result; 3 History-dependent variational inequalities; 3.1 Nonlinear equations with history-dependent operators; 3.1.1 Spaces of vector-valued functions; 3.1.2 Two examples; 3.1.3 The general case; 3.2 History-dependent quasivariational inequalities.
- 3.2.1 A basic existence and uniqueness result3.2.2 A convergence result; 3.3 Evolutionary variational inequalities; 3.3.1 Existence and uniqueness; 3.3.2 Convergence results; Part II Modelling and analysis of contact problems; 4 Modelling of contact problems; 4.1 Function spaces in contact mechanics; 4.1.1 Preliminaries; 4.1.2 Spaces for the displacement field; 4.1.3 Spaces for the stress field; 4.1.4 Spaces for piezoelectric contact problems; 4.2 Physical setting and constitutive laws; 4.2.1 Physical setting; 4.2.2 Elastic constitutive laws; 4.2.3 Viscoelastic constitutive laws.
- 4.2.4 Viscoplastic constitutive laws4.2.5 The von Mises convex; 4.3 Modelling of elastic contact problems; 4.3.1 Preliminaries; 4.3.2 Contact conditions; 4.3.3 Friction laws; Conclusion; 4.4 Modelling of elastic-viscoplastic contact problems; 4.4.1 Preliminaries; 4.4.2 Contact conditions and friction laws; Conclusion; 4.5 Modelling of piezoelectric contact problems; 4.5.1 Physical setting and preliminaries; 4.5.2 Constitutive laws; 4.5.3 Contact conditions; Conclusion; 5 Analysis of elastic contact problems; 5.1 The Signorini contact problem; 5.1.1 Problem statement.
- 5.1.2 Existence and uniqueness5.1.3 Penalization; 5.1.4 Dual variational formulation; 5.1.5 Minimization; 5.1.6 One-dimensional example; 5.2 Frictional contact problems; 5.2.1 Statement of the problems; 5.2.2 Existence and uniqueness; 5.2.3 A convergence result; 5.2.4 Regularization; 5.2.5 Dual variational formulation; 5.2.6 Minimization; 5.3 A frictional contact problem with normal compliance; 5.3.1 Problem statement; 5.3.2 The Banach fixed point argument; 5.3.3 The Schauder fixed point argument; 5.3.4 Convergence results; 6 Analysis of elastic-viscoplastic contact problems.