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1.

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:
2.

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:
3.

図書

図書
S.F. Borg
出版情報: Princeton, N.J. : D. Van Nostrand, c1963  xiv, 313 p. ; 23 cm
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4.

図書

図書
Clifford Truesdell, ... ; traduction francaise par Daniel Euvrard
出版情報: Paris : Masson, 1974  xvi, 367 p. ; 25 cm
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5.

図書

図書
by W. Noll, R. A. Toupin and C.-C. Wang ; with a preface by C. Truesdell
出版情報: Berlin ; Heidelberg ; New York : Springer-Verlag, 1968  1 v. (various pagings) ; 26 cm
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6.

図書

図書
Giuseppe Buttazzo ... [et al.], editors
出版情報: New York : Springer, c1998  x, 148 p. ; 25 cm
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7.

図書

図書
O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
出版情報: Amsterdam ; Oxford ; Tokyo : Elsevier Butterworth-Heinemann, 2005  xiv, 733 p., [4] p. of plates ; 26 cm
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The standard discrete system and origins of the finite element method
A direct physical approach to problems in elasticity: plane stress
Generalization of finite element concepts
Element shape functions
Mapped elements and numerical integration
Linear elasticity
Field problems
Automatic mesh generation
The patch test and reduced integration
Mixed formulation and constraints
Incompressible problems, mixed methods and other procedures of solution
Multidomain mixed approximations - domain decomposition and `frame' methods
Errors, recovery processes and error estimates
Adaptive finite element refinement
Point-based and partition of unity approximations
Semi-discretization and analytical solution
Discrete approximation in time
Coupled systems
Computer procedures for finite element analysis
Appendices
The standard discrete system and origins of the finite element method
A direct physical approach to problems in elasticity: plane stress
Generalization of finite element concepts
8.

