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作者 Mei, Chiang C
書名 Homogenization Methods For Multiscale Mechanics
出版項 Singapore : World Scientific Publishing Company, 2010
©2010
國際標準書號 9789814282451 (electronic bk.)
9789814282444
book jacket
說明 1 online resource (350 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Intro -- Contents -- Acknowledgments -- Preface -- 1. Introductory Examples of Homogenization Method -- 1.1. LongWaves in a Layered Elastic Medium -- 1.2. ShortWaves in aWeakly Stratified Elastic Medium -- 1.3. Dispersion of Passive Solute in Pipe Flow -- 1.3.1. Scale Estimates -- 1.3.2. Multiple-Scale Analysis -- 1.3.3. Dispersion Coefficient for Steady Flow -- 1.3.4. Dispersion Coefficient for Oscillatory Flow -- 1.4. Typical Procedure of Homogenization Analysis -- References -- 2. Diffusion in aComposite -- 2.1. Basic Equations for Two Components in Perfect Contact -- 2.2. Effective Equation on the Macroscale -- 2.3. Effective Boundary Condition -- 2.4. Symmetry and Positiveness of Effective Conductivity -- 2.5. Laminated Composites -- 2.6. Bounds for Effective Conductivity -- 2.6.1. First Variational Principle and the Upper Bound -- 2.6.2. Dual Variational Principle and the Lower Bound -- 2.7. Hashin-Shtrikman Bounds -- 2.7.1. Results and Implications -- 2.7.2. Derivation of Hashin-Shtrikman Bounds -- 2.8. Other Approximate Results for Dilute Inclusions -- 2.9. Thermal Resistance at the Interface -- 2.10. Laminated Composites with Thermal Resistance -- 2.10.1. Effective Coefficients -- 2.10.2. Application to Thermal Barrier Coatings -- 2.11. Bounds for the Effective Conductivity -- 2.11.1. Variational Principles and Bounds -- 2.11.2. Application to a Particulate Composite -- 2.12. Chemical Transport in Aggregated Soil -- Appendix 2A. Heat Transfer in a Two-Slab System -- References -- 3. Seepage in Rigid Porous Media -- 3.1. Equations for Seepage Flow and Darcy's Law -- 3.2. Uniqueness of the Cell Boundary-Value Problem -- 3.3. Symmetry and Positiveness of Hydraulic Conductivity -- 3.4. Numerical Computation of the Permeability Tensor -- 3.5. Seepage of a Compressible Fluid -- 3.6. Two-Dimensional FlowThrough a Three-Dimensional Matrix
3.6.1. Governing Equations -- 3.6.2. Homogenization -- 3.6.3. Numerical Results -- 3.7. Porous Media with Three Scales -- 3.7.1. Effective Equations -- 3.7.2. Properties of Hydraulic Conductivity -- 3.7.3. Macropermeability of a Laminated Medium -- 3.8. Brinkman's Modification of Darcy's Law -- 3.9. Effects ofWeak Fluid Inertia -- Appendix 3A. Spatial Averaging Theorem -- References -- 4. Dispersion in Periodic Media or Flows -- 4.1. Passive Solute in a Two-Scale Seepage Flow -- 4.1.1. The Solute Transport Equation and Scale Estimates -- 4.1.2. Macroscale Transport Equation -- 4.1.3. Numerical Computation of Dispersivity -- 4.2. Macrodispersion in a Three-Scale Porous Medium -- 4.2.1. From Micro- to Mesoscale -- 4.2.2. Mass Transport Equation on the Macroscale -- 4.2.3. Second-Order Seepage Velocity -- 4.3. Dispersion and Transport in aWave Boundary Layer Above the Seabed -- 4.3.1. Depth-Integrated Transport Equation in the Boundary Layer -- 4.3.2. Effective Convection Velocity -- 4.3.3. Correlation Coefficients (u(1)i C(1)) and Dispersivity Tensor -- 4.3.4. Dispersion Under a StandingWave in a Lake -- Appendix 4A. Derivation of Convection-Dispersion Equation -- Appendix 4B. An Alternate Form of Macrodispersion Tensor -- References -- 