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1.

図書

図書
Romesh C. Batra
出版情報: Reston, Va : American Institute of Aeronautics and Astronautics, c2006  xvii, 325 p. ; 24 cm
シリーズ名: AIAA education series
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Preface
Acknowledgements
Introduction / Chapter 1:
What is Mechanics? / 1.1:
Continuum Mechanics / 1.2:
An Example of an Ad-Hoc Approach / 1.3:
Mathematical Preliminaries / Chapter 2:
Summation Convention, Dummy Indices / 2.1:
Free Indices / 2.2:
Kronecker Delta / 2.3:
Index Notation / 2.4:
Permutation Symbol / 2.5:
Manipulations with the Indicial Notations / 2.6:
Translation and Rotation of Coordinate Axes / 2.7:
Tensors / 2.8:
The Divergence Theorem / 2.9:
Differentiation of Tensor Fields / 2.10:
References
Exercises
Kinematics / Chapter 3:
Description of motion and continuum / 3.1:
Referential and Special Descriptions / 3.2:
Displacement Vector / 3.3:
Restrictions on Continuous Deformation of a Deformable Body / 3.4:
Material Derivative / 3.5:
Finding Acceleration of a Particle from a Given Velocity Field / 3.6:
Deformation Gradient / 3.7:
Strain Tensors / 3.8:
Principle Strains / 3.9:
Deformation of Areas and Volumes / 3.10:
Mass Density, Equation and Continuity / 3.11:
Rate of Deformation, Strain-Rate Tensor, Spin / 3.12:
Polar Decomposition / 3.13:
Infinitesimal Deformations / 3.14:
Infinitesimal Deformations Superimposed Upon Finite / 3.15:
Volumetric and Deviatoric Strains / 3.16:
Transformation of Tensors Under a Change of Bases / 3.17:
Plain Strain Deformation / 3.18:
Solution of a Cubic Equation / Appendix A:
The Balance Laws, Stress Tensors / Chapter 4:
Kinetics of a Continuous Media / 4.1:
Traction Boundary Conditions / 4.2:
The Nominal Stress Tensor / 4.3:
Transformation of Stress Tensors Under the Rotation of Axes / 4.4:
Principle Stresses; Maximum Shear Stress / 4.5:
Relations Among Stress Tensors for Infinitesimal Deformations / 4.6:
Plane Stress / 4.7:
Deviatoric Stress, von-Mises Stress / 4.8:
Balance of Energy / 4.9:
Entropy Inequality, The Clausius-Duhem Inequality / 4.10:
Summary of Equations Governing Deformations of a Body / 4.11:
Nonuniquences of Solutions for Static Problems / 4.12:
The Transport Theorem / Appendix B:
Constitutive Relations / Chapter 5:
Introductory Remarks / 5.1:
Thermoelastic Material / 5.2:
Principle of Material Objectivity / 5.3:
Linear Constitutive Relations for Finite Deformations of a Thermoelastic Body / 5.4:
Isotropic Thermoelastic Materials / 5.5:
Comparison of Results from Four Linear Constitutive Relations in Isotropic Finite Elasticity / 5.6:
Transversely Isotropic Thermoelastic Materials / 5.7:
Orthotropic Thermoelastic Materials / 5.8:
Coincidence of Principle Axes of Stress and Strain in Isotropic Elastic Materials / 5.9:
Coincidence of Principle Axes of Stress and Strain in Transversely Isotropic Elastic Materials / 5.10:
Incompressible Elastic Materials / 5.11:
Comparison of Results fr5om Constitutive Relations / 5.12:
Constitutive Relations fro Infinitesimal Deformations of Elastic Materials / 5.13:
Constitutive Relations for Special Isotropic Nonlinear Elastic Materials / 5.14:
Infinitesimal Deformations Superimposed Upon Finite Deformations of an Isotropic Elastic Body / 5.15:
Constitutive Relations for Plane Deformations of a Thermoelastic Body / 5.16:
Thermoviscoelastic Materials / 5.17:
Summary / 5.18:
Torsion of a Circular Cylinder / Chapter 6:
Torsion of a Linear Elastic Circular Cylinder / 6.1:
Torsion of a Second Order Elastic Circular Cylinder / 6.2:
Infinitesimal Twist of a Finitely Stretched Circular Cylinder / 6.3:
Finite Torsion of a Circular Cylinder / 6.4:
A Uniqueness Theorem / Appendix C:
Exercise
Fluid Flow / Chapter 7:
Steady Flow Between Two Parallel Plates / 7.1:
Steady Isothermal Flow of an Incompressible Fluid Down an Inclined Plane / 7.2:
Steady Flow of an Incompressible Fluid in a Horizontal Circular Pipe / 7.3:
Bending of Beams / Chapter 8:
Bending of a Rectangular Beam / 8.1:
Bending of a Nonlinear Elastic Rectangular Beam / 8.2:
Air Stress Function for Bending of a Beam / 8.3:
Wave Propagation / Chapter 9:
Singular Surface / 9.1:
Kinematics of a Singular Surface / 9.2:
Acceleration Waves in Linear Elasticity / 9.3:
Progressive Waves / 9.4:
Incompressible Linear Elastic Materials / 9.5:
Acceleration Waves in Nonlinear Elastic Bodies / 9.6:
Infinitesimal Deformations Superimposed Upon Finite Deformations / 9.7:
Spherical and Cylindrical Pressure Vessels / Chapter 10:
Radial Expansion of a Spherical Pressure Vessel / 10.1:
Radial Expansion of an Incompressible Hookean Sphere / 10.2:
Radial Expansion of a Cylindrical Pressure Vessel / 10.3:
Radial Expansion of an Inhomogeneous and Incompressible Hookean Cylinder / 10.4:
Finite Radial Expansion of a NeoHookean Cylinder / 10.5:
Index
Supporting Materials
Preface
Acknowledgements
Introduction / Chapter 1:
2.

