1.
図書
Wilhelm Flügge
出版情報:
Berlin : Springer-Verlag, 1972 vii, 207 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
2.
図書
A.B. Bhatia, R.N. Singh
3.
図書
Morton E. Gurtin
目次情報:
続きを見る
Preface
Acknowledgments
Tensor Algebra
Tensor Analysis
Kinematics
Mass
Momentum
Force
Constitutive Assumptions
Inviscid Fluids
Change in Observer
Invariance of Material Response
Newtonian Fluids
The NavierStokes Equations
Finite Elasticity
Linear Elasticity
Appendix
References
Hints for Selected Exercises
Index
Preface
Acknowledgments
Tensor Algebra
4.
図書
C. Truesdell
5.
図書
O.C. Zienkiewicz
出版情報:
London ; New York : McGraw-Hill, c1977 xv, 787 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
6.
図書
G. Leibfried, N. Breuer
7.
図書
William Alan Day
8.
図書
L.I. Sedov
9.
図書
Gerhard A. Holzapfel
出版情報:
Chichester : John Wiley & Sons, c2000 xiv, 455 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
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
10.
図書
Peter Haupt ; Translated from German by Joan A. Kurth
目次情報:
続きを見る
Kinematics
Balance Relations of Mechanics
Balance Relations of Thermodynamics
Objectivity
Classical Theories of Continuum Mechanics
Experimental Observation and Mathematical Modelling
General Theory of Mechanical Material Behaviour
Dual Variables
Elasticity
Viscoelasticity
Plasticity
Viscoplasticity
Constitutive Models in Thermomechanics
References
Index
Kinematics
Balance Relations of Mechanics
Balance Relations of Thermodynamics
11.
図書
Giuseppe Buttazzo ... [et al.], editors
出版情報:
New York : Springer, c1998 x, 148 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
12.
図書
Hans-Dieter Alber
13.
図書
Donald A. Drew, Stephen L. Passman
14.
図書
R.M. Christensen
出版情報:
New York : Wiley, c1979 xiv, 348 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
15.
図書
edited by Howard Cook ... [et al.]
目次情報:
続きを見る
Expository and survey papers: matchbox manifolds / Part 1：
rotation sets for invariant continua
the fixed point property in dimension one
Menger manifolds
exactly k-to-1 functions - from pathological functions with finitely many discontinuities to well-behaved covering maps
a brief history of indecomposable continua
spans of continua and their applications
complex dynamics and continuum theory
continua on which 2-to-1 maps induce continuous involutions
Research papers / Part 2：
Expository and survey papers: matchbox manifolds / Part 1：
rotation sets for invariant continua
the fixed point property in dimension one
16.
図書
E.W. Billington
出版情報:
Bristol, England ; Boston : A. Hilger, c1986 xvi, 339 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
17.
図書
C. Truesdell
出版情報:
New York ; Tokyo : Springer-Verlag, [1985], c1966 279 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
18.
図書
[by] Mark J. Beran
19.
図書
O.C. Zienkiewicz and R.L. Taylor
目次情報:
続きを見る
Some preliminaries: The standard discrete system
A direct approach to problems in elasticity
Generalisation of the finite element concepts - Galerkin-weighted residual and variational approaches
Plane stress and plane strain
Axisymmetric stress analysis
Three-dimensional stress analysis
Steady-state field problems - heat conduction, electric and magnetic potential, fluid flow etc.
'Standard' and `hierarchical' element shape functions: some general familiarities of C0 continuity
Mapped elements and numerical integration - `infinite' and `singularity' elements
The patch test, reduced integration and non-conforming elements
Mixed formulation and constraints - complete field methods
Incompressible problems, mixed methods and other procedures of solution
Mixed formulation and constraints - incomplete (hybrid) field methods, boundary*Trefftz methods
Errors, recovery processes and error estimates
Adaptive finite element refinement
The time dimension semi-discretisation of field and dynamic problems and analytical solution procedures
The time dimension discrete approximation in time
Coupled systems
Computer procedures for finite element analysis
Appendices
Plate and shell bending approximation: thin (Kirchoff) plates and C1 continuity requirements / VOLUME 2：
'Thick' Reissner-Mindlin plates - irreducible and mixed formulations
Shells as an assembly of flat elements
Axisymmetric shells
Introduction and the equations of fluid dynamics / Volume 3：
Convection dominated problems - finite element
A general algorithm for compressible and incompressible flows - the characteristic based split (CBS) algorithm
Incompressible laminar flow - Newtonian and non-Newtonian fluids
Free surface, buoyancy and turbulent incompressible flows
Compressible high-speed gas flow
Shallow water problems
Waves
Computer implementation of the CBS algorithm
Some preliminaries: The standard discrete system
A direct approach to problems in elasticity
Generalisation of the finite element concepts - Galerkin-weighted residual and variational approaches
20.
図書
by Mysore N.L. Narasimhan
出版情報:
New York : J. Wiley & Sons, c1992 xiv, 567p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
21.
図書
edited by G.A. Maugin
22.
