Amazon cover image
Image from Amazon.com

Microstructures in Elastic Media : Principles and Computational Methods.

By: Contributor(s): Publisher: Cary : Oxford University Press, Incorporated, 1994Copyright date: ©1994Description: 1 online resource (257 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780195358070
Subject(s): Genre/Form: Additional physical formats: Print version:: Microstructures in Elastic Media : Principles and Computational MethodsDDC classification:
  • 620.11232
LOC classification:
  • QC191 -- .P43 1994eb
Online resources:
Contents:
Intro -- Contents -- 1 Fundamental Equations -- 1.1 Introduction and Motivation -- 1.2 Stress and Strain -- 1.3 Equations of Equilibrium -- 1.4 Strain Energy -- 1.4.1 Uniqueness -- 1.4.2 Extremum Principles -- 1.5 Betti's Reciprocal Theorem -- 1.6 Integral Representation -- 1.6.1 Classification of Integral Equations -- 1.6.2 Kelvin State -- 1.6.3 Integral Representation -- 1.6.4 Rigid Inclusion -- 1.6.5 Eliminating Single or Double Layer -- 1.7 Single and Double Layer Potentials -- 1.7.1 Single Layer -- 1.7.2 Double Layer -- 1.7.3 Liapunov-Tauber Theorem -- 1.8 Boundary Integral Equations -- 1.8.1 Direct BEM -- 1.8.2 Indirect BEM -- 1.9 Spectral Properties -- 1.9.1 Banach's Theorem -- 1.9.2 λ = -1 -- 1.9.3 λ = +1 -- 1.9.4 Type II Problems -- 1.9.5 Spectral Radius of Κ -- 1.10 Exercises -- 1.10.1 Rigid-Body Displacement -- 1.10.2 Stretching -- 1.10.3 Simple Shearing -- 1.10.4 Moduli of Elasticity -- 1.10.5 Integral Representation -- 1.10.6 Transmission of Force and Torque -- 1.10.7 Reciprocal Relation -- 1.10.8 Translating Rigid Sphere 1 -- 1.10.9 Translating Rigid Sphere 2 -- 1.10.10 Kelvin's Solution -- 1.10.11 On Green's Equations -- 1.10.12 Papkovich-Neuber Representation -- 1.10.13 Galerkin Vector -- 1.10.14 Self-Adjoint Property of G -- 1.10.15 Elastic Inclusion -- 1.10.16 Constant c[sub(ij)] -- 1.10.17 Thin, Rigid Inclusion -- 1.10.18 Liapunov-Tauber Theorem -- 2 Multipole Expansion and Rigid Inclusions -- 2.1 Singularity Solutions -- 2.1.1 Papkovich-Neuber Representation -- 2.1.2 Potential Deformation -- 2.1.3 Rotlet Deformation -- 2.1.4 Kelvinlet Deformation -- 2.1.5 Half-Space Solutions -- 2.1.6 Interior Deformation -- 2.2 Multipole Expansion -- 2.2.1 Stresslet -- 2.3 Spherical Rigid Inclusion -- 2.3.1 Translating a Rigid Sphere -- 2.3.2 Rotating a Rigid Sphere -- 2.3.3 Rigid Sphere in a Linear Deformation.