図書

図書
Marcelo Epstein
出版情報: Cambridge : Cambridge University Press, 2010  xii, 312 p. ; 26 cm
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Preface
Motivation and Background / Part 1:
The Case for Differential Geometry / 1:
Classical Space-Time and Fibre Bundles / 1.1:
Configuration Manifolds and Their Tangent and Cotangent Spaces / 1.2:
The Infinite-dimensional Case / 1.3:
Elasticity / 1.4:
Material or Configurational Forces / 1.5:
Vector and Affine Spaces / 2:
Vector Spaces: Definition and Examples / 2.1:
Linear Independence and Dimension / 2.2:
Change of Basis and the Summation Convention / 2.3:
The Dual Space / 2.4:
Linear Operators and the Tensor Product / 2.5:
Isomorphisms and Iterated Dual / 2.6:
Inner-product Spaces / 2.7:
Affine Spaces / 2.8:
Banach Spaces / 2.9:
Tensor Algebras and Multivectors / 3:
The Algebra of Tensors on a Vector Space / 3.1:
The Contravariant and Covariant Subalgebras / 3.2:
Exterior Algebra / 3.3:
Multivectors and Oriented Affine Simplexes / 3.4:
The Faces of an Oriented Affine Simplex / 3.5:
Multicovectors or r-Forms / 3.6:
The Physical Meaning of r-Forms / 3.7:
Some Useful Isomorphisms / 3.8:
Differential Geometry / Part 2:
Differentiable Manifolds / 4:
Introduction / 4.1:
Some Topological Notions / 4.2:
Topological Manifolds / 4.3:
Differentiability / 4.4:
Tangent Vectors / 4.6:
The Tangent Bundle / 4.7:
The Lie Bracket / 4.8:
The Differential of a Map / 4.9:
Immersions, Embeddings, Submanifolds / 4.10:
The Cotangent Bundle / 4.11:
Tensor Bundles / 4.12:
Pull-backs / 4.13:
Exterior Differentiation of Differential Forms / 4.14:
Some Properties of the Exterior Derivative / 4.15:
Riemannian Manifolds / 4.16:
Manifolds with Boundary / 4.17:
Differential Spaces and Generalized Bodies / 4.18:
Lie Derivatives, Lie Groups, Lie Algebras / 5:
The Fundamental Theorem of the Theory of ODEs / 5.1:
The Flow of a Vector Field / 5.3:
One-parameter Groups of Transformations Generated by Flows / 5.4:
Time-Dependent Vector Fields / 5.5:
The Lie Derivative / 5.6:
Invariant Tensor Fields / 5.7:
Lie Groups / 5.8:
Group Actions / 5.9:
"One-Parameter Subgroups / 5.10:
Left-and Right-Invariant Vector Fields on a Lie Group / 5.11:
The Lie Algebra of a Lie Group / 5.12:
Down-to-Earth Considerations / 5.13:
The Adjoint Representation / 5.14:
Integration and Fluxes / 6:
Integration of Forms in Affine Spaces / 6.1:
Integration of Forms on Chains in Manifolds / 6.2:
Integration of Forms on Oriented Manifolds / 6.3:
Fluxes in Continuum Physics / 6.4:
General Bodies and Whitney's Geometric Integration Theory / 6.5:
Further Topics / Part 3:
Fibre Bundles / 7:
Product Bundles / 7.1:
Trivial Bundles / 7.2:
General Fibre Bundles / 7.3:
The Fundamental Existence Theorem / 7.4:
The Tangent and Cotangent Bundles / 7.5:
The Bundle of Linear Frames / 7.6:
Principal Bundles / 7.7:
Associated Bundles / 7.8:
Fibre-Bundle Morphisms / 7.9:
Cross Sections / 7.10:
Iterated Fibre Bundles / 7.11:
Inhomogeneity Theory / 8:
Material Uniformity / 8.1:
The Material Lie groupoid / 8.2:
The Material Principal Bundle / 8.3:
Flatness and Homogeneity / 8.4:
Distributions and the Theorem of Frobenius / 8.5:
JetBundles-and -Differential Equations / 8.6:
Connection, Curvature, Torsion / 9:
Ehresmann Connection / 9.1:
Connections in Principal Bundles / 9.2:
Linear Connections / 9.3:
G-Connections / 9.4:
Riemannian Connections / 9.5:
Material Homogeneity / 9.6:
Homogeneity Criteria / 9.7:
A Primer in Continuum Mechanics / Appendix A:
Bodies and Configurations / A.1:
Observers and Frames / A.2:
Strain / A.3:
Volume and Area / A.4:
The Material Time Derivative / A.5:
Change of Reference / A.6:
Transport Theorems / A.7:
The General Balance Equation / A.8:
The Fundamental Balance Equations of Continuum Mechanics / A.9:
A Modicum of Constitutive Theory / A.10:
Index
Preface
Motivation and Background / Part 1:
The Case for Differential Geometry / 1:
3.