図書
Clifford A. Truesdell, III
23.
図書
by William Prager
24.
図書
[by] B.D. Coleman, H. Markovitz [and] W. Noll
25.
図書
S.F. Borg
出版情報:
Singapore : World Scientific, c1990 xvi, 336 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
26.
図書
A. Cemal Eringen
27.
図書
Clifford Truesdell, ... ; traduction francaise par Daniel Euvrard
出版情報:
Paris : Masson, 1974 xvi, 367 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
28.
図書
[by] D.C. Leigh
29.
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
子書誌情報:
loading…
所蔵情報:
loading…
30.
図書
Hans Ziegler
31.
図書
L.I. Sedov
32.
図書
L.I. Sedov
33.
図書
Attila Askar
34.
図書
Wai-Fah Chen and Atef F.Saleeb
35.
図書
出版情報:
New York : Wiley
子書誌情報:
loading…
所蔵情報:
loading…
36.
図書
C.-C. Wang
37.
図書
[by] J.T. Oden
38.
図書
Alexander L. Fetter, John Dirk Walecka
39.
図書
O. C. Zienkiewicz in collaboration with Y. K. Cheung
40.
図書
Roger Valid
41.
図書
O.C. Zienkiewicz and R.L. Taylor
42.
図書
[edited by] C. Truesdell
43.
図書
J.T. Oden, J.N. Reddy
出版情報:
Berlin ; New York : Springer-Verlag, 1976 x, 302 p. ; 25 cm
シリーズ名:
Universitext
子書誌情報:
loading…
所蔵情報:
loading…
44.
図書
Michael Renardy, William J. Hrusa & John A. Nohel
45.
図書
Y.C. Fung
出版情報:
Englewood Cliffs, N.J. : Prentice-Hall, c1977 xii, 340 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
46.
図書
W. Michael Lai, David Rubin, Erhard Krempl
出版情報:
Oxford ; New York : Pergamon Press, 1993 xiv, 556 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Chapter headings
Introduction
Tensors
Kinematics of a continuum
Stress
The elastic solid
Newtonian vicous fluid
Integral formulation of general principles
Non-Newtonian fluids
Index
Chapter headings
Introduction
Tensors
47.
図書
E.M. Hackett, K.-H. Schwalbe, and R.H. Dodds, Jr., editors
目次情報:
v. 2. Constraint effects in fracture : theory and applications
v. 2. Constraint effects in fracture : theory and applications
48.
図書
O.C. Zienkiewicz, R.L. Taylor, D.D. Fox
出版情報:
Oxford ; Tokyo : Butterworth-Heinemann, 2014 xxxi, 624 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
49.
図書
J.N. Reddy
出版情報:
Cambridge : Cambridge University Press, 2013 xxvi, 450 p. ; 26 cm
子書誌情報:
loading…
所蔵情報:
loading…
50.
図書
O.C. Zienkiewicz, R.L. Taylor
目次情報:
続きを見る
Some preliminaries: The standard discrete system
A direct approach to problems in elasticity
Generalization of the finite element concepts - Galerkin-weighted residual and variational approaches
Plane stress and plane strain
Axisymmetric stress analysis
Three-dimensional stress analysis
Steady-state field problems - heat conduction, electric and magnetic potential, fluid flow etc.
'Standard' and `hierarchical' element shape functions: some general familiarities of C0 continuity
Mapped elements and numerical integration - `infinite' and `singularity' elements
The patch test, reduced integration and non-conforming elements
Mixed formulation and constraints - complete field methods
Incompressible problems, mixed methods and other procedures of solution
Mixed formulation and constraints - incomplete (hybrid) field methods, boundary
Trefftz methods
Errors, recovery processes and error estimates
Adaptive finite element refinement
The time dimension - semi-discretization of field and dynamic problems and analytical solution procedures
The time dimension - discrete approximation in time
Coupled systems
Computer procedures for finite element analysis
Appendices
Some preliminaries: The standard discrete system
A direct approach to problems in elasticity
Generalization of the finite element concepts - Galerkin-weighted residual and variational approaches
51.
図書
O.C. Zienkiewicz, R.L. Taylor
目次情報:
続きを見る
General problems in solid mechanics
Solution of non-linear algebraic equations
Inelastic materials
Plate bending approximation
'Thick' Reissner-Mindlin plates
Shells as an assembly of flat elements
Axisymmetric shells
Shells as a special case
Semi-analytical finite element processes
Geometrically non-linear problems
Non-linear structural problems
Rigid and flexible solids
Computer procedures
Appendix: Tensor invariants
General problems in solid mechanics
Solution of non-linear algebraic equations
Inelastic materials
52.
図書
O.C. Zienkiewicz, R.L. Taylor
目次情報:
続きを見る
Introduction and the equations of fluid dynamics
Convection dominated problems - finite element
A general algorithm for compressible and incompressible flows - the characteristic based split (CBS) algorithm
Incompressible laminar flow - Newtonian and non-Newtonian fluids
Free surface, buoyancy and turbulent incompressible flows
Compressible high-speed gas flow
Shallow water problems
Waves
Computer implementation of the CBS algorithm
Introduction and the equations of fluid dynamics
Convection dominated problems - finite element
A general algorithm for compressible and incompressible flows - the characteristic based split (CBS) algorithm
53.
