Variational and quasi-variational inequalities in mechanics
著者
書誌事項
Variational and quasi-variational inequalities in mechanics
(Solid mechanics and its applications, v. 147)
Springer, c2007
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注記
Includes bibliographical references (p. [313]-324) and index
内容説明・目次
内容説明
The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling 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 their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.
目次
- 1. Notation and Basics: 1.1. Notations and Conventions
- 1.2. Functional spaces
- 1.3. Bases and complete systems. Existence theorem
- 1.4. Trace Theorem
- 1.5. The laws of thermodynamics
- 2. Variational Setting of Linear Steady-state Problems: 2.1. Problem of the equilibrium of system with a finite number of degrees of Freedom
- 2.2. Equilibrium of the simplest continuous systems governed by ordinary differential Equations
- 2.3. 3D and 2D problems on the equilibrium of linear elastic bodies
- 3.4. Positive definiteness of the potential energy of linear systems
- 3.Variational Theory for Nonlinear Smooth Systems: 3.1. Examples of nonlinear systems
- 3.2. Differentiation of operators and functionals
- 3.3. Existence and uniqueness theorems of the minimal point of a functional
- 3.4. Condition for the potentiality of an operator
- 3.5. Boundary value problems in the Hencky-Ilyushin theory of plasticity without discharge
- 3.6. Problems in the elastic bodies theory with finite displacements and strain
- 4. Unilateral Constraints and Non-Differentiable Functionals: 4.1. Introduction: systems with finite degrees of freedom
- 4.2. Variational methods in contact problems for deformed bodies without friction
- 4.3. Variational method in contact problem with friction
- 5. The Transformation of Variational Principles: 5.1. Friedrichs Transformation
- 5.2. Equilibrium, mixed and hybrid variational principles in the theory of elasticity
- 5.3. The Young-Fenchel-Moreau duality transformation
- 5.4. Applications of duality transformations in contact problems
- 6. Non-Stationary Problems and Thermodynamics: 6.1. Traditional principles and methods
- 6.2. Gurtin's method
- 6.3. Thermodynamics and mechanics of the deformed solids
- 6.4. The variational theory of adhesion and crack initiation
- 7. Solution Methods and Numerical implementation: 7.1. Frictionless contact problems: finite element method (FEM)
- 7.2. Friction contact problems: boundaryelement method (BEM)
- 8. Concluding Remarks: 8.1. Modelling. Identification problem. Optimization
- 8.2. Development of the contact problems with friction, wear and adhesion
- 8.3. Numerical implementation of the contact interaction phenomena
- References
- Index.
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