図書

図書
edited by Ray W. Ogden and David J. Steigmann
出版情報: Wien : SpringerWienNewYork , Udine : CISM, c2011  266 p. ; 25 cm
シリーズ名: CISM courses and lectures ; no. 527
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Electromagnetics in Deformable Solids / G.A. Maugin
Modeling Nonlinear Electroelastic Materials / A. Dorfmann
Magnetostatics: from Basic Principles to Nonlinear Interactions in Deformable Media / R. W. Ogden
Analysis of Nonlinear Electrostatic Membranes / J. Edmiston ; D.J. Steigmann
Computational Nonlinear Electro-Elasticity-Getting Started / P. Steinmann
Electro-Mechanical Response of Nematic Elastomers: an Introduction / A. DeSimone
Electromagnetics in Deformable Solids / G.A. Maugin
Modeling Nonlinear Electroelastic Materials / A. Dorfmann
Magnetostatics: from Basic Principles to Nonlinear Interactions in Deformable Media / R. W. Ogden
4.

図書

図書
L.I. Sedov
出版情報: Groningen : Wolters-Noordhoff, c1972  xx, 340 p. ; 23 cm
シリーズ名: A course in continuum mechanics / L.I. Sedov ; translation from the Russian, edited by J.R.M. Radok ; v. 3
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5.

図書

図書
Hans-Dieter Alber
出版情報: Berlin ; New York : Springer, c1998  x, 166 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1682
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6.

図書

図書
Donald A. Drew, Stephen L. Passman
出版情報: New York : Springer, c1999  x, 308 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 135
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7.