図書
Mario Pitteri, G. Zanzotto
目次情報:
続きを見る
List of figures
List of tables
Foreword
Introduction / 1：
Outline of chapter contents / 1.1：
Some experimental observations / 1.2：
Preliminaries / 2：
Basic notation / 2.1：
Some notions of elementary group theory / 2.2：
Basic definitions / 2.2.1：
Conjugacy / 2.2.2：
Group actions and symmetry / 2.2.3：
Linear and orthogonal transformations / 2.3：
Tensors with period two / 2.3.1：
Simple shears / 2.3.2：
Finite groups of tensors or matrices / 2.3.3：
Affine transformations / 2.4：
Continuum mechanics / 2.5：
Deformation / 2.5.1：
Thermodynamic potentials and their invariance / 2.5.2：
Stability of equilibrium / 2.5.3：
Simple lattices / 3：
Definitions and global symmetry / 3.1：
Geometric symmetry and crystal systems / 3.2：
Crystallographic point groups and holohedries / 3.2.1：
Crystal classes and crystal systems / 3.2.2：
Laue groups / 3.2.3：
Arithmetic symmetry and Bravais lattice types / 3.3：
Lattice groups / 3.3.1：
Conjugacy in O (crystal systems) and in GL(3, Z) (Bravais lattice types) / 3.3.2：
Centerings / 3.3.3：
The fourteen Bravais lattices / 3.4：
Fixed sets of lattice groups / 3.5：
An example / 3.5.1：
Symmetry-preserving stretches for simple lattices / 3.6：
Commutation relations / 3.6.1：
Structure of the fixed sets / 3.6.2：
The Bain stretch in the centered cubic lattices / 3.6.3：
Lattice subspaces, packings and indices / 3.7：
Lattice rows and lattice planes / 3.7.1：
Close-packed structures / 3.7.2：
Miller indices and crystallographic equivalence / 3.7.3：
Miller-Bravais indices for hexagonal lattices / 3.7.4：
Lattice groups and fixed sets for planar lattices / 3.8：
Weak-transformation neighborhoods and variants / 4：
Reconciliatio of global and local symmetries / 4.1：
Symmetry-breaking stretches for simple lattices / 4.2：
Small deformations and weak phase transformations / 4.3：
Small symmetry-preserving stretches / 4.3.1：
Small symmetry-breaking stretches / 4.3.2：
Constructing the small symmetry-breaking stretches / 4.4：
Variant structures (local orbits) in the wt-nbhds / 4.5：
General definitions / 4.5.1：
Variants and cosets / 4.5.3：
Variant structures and conjugacy classes / 4.5.4：
Explicit variant structures / 5：
Variant structures in cubic wt-nbhds / 5.1：
Tetragonal conjugacy class and variant structure / 5.1.1：
Rhombohedral conjugacy class and variant structure / 5.1.2：
Orthorhombic conjugacy classes and variant structures / 5.1.3：
Orthorhombic 'cubic edges' variants / 5.1.3.1：
Orthorhombic 'mixed axes' variants / 5.1.3.2：
Monoclinic conjugacy classes / 5.1.4：
Monoclinic 'cubic edges' variants / 5.1.4.1：
Monoclinic 'face-diagonals' variants / 5.1.4.2：
Triclinic conjugacy class and variant structure / 5.1.5：
Variant structures in hexagonal wt-nbhds / 5.2：
Orthorhombic conjugacy class and variant structure / 5.2.1：
Monoclinic conjugacy classes and variant structures / 5.2.2：
Monoclinic 'basal diagonals' variants / 5.2.2.1：
Monoclinic 'basal side-axes' variants / 5.2.2.2：
Monoclinic 'optic axis' variants / 5.2.2.3：
Kinematics of weak phase transformations / 5.2.3：
Irreducible invariant subspaces for the holohedries / 5.4：
General properties / 5.4.1：
Reduced actions and reduced symmetry groups on the i.i. subspaces / 5.4.2：
Decompositions of Sym under the action of the holohedries / 5.4.3：
Triclinic decompositions / 5.4.3.1：
Monoclinic decompositions / 5.4.3.2：
Orthorhombic decompositions / 5.4.3.3：
Rhombohedral decompositions / 5.4.3.4：
Tetragonal decompositions / 5.4.3.5：
Hexagonal decompositions / 5.4.3.6：
Cubic decompositions / 5.4.3.7：
Energetics / 6：
Invariance of simple-lattice energies / 6.1：
The Cauchy-Born hypothesis / 6.2：
The Born rule / 6.2.1：
Failures of the Born rule / 6.2.2：
Thermoelastic constitutive equations for crystals / 6.3：
Invariance of the response functions of elastic crystals / 6.3.1：
Energy minimizers and their general properties / 6.4：
Multiplicity of the symmetry-related minimizers / 6.4.1：
Multiphase crystals: minimizers that are not symmetry-related / 6.4.2：
Lack of convexity and symmetry-induced instabilities / 6.4.3：
Constitutive functions for weak phase transitions / 6.5：
Weak and symmetry-breaking transformations / 6.5.1：