図書

図書
O.C. Zienkiewicz, R.L. Taylor
出版情報: Oxford ; Tokyo : Elsevier Butterworth-Heinemann, 2005  xv, 631 p., [4] p. of plates ; 25 cm
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Preface
General problems in solid mechanics and non-linearity / 1:
Introduction / 1.1:
Small deformation solid mechanics problems / 1.2:
Variational forms for non-linear elasticity / 1.3:
Weak forms of governing equations / 1.4:
Concluding remarks / 1.5:
References
Galerkin method of approximation - irreducible and mixed forms / 2:
Finite element approximation - Galerkin method / 2.1:
Numerical integration - quadrature / 2.3:
Non-linear transient and steady-state problems / 2.4:
Boundary conditions: non-linear problems / 2.5:
Mixed or irreducible forms / 2.6:
Non-linear quasi-harmonic field problems / 2.7:
Typical examples of transient non-linear calculations / 2.8:
Solution of non-linear algebraic equations / 2.9:
Iterative techniques / 3.1:
General remarks - incremental and rate methods / 3.3:
Inelastic and non-linear materials / 4:
Viscoelasticity - history dependence of deformation / 4.1:
Classical time-independent plasticity theory / 4.3:
Computation of stress increments / 4.4:
Isotropic plasticity models / 4.5:
Generalized plasticity / 4.6:
Some examples of plastic computation / 4.7:
Basic formulation of creep problems / 4.8:
Viscoplasticity - a generalization / 4.9:
Some special problems of brittle materials / 4.10:
Non-uniqueness and localization in elasto-plastic deformations / 4.11:
Geometrically non-linear problems - finite deformation / 4.12:
Governing equations / 5.1:
Variational description for finite deformation / 5.3:
Two-dimensional forms / 5.4:
A three-field, mixed finite deformation formulation / 5.5:
A mixed-enhanced finite deformation formulation / 5.6:
Forces dependent on deformation - pressure loads / 5.7:
Material constitution for finite deformation / 5.8:
Isotropic elasticity / 6.1:
Isotropic viscoelasticity / 6.3:
Plasticity models / 6.4:
Incremental formulations / 6.5:
Rate constitutive models / 6.6:
Numerical examples / 6.7:
Treatment of constraints - contact and tied interfaces / 6.8:
Node-node contact: Hertzian contact / 7.1:
Tied interfaces / 7.3:
Node-surface contact / 7.4:
Surface-surface contact / 7.5:
Pseudo-rigid and rigid-flexible bodies / 7.6:
Pseudo-rigid motions / 8.1:
Rigid motions / 8.3:
Connecting a rigid body to a flexible body / 8.4:
Multibody coupling by joints / 8.5:
Discrete element methods / 8.6:
Early DEM formulations / 9.1:
Contact detection / 9.3:
Contact constraints and boundary conditions / 9.4:
Block deformability / 9.5:
Time integration for discrete element methods / 9.6:
Associated discontinuous modelling methodologies / 9.7:
Unifying aspects of discrete element methods / 9.8:
Structural mechanics problems in one dimension - rods / 9.9:
Weak (Galerkin) forms for rods / 10.1:
Finite element solution: Euler-Bernoulli rods / 10.4:
Finite element solution: Timoshenko rods / 10.5:
Forms without rotation parameters / 10.6:
Moment resisting frames / 10.7:
Plate bending approximation: thin (Kirchhoff) plates and C[subscript 1] continuity requirements / 10.8:
The plate problem: thick and thin formulations / 11.1:
Rectangular element with corner nodes (12 degrees of freedom) / 11.3:
Quadrilateral and parallelogram elements / 11.4:
Triangular element with corner nodes (9 degrees of freedom) / 11.5:
Triangular element of the simplest form (6 degrees of freedom) / 11.6:
The patch test - an analytical requirement / 11.7:
General remarks / 11.8:
Singular shape functions for the simple triangular element / 11.10:
An 18 degree-of-freedom triangular element with conforming shape functions / 11.11:
Compatible quadrilateral elements / 11.12:
Quasi-conforming elements / 11.13:
Hermitian rectangle shape function / 11.14:
The 21 and 18 degree-of-freedom triangle / 11.15:
Mixed formulations - general remarks / 11.16:
Hybrid plate elements / 11.17:
Discrete Kirchhoff constraints / 11.18:
Rotation-free elements / 11.19:
Inelastic material behaviour / 11.20:
Concluding remarks - which elements? / 11.21:
'Thick' Reissner-Mindlin plates - irreducible and mixed formulations / 12:
The irreducible formulation - reduced integration / 12.1:
Mixed formulation for thick plates / 12.3:
The patch test for plate bending elements / 12.4:
Elements with discrete collocation constraints / 12.5:
Elements with rotational bubble or enhanced modes / 12.6:
Linked interpolation - an improvement of accuracy / 12.7:
Discrete 'exact' thin plate limit / 12.8:
Performance of various 'thick' plate elements - limitations of thin plate theory / 12.9:
Concluding remarks - adaptive refinement / 12.10:
Shells as an assembly of flat elements / 13:
Stiffness of a plane element in local coordinates / 13.1:
Transformation to global coordinates and assembly of elements / 13.3:
Local direction cosines / 13.4:
'Drilling' rotational stiffness - 6 degree-of-freedom assembly / 13.5:
Elements with mid-side slope connections only / 13.6:
Choice of element / 13.7:
Practical examples / 13.8:
Curved rods and axisymmetric shells / 14:
Straight element / 14.1:
Curved elements / 14.3:
Independent slope-displacement interpolation with penalty functions (thick or thin shell formulations) / 14.4:
Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions / 15:
Shell element with displacement and rotation parameters / 15.1:
Special case of axisymmetric, curved, thick shells / 15.3:
Special case of thick plates / 15.4:
Convergence / 15.5:
Inelastic behaviour / 15.6:
Some shell examples / 15.7:
Semi-analytical finite element processes - use of orthogonal functions and 'finite strip' methods / 15.8:
Prismatic bar / 16.1:
Thin membrane box structures / 16.3:
Plates and boxes with flexure / 16.4:
Axisymmetric solids with non-symmetrical load / 16.5:
Axisymmetric shells with non-symmetrical load / 16.6:
Non-linear structural problems - large displacement and instability / 16.7:
Large displacement theory of beams / 17.1:
Elastic stability - energy interpretation / 17.3:
Large displacement theory of thick plates / 17.4:
Large displacement theory of thin plates / 17.5:
Solution of large deflection problems / 17.6:
Shells / 17.7:
Multiscale modelling / 17.8:
Asymptotic analysis / 18.1:
Statement of the problem and assumptions / 18.3:
Formalism of the homogenization procedure / 18.4:
Global solution / 18.5:
Local approximation of the stress vector / 18.6:
Finite element analysis applied to the local problem / 18.7:
The non-linear case and bridging over several scales / 18.8:
Asymptotic homogenization at three levels: micro, meso and macro / 18.9:
Recovery of the micro description of the variables of the problem / 18.10:
Material characteristics and homogenization results / 18.11:
Multilevel procedures which use homogenization as an ingredient / 18.12:
General first-order and second-order procedures / 18.13:
Discrete-to-continuum linkage / 18.14:
Local analysis of a unit cell / 18.15:
Homogenization procedure - definition of successive yield surfaces / 18.16:
Numerically developed global self-consistent elastic-plastic constitutive law / 18.17:
Global solution and stress-recovery procedure / 18.18:
Computer procedures for finite element analysis / 18.19:
Solution of non-linear problems / 19.1:
Eigensolutions / 19.3:
Restart option / 19.4:
Isoparametric finite element approximations / 19.5:
Invariants of second-order tensors / Appendix B:
Author index
Subject index
Preface
General problems in solid mechanics and non-linearity / 1:
Introduction / 1.1:
9.

図書

図書
出版情報: New York : Wiley
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10.

図書

図書
L.I. Sedov ; translated from the Russian by Rebecca Schoenfeld-Reiner ; English translation edited by J.E. Adkins and A.J.M. Spencer
出版情報: Oxford ; New York : Pergamon Press, 1966  xvi, 252 p. ; 24 cm
シリーズ名: International series of monographs in interdisciplinary and advanced topics in science and engineering ; v. 1
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