ISBN: 9789048176199
The variational method is a powerful tool to investigate states and processes in technical devices, nature, living organisms, systems, and economics. The power of the variational method consists in the fact that many of its sta- ments are physical or natural laws themselves. The essence of the variational approach for the solution of problems rel- ing to the determination of the real state of systems or processes consists in thecomparisonofclosestates.Theselectioncriteriafortheactualstatesmust be such that all the equations and conditions of the mathematical model are satis?ed. Historically, the ?rst variational theory was the Lagrange theory created to investigate the equilibrium of ?nite-dimensional mechanical systems under holonomic bilateral constraints (bonds). The selection criterion proposed by Lagrange is the admissible displacement principle. In accordance with this principle, the work of the prescribed forces (supposed to be constant) on in?nitesimally small, kinematically admissible (virtual) displacements is zero. It is known that equating the virtual work performed for potential systems to zero is equivalent to the stationarity conditions for the total energy of the system. The transition from bilateral constraints to unilateral ones was performed by O. L. Fourier. Fourier demonstrated that the virtual work on small dist- bances of a stable equilibrium state of a mechanical system under unilateral constraints must be positive (or, at least, nonnegative). Therefore, for such a system the corresponding mathematical model is reduced to an inequality and the problem becomes nonlinear. Books > Science & Nature > Science > Engineering > Mechanical List_Books
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Variational and QuasiVariational Inequalities in Mechanics 147 Solid Mechanics and Its Applications - pocketboek
2010, ISBN: 9048176190
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Variational and Quasi-Variational Inequalities in Mechanics (Solid Mechanics and Its Applications) - pocketboek
ISBN: 9789048176199
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ISBN: 9789048176199
The variational method is a powerful tool to investigate states and processes in technical devices, nature, living organisms, systems, and economics. The power of the variational method c… Meer...
Alexander S. Kravchuk:
Variational and QuasiVariational Inequalities in Mechanics 147 Solid Mechanics and Its Applications - pocketboek2010, ISBN: 9048176190
[EAN: 9789048176199], Nieuw boek, [SC: 4.42], [PU: Springer], New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000., Books
Variational and Quasi-Variational Inequalities in Mechanics (Solid Mechanics and Its Applications) - pocketboek
ISBN: 9789048176199
Springer Netherlands. Paperback. New., Springer Netherlands, 6
2010, ISBN: 9048176190
[EAN: 9789048176199], Nieuw boek, [SC: 6.9], [PU: Springer 2010-11], Books
2010, ISBN: 9048176190
[EAN: 9789048176199], Nieuw boek, [SC: 54.84], [PU: - -], Books
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| Titel: | |
| ISBN: |
Gedetalleerde informatie over het boek. - Variational and Quasi-Variational Inequalities in Mechanics
EAN (ISBN-13): 9789048176199
ISBN (ISBN-10): 9048176190
Gebonden uitgave
pocket book
Verschijningsjaar: 2010
Uitgever: Springer
352 Bladzijden
Gewicht: 0,532 kg
Taal: eng/Englisch
Boek bevindt zich in het datenbestand sinds 2011-03-02T07:28:36+01:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2022-01-22T05:11:40+01:00 (Amsterdam)
ISBN/EAN: 9789048176199
ISBN - alternatieve schrijfwijzen:
90-481-7619-0, 978-90-481-7619-9
Gegevens van de uitgever
Auteur: Alexander S. Kravchuk; Pekka J. Neittaanmäki
Titel: Solid Mechanics and Its Applications; Variational and Quasi-Variational Inequalities in Mechanics
Uitgeverij: Springer; Springer Netherland
337 Bladzijden
Verschijningsjaar: 2010-11-20
Dordrecht; NL
Gedrukt / Gemaakt in
Gewicht: 0,581 kg
Taal: Engels
139,09 € (DE)
142,99 € (AT)
153,50 CHF (CH)
POD
XIII, 337 p.
BC; Previously published in hardcover; Hardcover, Softcover / Technik/Maschinenbau, Fertigungstechnik; Maschinenbau; Verstehen; 3D; Transformation; construction; development; mathematical modeling; mechanics; modeling; modelling; operator; optimization; quality; thermodynamics; C; Mechanical Engineering; Classical Mechanics; Solid Mechanics; Computational Intelligence; Mechanical Engineering; Classical Mechanics; Solid Mechanics; Computational Intelligence; Engineering; Klassische Mechanik; Maschinenbau: Festkörpermechanik; Künstliche Intelligenz; BB
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.Andere boeken die eventueel grote overeenkomsten met dit boek kunnen hebben:
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