Domain restrictions for the constitutive functions / 6.5.2：
Energy wells in the wt-nbhds / 6.5.3：
In the vicinity of an energy well / 6.6：
Thermal expansion and compressibility of a crystal / 6.6.1：
The elasticity tensor / 6.6.2：
Temperature-dependence of the elastic moduli / 6.6.3：
Anisotropic elasticity / 6.7：
Bifurcation patterns / 7：
The Landau theory / 7.1：
Isolated critical points and bifurcation points / 7.2：
Neighborhoods of bifurcation points / 7.2.1：
Genericity / 7.2.2：
Reduced bifurcation problems; order parameters / 7.3：
Analysis of the reduced bifurcation problems / 7.4：
Reduced problem (1) / 7.4.1：
Reduced problem (2) / 7.4.2：
Reduced problem (3) / 7.4.3：
Reduced problem (4) / 7.4.4：
Reduced problem (5) / 7.4.5：
Reduced problem (6) / 7.4.6：
Comparison with the kinematic transitions of [section]5.3 / 7.4.7：
Behavior of the moduli along the transitions / 7.5：
Examples of energy functions for simple lattices / 7.6：
A schematic 1-dimensional example / 7.6.1：
Energies for cubic-to-tetragonal and for tetragonal-to-monoclinic transitions / 7.6.2：
Orientation relationships and lattice correspondence / 7.6.3：
Relation with the Landau theory / 7.7：
General references / 7.8：
Mechanical twinning / 8：
Coherence and rank-1 connections / 8.1：
The twinning equation / 8.2：
Solutions of the twinning equation / 8.3：
Different descriptions of the same twin and cosets / 8.3.1：
Crystallographically equivalent twins / 8.3.2：
Reciprocal twins / 8.3.3：
Generic twins / 8.3.4：
Type-1 and Type-2 (conventional) twins / 8.3.5：
Compound twins / 8.3.6：
Conventional twins and rationality conditions / 8.3.7：
Short remarks / 8.4：
Experimental data / 8.4.1：
Mechanical twinning and the Born rule / 8.4.2：
Growth twins / 8.4.3：
Transformation twins / 9：
Procedure to determine the transformation twins / 9.1：
Rk-1 connections in a cubic wt-nbhd / 9.2：
Tetragonal variant structure / 9.2.1：
Rhombohedral variant structure / 9.2.2：
Orthorhombic variant structures / 9.2.3：
Orthorhombic 'cubic edges' wells / 9.2.3.1：
Orthorhombic 'mixed axes' wells / 9.2.3.2：
Monoclinic variant structures / 9.2.4：
Monoclinic 'cubic edges' wells / 9.2.4.1：
Monoclinic 'face-diagonals' wells / 9.2.4.2：
Triclinic variant structure / 9.2.5：
Rk-1 connections in a hexagonal wt-nbhd / 9.3：
Orthorhombic variant structure / 9.3.1：
Monoclinic 'basal diagonals' wells / 9.3.2：
Monoclinic 'basal side-axes' wells / 9.3.2.2：
Monoclinic 'optic axis' wells / 9.3.2.3：
The Mallard law / 9.3.3：
Microstructures / 10：
Piecewise homogeneous equilibria / 10.1：
Generalized solutions / 10.2：
The minors relations / 10.2.1：
The N-well problem / 10.2.2：
Examples of microstructures that are not laminates / 10.3：
Habit planes in martensite / 10.4：
Geometrically nonlinear theory / 10.4.1：
Self-accommodation in shape memory alloys / 10.4.2：
Wedges and other microstructures / 10.4.3：
Kinematics of multilattices / 11：
Crystals as multilattices / 11.1：
Descriptors and configuration spaces for deformable multilattices / 11.1.1：
Essential descriptions of multilattices / 11.1.2：
The global symmetry of multilattices / 11.2：
Indeterminateness of the descriptors (P[subscript 0,...], P[subscript n-1], e[subscript a]) / 11.2.1：
Indeterminateness of the descriptors (P[subscript 0], [varepsilon subscript [sigma]) / 11.2.2：
Nonessential descriptors of multilattices / 11.2.3：
The affine symmetry of multilattices / 11.3：
Space groups; crystal class and crystal system of a multilattice / 11.3.1：
The arithmetic symmetry of multilattices / 11.4：
Lattice groups of multilattices / 11.4.1：
Relation between the arithmetic and the space-group symmetries / 11.4.2：
Examples / 11.5：
Three-dimensional 2-lattices and hexagonal close-packed structures / 11.5.1：
The structure of quartz as a 3-lattice / 11.5.2：
Weak-transformation neighborhoods / 11.6：
The energy of a multilattice and its invariance / 11.7：
Minimizing out the internal variables of complex crystals / 11.7.1：
Local invariance of multilattice energies; the example of quartz / 11.7.2：
Twinning in multilattices / 11.8：
A proposal for a class of twins / 11.8.1：
Two examples / 11.8.2：
A model for stress relaxation / 11.8.3：
References
Index
List of figures
List of tables
Foreword
54.
