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Viser: Mathematical Foundations of Elasticity
Mathematical Foundations of Elasticity Vital Source e-bog
Jerrold E. Marsden
(2012)
Mathematical Foundations of Elasticity
Jerrold E. Marsden og Thomas J. R. Hughes
(2003)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- Vital Source searchable e-book (Reflowable pages): 556 sider
- Udgiver: Dover Publications (Oktober 2012)
- ISBN: 9780486142272
Bookshelf online: 5 år fra købsdato.
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Detaljer om varen
- Paperback: 556 sider
- Udgiver: Dover Publications, Incorporated (Marts 2003)
- Forfattere: Jerrold E. Marsden og Thomas J. R. Hughes
- ISBN: 9780486678658
1. Kinematics
2. Balance laws
3. Elastic materials
4. Boundary value problems
5. Constitutive inequalities
6. The role of geometry and functional analysis1. Geometry and kinematics of bodies
1.1 Motions of simple bodies
1.2 Vector fields, one-forms, and pull-backs
1.3 The deformation gradient
1.4 Tensors, two-point tensors, and the covariant derivative
1.5 Conservation of mass
1.6 Flows and lie derivatives
1.7 Differential forms and the Piola transformation2. Balance principles
2.1 The master balance law
2.2 The stress tensor and balance of momentum
2.3 Balance of energy
2.4 Classical spacetimes, covariant balance of energy, and the principle of virtual work
2.5 Thermodynamics II; the second law3. Constitutive theory
3.1 The constitutive hypothesis
3.2 Consequences of thermodynamics, locality, and material frame indifference
3.3 Covariant constitutive theory
3.4 The elasticity tensor and thermoelastic solids
3.5 Material symmetries and isotropic elasticity4. Linearization
4.1 The implicit function theorem
4.2 Linearization of nonlinear elasticity
4.3 Linear elasticity
4.4 Linearization stability5. Hamiltonian and variational principles
5.1 The formal variational structure of elasticity
5.2 Linear Hamiltonian systems and classical elasticity
5.3 Abstract Hamiltonian and Lagrangian systems
5.4 Lagrangian field theory and nonlinear elasticity
5.5 Conservation laws
5.6 Reciprocity
5.7 Relativistic elasticity6. Methods of functional analysis in elasticity
6.1 Elliptic operators and linear elastostatics
6.2 Abstract semigroup theory
6.3 Linear elastodynamics
6.4 Nonlinear elastostatics
6.5 Nonlinear elastodynamics
6.6 The energy criterion
6.7 A control problem for a beam equation7. Selected topics in bifurcation theory
7.1 Basic ideas of static bifurcation theory
7.2 A survey of some applications to elastostatics
7.3 The traction problem near a natural state (Signorini's problem)
7.4 Basic ideas of dynamic bifurcation theory
7.5 A survey of some applications to elastodynamics
7.6 Bifurcations in the forced oscillations of a beam Bibliography, Index