5. Heterogeneous Elastic Materials -- 5.1. Effective Equations on the Macroscale -- 5.2. The Effective Elastic Coefficients -- 5.3. Application to Fiber-Reinforced Composite -- 5.4. Elastic Panels with Periodic Microstructure -- 5.4.1. Order Estimates -- 5.4.2. Two-Scale Analysis and Effective Equations -- 5.4.3. Homogeneous Plate - A Limiting Case -- 5.5. Variational Principles and Bounds for the Elastic Moduli -- 5.5.1. First Variational Principle and the Upper Bound -- 5.5.2. Second Variational Principle and the Lower Bound -- 5.6. Hashin-Shtrikman Bounds -- 5.7. Partially Cohesive Composites
5.7.1. Effective Equations on the Macroscale -- 5.7.2. Variational Principles -- 5.7.3. Bounds for Particulate Composites -- 5.7.4. Size Effects for Particulate Composites -- 5.7.5. Critical Radii for Particulate Composites -- Appendix 5A. Properties of a Tensor of Fourth Rank -- References -- 6. Deformable PorousMedia -- 6.1. Basic Equations for Fluid and Solid Phases -- 6.2. Scale Estimates -- 6.2.1. Quasi-Static Poroelasticity -- 6.2.2. Dynamic Poroelasticity -- 6.3. Multiple-Scale Expansions -- 6.4. Averaged Total Momentum of the Composite -- 6.5. Averaged Mass Conservation of Fluid Phase -- 6.6. Averaged Fluid Momentum -- 6.6.1. Quasi-Static Case -- 6.6.2. Dynamic Case -- 6.7. Time-Harmonic Motion -- 6.8. Properties of the Effective Coefficients -- 6.8.1. Three Identities for General Media -- 6.8.2. Homogeneous and Isotropic Grains -- 6.9. Computed Elastic Coefficients -- 6.10. Boundary-Layer Approximation for Macroscale Problems -- 6.10.1. The Outer Approximation -- 6.10.2. Boundary-Layer Correction -- 6.10.3. Plane RayleighWave in a Poroelastic Half Space -- Appendix 6A. Properties of the Compliance Tensor -- Appendix 6B. Variational Principle for the Elastostatic Problem in a Cell -- References -- 7. Wave Propagation in Inhomogeneous Media -- 7.1. LongWave Through a Compact Cylinder Array -- 7.2. Bragg Scattering of ShortWaves by a Cylinder Array -- 7.2.1. Envelope Equations -- 7.2.2. Dispersion Relation for a DetunedWave Train -- 7.2.3. Scattering by a Finite Strip of Periodic Cylinders -- 7.3. Sound Propagation in a Bubbly Liquid -- 7.3.1. Scale and Order Estimates -- 7.3.2. Near Field of a Spherical Bubble -- 7.3.3. The Intermediate Field -- 7.3.4. The Macroscale Equation -- 7.4. One-Dimensional Sound Through a Weakly Random Medium -- 7.5. Weakly Nonlinear DispersiveWaves in a Random Medium -- 7.5.1. Envelope Equation
7.5.2. Modulational Instability -- 7.6. Harmonic Generation in Random Media -- 7.6.1. LongWaves in ShallowWater -- 7.6.2. Harmonic Amplitudes -- 7.6.3. Gaussian Disorder -- References -- Additional References on Homogenization Theory -- Subject Index
Key Features:Primary emphasis on the derivation of approximate equations. Less effort is devoted to their solutions and the implied physical significanceLimits the mathematics to the level commonly taught to graduate students of engineering and physical sciencesDetails are explained from ground zeroUseful to a audience engaging in both theoretical and applied research of multiphase mechanics
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Mei, Chiang C Homogenization Methods For Multiscale Mechanics Singapore : World Scientific Publishing Company,c2010 9789814282444
主題 Homogenization (Differential equations);Mathematical physics
Electronic books
Alt Author Vernescu, Bogdan
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