図書
O. C. Zienkiewicz in collaboration with Y. K. Cheung
55.
図書
Javier Bonet, Richard D. Wood
出版情報:
Cambridge, UK ; New York : Cambridge University Press, 2008 xx, 318 p. ; 26 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
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：
56.
図書
A.J.M. Spencer
出版情報:
Mineola, N.Y. : Dover Publications, 2004 183 p. ; 22 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Preface
Introduction / 1：
Continuum mechanics / 1.1：
Introductory matrix algebra / 2：
Matrices / 2.1：
The summation convention / 2.2：
Eigenvalues and eigenvectors / 2.3：
The Cayley-Hamilton theorem / 2.4：
The polar decomposition theorem / 2.5：
Vectors and cartesian tensors / 3：
Vectors / 3.1：
Coordinate transformations / 3.2：
The dyadic product / 3.3：
Cartesian tensors / 3.4：
Isotropic tensors / 3.5：
Multiplication of tensors / 3.6：
Tensor and matrix notation / 3.7：
Invariants of a second-order tensor / 3.8：
Deviatoric tensors / 3.9：
Vector and tensor calculus / 3.10：
Particle kinematics / 4：
Bodies and their configurations / 4.1：
Displacement and velocity / 4.2：
Time rates of change / 4.3：
Acceleration / 4.4：
Steady motion. Particle paths and streamlines / 4.5：
Problems / 4.6：
Stress / 5：
Surface traction / 5.1：
Components of stress / 5.2：
The traction on any surface / 5.3：
Transformation of stress components / 5.4：
Equations of equilibrium / 5.5：
Principal stress components, principal axes of stress and stress invariants / 5.6：
The stress deviator tensor / 5.7：
Shear stress / 5.8：
Some simple states of stress / 5.9：
Motions and deformations / 5.10：
Rigid-body motions / 6.1：
Extension of a material line element / 6.2：
The deformation gradient tensor / 6.3：
Finite deformation and strain tensors / 6.4：
Some simple finite deformations / 6.5：
Infinitesimal strain / 6.6：
Infinitesimal rotation / 6.7：
The rate-of-deformation tensor / 6.8：
The velocity gradient and spin tensors / 6.9：
Some simple flows / 6.10：
Conservation laws / 6.11：
Conservation laws of physics / 7.1：
Conservation of mass / 7.2：
The material time derivative of a volume integral / 7.3：
Conservation of linear momentum / 7.4：
Conservation of angular momentum / 7.5：
Conservation of energy / 7.6：
The principle of virtual work / 7.7：
Linear constitutive equations / 7.8：
Constitutive equations and ideal materials / 8.1：
Material symmetry / 8.2：
Linear elasticity / 8.3：
Newtonian viscous fluids / 8.4：
Linear viscoelasticity / 8.5：
Further analysis of finite deformation / 8.6：
Deformation of a surface element / 9.1：
Decomposition of a deformation / 9.2：
Principal stretches and principal axes of deformation / 9.3：
Strain invariants / 9.4：
Alternative stress measures / 9.5：
Non-linear constitutive equations / 9.6：
Non-linear theories / 10.1：
The theory of finite elastic deformations / 10.2：
A non-linear viscous fluid / 10.3：
Non-linear viscoelasticity / 10.4：
Plasticity / 10.5：
Cylindrical and spherical polar coordinates / 10.6：
Curvilinear coordinates / 11.1：
Cylindrical polar coordinates / 11.2：
Spherical polar coordinates / 11.3：
Representation theorem for an isotropic tensor function / 11.4：
Answers
Further reading
Index
Preface
Introduction / 1：
Continuum mechanics / 1.1：
57.
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
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
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：
58.
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
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
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
59.
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
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
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：
60.
図書
edited by Ray W. Ogden and David J. Steigmann
目次情報:
続きを見る
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
61.
図書
Marcelo Epstein
出版情報:
Cambridge : Cambridge University Press, 2010 xii, 312 p. ; 26 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
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：
62.
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
63.
図書
Michał Kleiber ; translation editor, C.T.F. Ross
64.
図書
L.I. Sedov
65.
図書
edited by Carlo Sansour, Sebastian Skatulla
目次情報:
続きを見る
Defects, dislocations and the general theory of material inhomogeneity / G.A. Maugin
Approaches to generalized continua / Carlo Sansour and Sebastian Skatulla
Generalized continuum modelling of crystal plasticity / Samuel Forest
Introduction to discrete dislocation dynamics / Hussein. M. Zbib
Defects, dislocations and the general theory of material inhomogeneity / G.A. Maugin
Approaches to generalized continua / Carlo Sansour and Sebastian Skatulla
Generalized continuum modelling of crystal plasticity / Samuel Forest
66.
図書
A. Cemal Eringen
出版情報:
New York : Wiley, c1967 xv, 502 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
67.