2.3.4 Rigid Sphere in a Quadratic Ambient Field -- 2.3.5 Translating an Elastic Spherical Inclusion -- 2.4 Exercises -- 2.4.1 Navier Solutions -- 2.4.2 Navier Solutions -- 2.4.3 Navier Solutions -- 2.4.4 Galerkin Vector -- 2.4.5 Force and Torque on a Rigid Spherical Inclusion -- 2.4.6 Rigid Spherical Inclusion in High-Order Field -- 3 Faxén Relations and Ellipsoidal Inclusions -- 3.1 Faxén Relations -- 3.2 Rigid Spherical Inclusion -- 3.3 Rigid Ellipsoidal Inclusion -- 3.3.1 Singularity Solution for Translation -- 3.3.2 Singularity Solution for Linear Ambient Field -- 3.3.3 Degenerate Cases -- 3.3.4 Faxén Relations for the Rigid Ellipsoid -- 3.3.5 Interactions between Two Ellipsoids -- 3.4 Exercises -- 3.4.1 Traction Functionals -- 3.4.2 Faxén Relations for Torque and Stresslet -- 3.4.3 Multipole Expansion for Ellipsoids -- 3.4.4 Tractions for the Translating Ellipsoid -- 4 Load Transfer Problem and Boundary Collocation -- 4.1 The Method of Reflection -- 4.2 Load Transfer between Two Spheres -- 4.2.1 Far Field by Reflection -- 4.2.2 Near Touching -- 4.3 Kelvin Solutions -- 4.3.1 Spherical Harmonics -- 4.3.2 Kelvin's General Solutions -- 4.4 Boundary Collocation -- 4.4.1 Twin Multipole Expansions -- 4.4.2 Collocation Equations for Translation Problems -- 4.5 Comparison -- 4.6 Constitutive Relation -- 4.6.1 Constitutive Theory -- 4.6.2 Cubic Lattices -- 4.7 Kelvinlet near a Rigid Sphere -- 4.7.1 The Axisymmetric Kelvinlet -- 4.7.2 The Transverse Kelvinlet -- 4.8 Exercises -- 4.8.1 Solid Spherical Harmonics -- 4.8.2 Lurié Solution -- 4.8.3 Type I Problems -- 5 Completed Double Layer Boundary Element Method -- 5.1 Introduction -- 5.2 Direct Formulation -- 5.3 Completed Double Layer Boundary Element Method -- 5.3.1 Range Completer -- 5.3.2 Null Functions of (1+Κ) -- 5.3.3 Completion Process -- 5.3.4 Container Surface -- 5.3.5 A Summary.
5.4 Rigid Inclusion -- 5.4.1 Translational Displacement -- 5.4.2 On Picard Iteration -- 5.4.3 Rotational Displacement -- 5.4.4 Homogeneous Deformation -- 5.5 Stresslet -- 5.6 Spectrum for a Sphere -- 5.6.1 Type I Problems - Ill-posed -- 5.7 Completed Double Layer Traction Problem -- 5.8 Exercises -- 5.8.1 Symmetry Relations -- 5.8.2 On Eigenfunctions -- 5.8.3 Incompressible Case -- 5.8.4 Gram-Schmidt Orthonormalization -- 5.8.5 Hadamard Ill-posed Problem -- 6 Numerical Implementation -- 6.1 Numerical Quadrature -- 6.2 Boundary Discretization -- 6.2.1 Constant Element -- 6.2.2 Higher Order Element -- 6.3 Evaluation of Boundary Integrals -- 6.3.1 Multivalued Traction -- 6.3.2 Regular Integrals -- 6.3.3 Singular Integrals -- 6.3.4 Rigid-Body Displacement -- 6.3.5 Adaptive Integration Schemes -- 6.3.6 Far-Field Approximation -- 6.4 Solution Methods -- 6.4.1 Direct Solver -- 6.4.2 Iterative Methods -- 6.4.3 Domain Decomposition -- 6.5 Distributed Computing under PVM -- 6.5.1 Some Concepts in Distributed Computing -- 6.5.2 Master/Slave Implementation -- 6.6 Exercises -- 6.6.1 Newton-Cotes rules -- 6.6.2 Quadrature -- 6.6.3 Galerkin Expansion -- 6.6.4 Jacobian -- 6.6.5 Evaluation of ∫[sub(Δ)] G[sub(ij)]dS and ∫[sub(Δ)] K[sub(ij)]dS -- 7 Some Applications of CDL-BIEM -- 7.1 Translating Sphere -- 7.1.1 Direct Formulation -- 7.1.2 CDL-BIEM -- 7.2 Sphere in Homogeneous Deformation -- 7.3 Two Spheroids -- 7.4 CDL in Half-Space -- 7.5 Container Surface -- 7.6 Deformation of a Cluster -- 7.7 Distributed Computing under PVM -- 7.7.1 Arrays of Spheres -- 7.7.2 Epilogue: Sedimentation through an Array of Spheres -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.