図書

図書
Javier Bonet, Richard D. Wood
出版情報: Cambridge, UK ; New York : Cambridge University Press, 2008  xx, 318 p. ; 26 cm
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Preface
Introduction / 1:
Nonlinear Computational Mechanics / 1.1:
Simple Examples of Nonlinear Structural Behavior / 1.2:
Cantilever / 1.2.1:
Column / 1.2.2:
Nonlinear Strain Measures / 1.3:
One-Dimensional Strain Measures / 1.3.1:
Nonlinear Truss Example / 1.3.2:
Continuum Strain Measures / 1.3.3:
Directional Derivative, Linearization and Equation Solution / 1.4:
Directional Derivative / 1.4.1:
Linearization and Solution of Nonlinear Algebraic Equations / 1.4.2:
Mathematical Preliminaries / 2:
Vector and Tensor Algebra / 2.1:
Vectors / 2.2.1:
Second-Order Tensors / 2.2.2:
Vector and Tensor Invariants / 2.2.3:
Higher-Order Tensors / 2.2.4:
Linearization and the Directional Derivative / 2.3:
One Degree of Freedom / 2.3.1:
General Solution to a Nonlinear Problem / 2.3.2:
Properties of the Directional Derivative / 2.3.3:
Examples of Linearization / 2.3.4:
Tensor Analysis / 2.4:
The Gradient and Divergence Operators / 2.4.1:
Integration Theorems / 2.4.2:
Analysis of Three-Dimensional Truss Structures / 3:
Kinematics / 3.1:
Linearization of Geometrical Descriptors / 3.2.1:
Internal Forces and Hyperelastic Constitutive Equations / 3.3:
Nonlinear Equilibrium Equations and the Newton-Raphson Solution / 3.4:
Equilibrium Equations / 3.4.1:
Newton-Raphson Procedure / 3.4.2:
Tangent Elastic Stiffness Matrix / 3.4.3:
Elasto-Plastic Behavior / 3.5:
Multiplicative Decomposition of the Stretch / 3.5.1:
Rate-independent Plasticity / 3.5.2:
Incremental Kinematics / 3.5.3:
Time Integration / 3.5.4:
Stress Update and Return Mapping / 3.5.5:
Algorithmic Tangent Modulus / 3.5.6:
Revised Newton-Raphson Procedure / 3.5.7:
Examples / 3.6:
Inclined Axial Rod / 3.6.1:
Trussed Frame / 3.6.2:
The Motion / 4:
Material and Spatial Descriptions / 4.3:
Deformation Gradient / 4.4:
Strain / 4.5:
Polar Decomposition / 4.6:
Volume Change / 4.7:
Distortional Component of the Deformation Gradient / 4.8:
Area Change / 4.9:
Linearized Kinematics / 4.10:
Linearized Deformation Gradient / 4.10.1:
Linearized Strain / 4.10.2:
Linearized Volume Change / 4.10.3:
Velocity and Material Time Derivatives / 4.11:
Velocity / 4.11.1:
Material Time Derivative / 4.11.2:
Directional Derivative and Time Rates / 4.11.3:
Velocity Gradient / 4.11.4:
Rate of Deformation / 4.12:
Spin Tensor / 4.13:
Rate of Change of Volume / 4.14:
Superimposed Rigid Body Motions and Objectivity / 4.15:
Stress and Equilibrium / 5:
Cauchy Stress Tensor / 5.1:
Definition / 5.2.1:
Stress Objectivity / 5.2.2:
Equilibrium / 5.3:
Translational Equilibrium / 5.3.1:
Rotational Equilibrium / 5.3.2:
Principle of Virtual Work / 5.4:
Work Conjugacy and Alternative Stress Representations / 5.5:
The Kirchhoff Stress Tensor / 5.5.1:
The First Piola-Kirchhoff Stress Tensor / 5.5.2:
The Second Piola-Kirchhoff Stress Tensor / 5.5.3:
Deviatoric and Pressure Components / 5.5.4:
Stress Rates / 5.6:
Hyperelasticity / 6:
Elasticity Tensor / 6.1:
The Material or Lagrangian Elasticity Tensor / 6.3.1:
The Spatial or Eulerian Elasticity Tensor / 6.3.2:
Isotropic Hyperelasticity / 6.4:
Material Description / 6.4.1:
Spatial Description / 6.4.2:
Compressible Neo-Hookean Material / 6.4.3:
Incompressible and Nearly Incompressible Materials / 6.5:
Incompressible Elasticity / 6.5.1:
Incompressible Neo-Hookean Material / 6.5.2:
Nearly Incompressible Hyperelastic Materials / 6.5.3:
Isotropic Elasticity in Principal Directions / 6.6:
Material Elasticity Tensor / 6.6.1:
Spatial Elasticity Tensor / 6.6.4:
A Simple Stretch-based Hyperelastic Material / 6.6.5:
Nearly Incompressible Material in Principal Directions / 6.6.6:
Plane Strain and Plane Stress Cases / 6.6.7:
Uniaxial Rod Case / 6.6.8:
Large Elasto-Plastic Deformations / 7:
The Multiplicative Decomposition / 7.1:
Rate Kinematics / 7.3:
Rate-Independent Plasticity / 7.4:
Principal Directions / 7.5:
The Radial Return Mapping / 7.6:
Two-Dimensional Cases / 7.6.2:
Linearized Equilibrium Equations / 8:
Linearization and Newton-Raphson Process / 8.1:
Lagrangian Linearized Internal Virtual Work / 8.3:
Eulerian Linearized Internal Virtual Work / 8.4:
Linearized External Virtual Work / 8.5:
Body Forces / 8.5.1:
Surface Forces / 8.5.2:
Variational Methods and Incompressibility / 8.6:
Total Potential Energy and Equilibrium / 8.6.1:
Lagrange Multiplier Approach to Incompressibility / 8.6.2:
Penalty Methods for Incompressibility / 8.6.3:
Hu-Washizu Variational Principle for Incompressibility / 8.6.4:
Mean Dilatation Procedure / 8.6.5:
Discretization and Solution / 9:
Discretized Kinematics / 9.1:
Discretized Equilibrium Equations / 9.3:
General Derivation / 9.3.1:
Derivation in Matrix Notation / 9.3.2:
Discretization of the Linearized Equilibrium Equations / 9.4:
Constitutive Component: Indicial Form / 9.4.1:
Constitutive Component: Matrix Form / 9.4.2:
Initial Stress Component / 9.4.3:
External Force Component / 9.4.4:
Tangent Matrix / 9.4.5:
Mean Dilatation Method for Incompressibility / 9.5:
Implementation of the Mean Dilatation Method / 9.5.1:
Newton-Raphson Iteration and Solution Procedure / 9.6:
Newton-Raphson Solution Algorithm / 9.6.1:
Line Search Method / 9.6.2:
Arc-Length Method / 9.6.3:
Computer Implementation / 10:
User Instructions / 10.1:
Output File Description / 10.3:
Element Types / 10.4:
Solver Details / 10.5:
Constitutive Equation Summary / 10.6:
Program Structure / 10.7:
Main Routine flagshyp / 10.8:
Routine elemtk / 10.9:
Routine radialrtn / 10.10:
Routine ksigma / 10.11:
Routine bpress / 10.12:
Simple Patch Test / 10.13:
Nonlinear Truss / 10.13.2:
Strip With a Hole / 10.13.3:
Plane Strain Nearly Incompressible Strip / 10.13.4:
Elasto-plastic Cantilever / 10.13.5:
Appendix: Dictionary of Main Variables / 10.14:
Bibliography
Index
Preface
Introduction / 1:
Nonlinear Computational Mechanics / 1.1:
8.

図書

図書
Gerhard A. Holzapfel
出版情報: Chichester : John Wiley & Sons, c2000  xiv, 455 p. ; 25 cm
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Introduction to Vectors and Tensors
Kinematics
The Concept of Stress
Balance Principles
Some Aspects of Objectivity
Hyperelastic Materials
Thermodynamics of Materials
Variational Principles
References
Index
Introduction to Vectors and Tensors
Kinematics
The Concept of Stress
9.

図書

図書
G. Leibfried, N. Breuer
出版情報: Berlin ; New York : Springer-Verlag, 1978  xiv, 342 p. ; 25 cm
シリーズ名: Springer tracts in modern physics : Ergebnisse der exakten Naturwissenschaften / editor, G. Höhler ; 81 . Point defects in metals ; v.1
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10.

図書

図書
William Alan Day
出版情報: Berlin ; New York : Springer-Verlag, 1972  x, 134 p. ; 24 cm
シリーズ名: Springer tracts in natural philosophy ; v. 22
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