図書
S.C. Hunter
68.
図書
C. Truesdell
出版情報:
New York : Springer-Verlag, c1966 279 p. ; 28 cm
子書誌情報:
loading…
所蔵情報:
loading…
69.
図書
S.F. Borg
出版情報:
Princeton, N.J. : D. Van Nostrand, c1963 xiv, 313 p. ; 23 cm
子書誌情報:
loading…
所蔵情報:
loading…
70.
図書
E. W. Billington and A. Tate
出版情報:
New York ; London : McGraw-Hill International Book Co., c1981 xx, 626 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
71.
図書
[by] Lawrence E. Malvern
目次情報:
続きを見る
Vectors and Tensors / 1：
Strain and Deformation / 2：
General Principles / 3：
Constitutive Equations / 4：
Fluid Mechanics / 5：
Linearized Theory of Elasticity / 6：
Tensors / Appendix I：
Orthogonal Curvilinear / Appendix II：
Vectors and Tensors / 1：
Strain and Deformation / 2：
General Principles / 3：
72.
図書
C.C. Wang
73.
ＥＢ
Lallit Anand and Sanjay Govindjee
出版情報:
1 online resource
シリーズ名:
Oxford graduate texts ;
子書誌情報:
loading…
所蔵情報:
loading…
74.
ＥＢ
C. S. Jog
出版情報:
1 online resource (xxiii, 852 p.)
シリーズ名:
Foundations and applications of mechanics ; Cambridge - IISc series ; volume 1
子書誌情報:
loading…
所蔵情報:
loading…
75.
ＥＢ
Manuel de León, Marcelo Epstein, Víctor Jiménez
出版情報:
World Scientific eBooks 1 online resource (xvi, 209 p.)
子書誌情報:
loading…
所蔵情報:
loading…
76.
ＥＢ
David J. Steigmann
出版情報:
Oxford University Press 1 online resource
シリーズ名:
Oxford scholarship online ;
子書誌情報:
loading…
所蔵情報:
loading…
77.
図書
by Yves R. Talpaert
出版情報:
Dordrecht : Kluwer Academic Publishers, c2002 xvi, 591 p ; 25 cm.
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Preface
Tensors / Chapter 1：
First Steps with Tensors / 1.：
Multilinear forms / 1.1：
Linear mapping
Multilinear form
Dual space, vectors and covectors / 1.2：
Dual space
Expression of a covector
Einstein summation convention
Change of basis and cobasis
Tensors and tensor product / 1.3：
Tensor product of multilinear forms
Tensor of type (0/1)
Tensor of type (1/0)
Tensor of type (0/2)
Tensor of type (2/0)
Tensor of type (1/1)
Tensor of type (q/p)
Symmetric and antisymmetric tensors
Operations on Tensors / 2.：
Tensor algebra / 2.1：
Addition of tensors
Multiplication of a tensor by a scalar
Tensor multiplication
Contraction and tensor criteria / 2.2：
Contraction
Tensor criteria
Euclidean Vector Space / 3.：
Pre-Euclidean vector space / 3.1：
Scalar multiplication and pre-Euclidean space
Fundamental tensor
Canonical isomorphism and conjugate tensor / 3.2：
Canonical isomorphism
Conjugate tensor and reciprocal basis
Covariant and contravariant representations of vectors
Representation of tensors of order 2 and contracted products
Euclidean vector spaces / 3.3：
Exterior Algebra / 4.：
p-forms / 4.1：
Definition of a p-form
Exterior product of 1-forms
Expression of a p-form
Exterior product of p-forms
Exterior algebra
q-vectors / 4.2：
Point Spaces / 5.：
Point space and natural frame / 5.1：
Point space
Coordinate system and frame of reference
Natural frame
Tensor fields and metric element / 5.2：
Transformations of curvilinear coordinates
Tensor fields
Metric element
Christoffel symbols / 5.3：
Definition of Christoffel symbols
Ricci identities and Christoffel formulae
Absolute differential, Covariant derivative, Geodesic / 5.4：
Absolute differential of a vector, covariant derivatives
Absolute differential of a tensor, covariant derivatives
Geodesic and Euler's equations
Absolute derivative of a vector (along a curve)
Volume form and adjoint / 5.5：
Volume form
Adjoint
Differential operators / 5.6：
Gradient
Divergence
Curl
Laplacian
Exercises
Lagrangian and Eulerian Descriptions / Chapter 2：
Lagrangian Description
Configuration
Deformation and Lagrangian Description
Flow and hypotheses of continuity
Trajectories / 1.4：
Streakline / 1.5：
Velocity and acceleration of a particle / 1.6：
Abstract configuration / 1.7：
Eulerian Description
Definition; Comparison between L- and E-descriptions
Trajectory and velocity
Streamline / 2.3：
Steady motion / 2.4：
Deformations / Chapter 3：
Homogeneous Transformation
Definition of homogeneous transformations
Convective transport
Convective transport of a vector
Convective transport of a volume
Simple shear
Cauchy-Green deformation tensor and stretch
(Right) Cauchy-Green deformation tensor
Stretch
Shear angle
Principal stretches
Finite strain tensor
Polar decomposition
Pure stretch and rotation