Summary: 1. Fundamental Equations2. Multipole Expansion and Rigid Inclusions3. Faxen Relations and Ellipsoidal Inclusions4. Load Transfer Problem and Boundary Collocation5. Completed Double Layer Boundary Element Method6. Numerical Implementation7. Some Applications of CDL-BIEM.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF00013159
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP00013159
Ebrary Ebrary Sudan Available
Ebrary Ebrary Tunisia Available
Total holds: 0

Intro -- Contents -- 1 Fundamental Equations -- 1.1 Introduction and Motivation -- 1.2 Stress and Strain -- 1.3 Equations of Equilibrium -- 1.4 Strain Energy -- 1.4.1 Uniqueness -- 1.4.2 Extremum Principles -- 1.5 Betti's Reciprocal Theorem -- 1.6 Integral Representation -- 1.6.1 Classification of Integral Equations -- 1.6.2 Kelvin State -- 1.6.3 Integral Representation -- 1.6.4 Rigid Inclusion -- 1.6.5 Eliminating Single or Double Layer -- 1.7 Single and Double Layer Potentials -- 1.7.1 Single Layer -- 1.7.2 Double Layer -- 1.7.3 Liapunov-Tauber Theorem -- 1.8 Boundary Integral Equations -- 1.8.1 Direct BEM -- 1.8.2 Indirect BEM -- 1.9 Spectral Properties -- 1.9.1 Banach's Theorem -- 1.9.2 λ = -1 -- 1.9.3 λ = +1 -- 1.9.4 Type II Problems -- 1.9.5 Spectral Radius of Κ -- 1.10 Exercises -- 1.10.1 Rigid-Body Displacement -- 1.10.2 Stretching -- 1.10.3 Simple Shearing -- 1.10.4 Moduli of Elasticity -- 1.10.5 Integral Representation -- 1.10.6 Transmission of Force and Torque -- 1.10.7 Reciprocal Relation -- 1.10.8 Translating Rigid Sphere 1 -- 1.10.9 Translating Rigid Sphere 2 -- 1.10.10 Kelvin's Solution -- 1.10.11 On Green's Equations -- 1.10.12 Papkovich-Neuber Representation -- 1.10.13 Galerkin Vector -- 1.10.14 Self-Adjoint Property of G -- 1.10.15 Elastic Inclusion -- 1.10.16 Constant c[sub(ij)] -- 1.10.17 Thin, Rigid Inclusion -- 1.10.18 Liapunov-Tauber Theorem -- 2 Multipole Expansion and Rigid Inclusions -- 2.1 Singularity Solutions -- 2.1.1 Papkovich-Neuber Representation -- 2.1.2 Potential Deformation -- 2.1.3 Rotlet Deformation -- 2.1.4 Kelvinlet Deformation -- 2.1.5 Half-Space Solutions -- 2.1.6 Interior Deformation -- 2.2 Multipole Expansion -- 2.2.1 Stresslet -- 2.3 Spherical Rigid Inclusion -- 2.3.1 Translating a Rigid Sphere -- 2.3.2 Rotating a Rigid Sphere -- 2.3.3 Rigid Sphere in a Linear Deformation.

