Variational and quasi-variational inequalities in mechanics

著者

• Kravchuk, A. S. (Aleksandr Stepanovich)
• Neittaanmäki, P. (Pekka)

書誌事項

Variational and quasi-variational inequalities in mechanics

by Alexander S. Kravchuk and Pekka J. Neittaanmäki

（Solid mechanics and its applications, v. 147）

Springer, c2007

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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詳細情報

• NII書誌ID(NCID): BA8342526X
• ISBN:
  • 9781402063763
• 出版国コード: ne
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Dordrecht
• ページ数/冊数: xiii, 329 p.
• 大きさ: 25 cm
• 親書誌ID:
  • BA08040895