Euler-Almansi strain tensor
Rigid body transformation
Tangential Homogeneous Transformation
Deformation gradient
Homogeneous transformations of elements
Transport of vectors, volume deformation, and area deformation
Stretches
Strain
Displacement and gradient
Material displacement gradient
Spatial displacement gradient
Curvilinear coordinate system
Infinitesimal Transformation
Tensor notions relating to infinitesimal transformations
Compatibility conditions
Kinematics of Continua / Chapter 4：
Lagrangian Kinematics
Homogeneous transformation motion
General motion and gradient
Eulerian Kinematics
Velocity field
Material derivative of a vector
Material derivative of a volume
Eulerian rates
General motion and velocity gradient
Velocity gradient tensor and Eulerian rates
Lagrangian and Eulerian strain tensors
Rate of rotation
Decomposition of motion
Rigid body motion
Material Derivatives of Circulation, Flux, and Volume
About the particle derivative
Physical quantity
Vector field
Tensor field
Material derivative of circulation
Material derivative of flux
Material derivative of volume integral / 3.4：
Lagrangian and Eulerian approaches
Proper motion case
Fundamental Laws; Principle of Virtual Work / Chapter 5：
Conservation of Mass and Continuity Equation
Axiom of mass conservation
Continuity equation
Continuity equation in the Lagrangian description
Continuity equation in the Eulerian description
Mass flow rate
Material derivative of integral of mass density
Isochoric motion, steady and irrotational flows
Isochoric motion
Steady flow
Steady isochoric flow
Irrotational flow
Isochoric irrotational flow
Fundamental Laws of Dynamics
Body forces and surface forces
Principles of linear momentum and moment of momentum
Cauchy's stress tensor
Cauchy's stress tensor and principles of dynamics
Linear momentum principle and equilibrium equations
Moment of momentum principle
The generalized Cauchy's theorem
Poisson's theorem
Theorem of Kinetic Energy
Theorem of kinetic energy in the Eulerian description
Theorem of kinetic energy in the Lagrangian description
Study of Stresses
Reciprocity of stresses
Principal stresses
Stress invariants; deviator / 4.3：
Stress quadric of Cauchy and Lame stress ellipsoid / 4.4：
Geometrical constructions and Mohr's circles / 4.5：
(Mohr's) stress plane
Stress vector and plane of Mohr
Description of Mohr's circles
Particular stresses
Principle of Virtual Work
Preliminary recalls
Expressions of virtual power (and virtual work)
Principle of virtual work
Thermomechanics and Balance Equations / 6.：
Balance equation / 6.1：
Proper motion
Material domain
Fixed domain
First principle of thermodynamics / 6.2：
Principle
Balance equations and local forms
Potential energy of body forces
Internal energy and balance equation
Second principle of thermodynamics / 6.3：
Clausius-Duhem inequality
Dissipation and reversibility
Conclusion and constitutive equations / 6.4：
Linear Elasticity / Chapter 6：
Elasticity and Tests
Generalized Hooke's Law in Linear Elasticity
Generalized Hooke's law
Quadratic forms and strain energy function
Isotropic material and Lame coefficients
Constitutive equations
Young's modulus and Poisson's ratio
Bulk modulus
Shear modulus
Hooke's law's expression in a general coordinate system
Navier's equations of motion
Equations and Principles in Elastostatics
Navier's equation; the Beltrami equations of compatibility
Principle of superposition
Saint-Venant's principle
Classical Problems
Plane problems
Plane stress problems
Plane strain problems
Classical problems in elastostatics
Uniaxial stresses
Torsion of a circular cylinder body
Torsion of cylindrical shafts
Summary of Formulae
Bibliography
Glossary of Symbols
Index
Preface
Tensors / Chapter 1：
First Steps with Tensors / 1.：
78.
ＥＢ
Javier Bonet, Antonio J. Gil, Richard D. Wood
出版情報:
1 online resource (xviii, 331 p.)
子書誌情報:
loading…
所蔵情報:
loading…
79.
図書
by L.D. Landau and E.M. Lifshitz ; translated from the Russian by J.B. Sykes, J.S. Bell and M.J. Kearsley
目次情報:
続きを見る
Electrostatics of conductors
Static magnetic field
Superconductivity
The propagation of electromagnetic waves
Spatial dispersion
Diffraction of X rays in crystals
Electrostatics of conductors
Static magnetic field
Superconductivity
80.