2.3.4 Rigid Sphere in a Quadratic Ambient Field -- 2.3.5 Translating an Elastic Spherical Inclusion -- 2.4 Exercises -- 2.4.1 Navier Solutions -- 2.4.2 Navier Solutions -- 2.4.3 Navier Solutions -- 2.4.4 Galerkin Vector -- 2.4.5 Force and Torque on a Rigid Spherical Inclusion -- 2.4.6 Rigid Spherical Inclusion in High-Order Field -- 3 Faxén Relations and Ellipsoidal Inclusions -- 3.1 Faxén Relations -- 3.2 Rigid Spherical Inclusion -- 3.3 Rigid Ellipsoidal Inclusion -- 3.3.1 Singularity Solution for Translation -- 3.3.2 Singularity Solution for Linear Ambient Field -- 3.3.3 Degenerate Cases -- 3.3.4 Faxén Relations for the Rigid Ellipsoid -- 3.3.5 Interactions between Two Ellipsoids -- 3.4 Exercises -- 3.4.1 Traction Functionals -- 3.4.2 Faxén Relations for Torque and Stresslet -- 3.4.3 Multipole Expansion for Ellipsoids -- 3.4.4 Tractions for the Translating Ellipsoid -- 4 Load Transfer Problem and Boundary Collocation -- 4.1 The Method of Reflection -- 4.2 Load Transfer between Two Spheres -- 4.2.1 Far Field by Reflection -- 4.2.2 Near Touching -- 4.3 Kelvin Solutions -- 4.3.1 Spherical Harmonics -- 4.3.2 Kelvin's General Solutions -- 4.4 Boundary Collocation -- 4.4.1 Twin Multipole Expansions -- 4.4.2 Collocation Equations for Translation Problems -- 4.5 Comparison -- 4.6 Constitutive Relation -- 4.6.1 Constitutive Theory -- 4.6.2 Cubic Lattices -- 4.7 Kelvinlet near a Rigid Sphere -- 4.7.1 The Axisymmetric Kelvinlet -- 4.7.2 The Transverse Kelvinlet -- 4.8 Exercises -- 4.8.1 Solid Spherical Harmonics -- 4.8.2 Lurié Solution -- 4.8.3 Type I Problems -- 5 Completed Double Layer Boundary Element Method -- 5.1 Introduction -- 5.2 Direct Formulation -- 5.3 Completed Double Layer Boundary Element Method -- 5.3.1 Range Completer -- 5.3.2 Null Functions of (1+Κ) -- 5.3.3 Completion Process -- 5.3.4 Container Surface -- 5.3.5 A Summary.

5.4 Rigid Inclusion -- 5.4.1 Translational Displacement -- 5.4.2 On Picard Iteration -- 5.4.3 Rotational Displacement -- 5.4.4 Homogeneous Deformation -- 5.5 Stresslet -- 5.6 Spectrum for a Sphere -- 5.6.1 Type I Problems - Ill-posed -- 5.7 Completed Double Layer Traction Problem -- 5.8 Exercises -- 5.8.1 Symmetry Relations -- 5.8.2 On Eigenfunctions -- 5.8.3 Incompressible Case -- 5.8.4 Gram-Schmidt Orthonormalization -- 5.8.5 Hadamard Ill-posed Problem -- 6 Numerical Implementation -- 6.1 Numerical Quadrature -- 6.2 Boundary Discretization -- 6.2.1 Constant Element -- 6.2.2 Higher Order Element -- 6.3 Evaluation of Boundary Integrals -- 6.3.1 Multivalued Traction -- 6.3.2 Regular Integrals -- 6.3.3 Singular Integrals -- 6.3.4 Rigid-Body Displacement -- 6.3.5 Adaptive Integration Schemes -- 6.3.6 Far-Field Approximation -- 6.4 Solution Methods -- 6.4.1 Direct Solver -- 6.4.2 Iterative Methods -- 6.4.3 Domain Decomposition -- 6.5 Distributed Computing under PVM -- 6.5.1 Some Concepts in Distributed Computing -- 6.5.2 Master/Slave Implementation -- 6.6 Exercises -- 6.6.1 Newton-Cotes rules -- 6.6.2 Quadrature -- 6.6.3 Galerkin Expansion -- 6.6.4 Jacobian -- 6.6.5 Evaluation of ∫[sub(Δ)] G[sub(ij)]dS and ∫[sub(Δ)] K[sub(ij)]dS -- 7 Some Applications of CDL-BIEM -- 7.1 Translating Sphere -- 7.1.1 Direct Formulation -- 7.1.2 CDL-BIEM -- 7.2 Sphere in Homogeneous Deformation -- 7.3 Two Spheroids -- 7.4 CDL in Half-Space -- 7.5 Container Surface -- 7.6 Deformation of a Cluster -- 7.7 Distributed Computing under PVM -- 7.7.1 Arrays of Spheres -- 7.7.2 Epilogue: Sedimentation through an Array of Spheres -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.

1. Fundamental Equations2. Multipole Expansion and Rigid Inclusions3. Faxen Relations and Ellipsoidal Inclusions4. Load Transfer Problem and Boundary Collocation5. Completed Double Layer Boundary Element Method6. Numerical Implementation7. Some Applications of CDL-BIEM.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.