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Discrete Mechanics : Concepts and Applications.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Newark :
John Wiley & Sons, Incorporated,
2019.
|
| Edición: | 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-Title Page; Title Page; Copyright Page; Contents; Preface; Introduction; List of Symbols; 1. Fundamental Principles of Discrete Mechanics; 1.1. Definitions of discrete mechanics; 1.1.1. Notion of discrete space-time; 1.1.2. Notion of a discrete medium; 1.2. Properties of discrete operators; 1.3. Invariance under translation and rotation; 1.4. Weak equivalence principle; 1.5. Principle of accumulation of stresses; 1.6. Duality-of-action principle; 1.7. Physical characteristics of a medium; 1.8. Composition of velocities and accelerations; 1.9. Discrete curvature
- 1.10. Axioms of discrete mechanics2. Conservation of Acceleration; 2.1. General principles; 2.2. Continuous memory; 2.3. Modeling the compression stress; 2.3.1. Compression experiment; 2.3.2. Modeling the stress in a solid; 2.3.3. Modeling the stress in a fluid; 2.3.4. Compression with small time constants; 2.3.5. Modeling the accumulation of the normal stress; 2.3.6. The energy formula, e = mc2; 2.4. Modeling the rotation stress; 2.4.1. Couette's experiment; 2.4.2. Behavior over time; 2.4.3. Rotation stress in solids; 2.4.4. Rotation stress in fluids
- 2.4.5. Stresses in a porous medium, Darcy's law2.4.6. Modeling the accumulation of the rotation stress; 2.4.7. Rotation in Couette and Poiseuille flows; 2.5. Modeling other effects; 2.5.1. Gravitational effects; 2.5.2. Inertial effects; 2.6. Discrete equations of motion; 2.6.1. Geometric description; 2.6.2. Derivation of the equations of motion; 2.6.3. Dissipation of energy; 2.7. Coupling conditions; 2.8. Formulation of the equations of motion at a discontinuity; 2.9. Other forms of the equations of motion; 2.9.1. Curl and vector potential formulation
- 2.9.2. Conservative form of the equations of motion2.10. Incompressible models derived from the discrete formulation; 2.10.1. Kinematic projection methods; 2.10.2. Incompressibility in discrete mechanics; 2.11. Consequences on the dynamics of the vorticity; 3. Conservation of Mass, Flux and Energy; 3.1. Conservation of mass in a homogeneous medium; 3.1.1. In continuum mechanics; 3.1.2. In discrete mechanics; 3.2. Transport within multicomponent mixtures; 3.2.1. Classical approach; 3.2.2. Discrete model for the transport of chemical species; 3.2.3. Equilibrium in a binary mixture
- 3.3. Advection3.4. Conservation of flux; 3.4.1. General remarks; 3.4.2. Model; 3.5. Conservation of energy; 3.5.1. Conservation of total energy; 3.5.2. Conservation of kinetic energy; 3.5.3. Conservation of internal energy; 3.5.4. Monotonically decreasing kinetic energy; 3.6. A complete system of equations; 3.7. A simple heat conduction problem; 3.7.1. Case of anisotropic materials; 3.8. Phase change; 3.8.1. The Stefan problem; 3.8.2. Condensation; 4. Properties of the Discrete Formulation; 4.1. Fundamental properties; 4.1.1. Limitations on the velocity