図書
P.H. Dederichs, K. Schroeder and R. Zeller
目次情報:
続きを見る
Introduction: Machine Learning for Intelligent Optimization / 1：
Parameter Tuning and Intelligent Optimization / 1.1：
Book Outline / 1.2：
Reacting on the Neighborhood / 2：
Local Search Based on Perturbations / 2.1：
Learning How to Evaluate the Neighborhood / 2.2：
Learning the Appropriate Neighborhood in Variable Neighborhood Search / 2.3：
Iterated Local Search / 2.4：
Reacting on the Annealing Schedule / 3：
Stochasticity in Local Moves and Controlled Worsening of Solution Values / 3.1：
Simulated Annealing and Asymptotics / 3.2：
Asymptotic Convergence Results / 3.2.1：
Online Learning Strategies in Simulated Annealing / 3.3：
Combinatorial Optimization Problems / 3.3.1：
Global Optimization of Continuous Functions / 3.3.2：
Reactive Prohibitions / 4：
Prohibitions for Diversification / 4.1：
Forms of Prohibition-Based Search / 4.1.1：
Dynamical Systems / 4.1.2：
A Worked-Out Example of Fixed Tabu Search / 4.1.3：
Relationship Between Prohibition and Diversification / 4.1.4：
How to Escape from an Attractor / 4.1.5：
Reactive Tabu Search: Self-Adjusted Prohibition Period / 4.2：
The Escape Mechanism / 4.2.1：
Applications of Reactive Tabu Search / 4.2.2：
Implementation: Storing and Using the Search History / 4.3：
Fast Algorithms for Using the Search History / 4.3.1：
Persistent Dynamic Sets / 4.3.2：
Reacting on the Objective Function / 5：
Dynamic Landscape Modifications to Influence Trajectories / 5.1：
Adapting Noise Levels / 5.1.1：
Guided Local Search / 5.1.2：
Eliminating Plateaus by Looking Inside the Problem Structure / 5.2：
Nonoblivious Local Search for SAt / 5.2.1：
Model-Based Search / 6：
Models of a Problem / 6.1：
An Example / 6.2：
Dependent Probabilities / 6.3：
The Cross-Entropy Model / 6.4：
Adaptive Solution Construction with Ant Colonies / 6.5：
Modeling Surfaces for Continuous Optimization / 6.6：
Supervised Learning / 7：
Learning to Optimize, from Examples / 7.1：
Techniques / 7.2：
Linear Regression / 7.2.1：
Bayesian Locally Weighted Regression / 7.2.2：
Using Linear Functions for Classification / 7.2.3：
Multilayer Perceptrons / 7.2.4：
Statistical Learning Theory and Support Vector Machines / 7.2.5：
Nearest Neighbor's Methods / 7.2.6：
Selecting Features / 7.3：
Correlation Coefficient / 7.3.1：
Correlation Ratio / 7.3.2：
Entropy and Mutual Information / 7.3.3：
Applications / 7.4：
Learning a Model of the Solver / 7.4.1：
Reinforcement Learning / 8：
Reinforcement Learning Basics: Learning from a Critic / 8.1：
Markov Decision Processes / 8.1.1：
Dynamic Programming / 8.1.2：
Approximations: Reinforcement Learning and Neuro-Dynamic Programming / 8.1.3：
Relationships Between Reinforcement Learning and Optimization / 8.2：
Algorithm Portfolios and Restart Strategies / 9：
Introduction: Portfolios and Restarts / 9.1：
Predicting the Performance of a Portfolio from its Component Algorithms / 9.2：
Parallel Processing / 9.2.1：
Reactive Portfolios / 9.3：
Defining an Optimal Restart Time / 9.4：
Reactive Restarts / 9.5：
Racing / 10：
Exploration and Exploitation of Candidate Algorithms / 10.1：
Racing to Maximize Cumulative Reward by Interval Estimation / 10.2：
Aiming at the Maximum with Threshold Ascent / 10.3：
Racing for Off-Line Configuration of Metaheuristics / 10.4：
Teams of Interacting Solvers / 11：
Complex Interaction and Coordination Schemes / 11.1：
Genetic Algorithms and Evolution Strategies / 11.2：
Intelligent and Reactive Solver Teams / 11.3：
An Example: Gossiping Optimization / 11.4：
Epidemic Communication for Optimization / 11.4.1：
Metrics, Landscapes, and Features / 12：
How to Measure and Model Problem Difficulty / 12.1：
Phase Transitions in Combinatorial Problems / 12.2：
Empirical Models for Fitness Surfaces / 12.3：
Tunable Landscapes / 12.3.1：
Measuring Local Search Components: Diversification and Bias / 12.4：
The Diversification-Bias Compromise (D-B Plots) / 12.4.1：
A Conjecture: Better Algorithms are Pareto-Optimal in D-B Plots / 12.4.2：
Open Problems / 13：
References
Index
Introduction: Machine Learning for Intelligent Optimization / 1：
Parameter Tuning and Intelligent Optimization / 1.1：
Book Outline / 1.2：
81.
図書
Frederick Fongsun Ling
出版情報:
New York : Wiley, c1973 xv, 320 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
82.
図書
by L.D. Landau and E.M. Lifshitz ; translated from the Russian by J.B. Sykes, J.S. Bell and M.J. Kearsley
83.
図書
P. Chadwick
出版情報:
Mineola, N.Y. : Dover Publications, 1999 187 p. ; 22 cm
子書誌情報:
loading…
所蔵情報:
loading…
図書
ＥＢ
