1.
図書
Hayrettin Kardestuncer
2.
図書
edited Ernest Hinton and Roger Owen
出版情報:
Swansea : Pineridge, 1986 x, 384 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
3.
図書
Peter S. Huyakorn, George F. Pinder
出版情報:
Orland ; Tokyo : Academic Press, 1983 xiii, 473 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
4.
図書
Tsutomu Ikeda
5.
図書
edited by M.V.K. Chari and P.P. Silvester
6.
図書
T.J. Chung
出版情報:
New York : McGraw-Hill International Book Co., c1978 xiii, 378 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
7.
図書
R.K. Livesley
出版情報:
Cambridge ; New York : Cambridge University Press, 1983 x, 199 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Preface
Preliminaries / 1：
The finite-element method introduced / 2：
Elastic stress analysis using linear triangular elements / 3：
Higher-order approximations: (1) fixed element shapes / 4：
Higher-order approximations: (2) generalising the element geometry / 5：
Axial symmetry and harmonic analysis / 6：
The elastic analysis of beams, plates and shells / 7：
Programming the finite-element method / 8：
References
Notation
Index
Preface
Preliminaries / 1：
The finite-element method introduced / 2：
8.
図書
J.J. Connor, C.A. Brebbia
出版情報:
London ; Boston : Newnes-Butterworths, 1976 310 p. ; 23 cm
子書誌情報:
loading…
所蔵情報:
loading…
9.
図書
C. A. Brebbia
出版情報:
London : Pentech Press, 1978 189 p. ; 23 cm
子書誌情報:
loading…
所蔵情報:
loading…
10.
図書
H. Kardestuncer, editor-in-chief ; D.H. Norrie, project editor ; editors, F. Brezzi ... [et al.]
出版情報:
New York ; Tokyo : McGraw-Hill, c1987 xxiv, [1380] p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
11.
図書
M. A. Crisfield
12.
図書
Thomas J.R. Hughes
出版情報:
Englewood Cliffs, N.J. : Prentice-Hall, c1987 xxvii, 803 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
13.
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…
14.
図書
Klaus-Jürgen Bathe, Edward L. Wilson
15.
図書
Klaus-Jürgen Bathe
16.
図書
Roland W. Lewis, Bernard A. Schrefler
17.
図書
John O. Dow
出版情報:
San Diego : Academic Press, 1998 xxiv, 533 p. ; 26 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
General Introduction
Problem Definition and Development: Introduction
Principle of Minimum Potential Energy
Elements of the Calculus of Variations
Derivation of the Plane Stress Problem
Rayleigh-Ritz Variational Solution Technique
Physically Interpretable Displacement Polynomials
Strain Gradient Notation: Introduction
Strain Gradient Notation
Strain Gradient Representation of Discrete Structures
Strain Transformations
A-Priori Error Analysis Procedures: Introduction
The Development of Strain Gradient Based Finite Elements
Four Node Quadrilateral Element
Six Node Linear Strain Element
Eight and Nine Node Elements
Shear Locking and Aspect Ratio Stiffening
The Strain Gradient Reformation of the Finite Differences Method: Introduction
Elements of the Finite Difference Method
Finite Difference Boundary Condition Models
Extensions to the Finite Difference Method
A-Posteriori Error Analysis Procedures: Introduction
The Zienkiewicz/Zhu Error Estimation Procedure
Error Estimation Based on Finite Difference Smoothing
Point-Wise Error Estimates
Super-Convergence of the Augmented Finite Element Results
Adaptive Refinement of Finite Difference Models
Subject Index
General Introduction
Problem Definition and Development: Introduction
Principle of Minimum Potential Energy
18.
図書
P.M. Gresho, R.L. Sani ; in collaboration with M.S. Engelman
目次情報:
続きを見る
Preface
Glossary of Abbreviations
Introduction / 1：
Incompressible Flow / 1.1：
The Finite Element Method / 1.3：
Incompressible Flow and the Finite Element Method / 1.4：
Overview of this Volume / 1.5：
Some Subjective Discussion / 1.6：
Why Finite Elements? Why Not Finite Volumes? / 1.7：
The Advection-Diffusion Equation / 2：
The Continuum Equation / 2.1：
The Finite Element Equations / 2.2：
Discretization of the Weak Form
Some Semi-Discrete Equations / 2.3：
Open Boundary Conditions (OBC's) / 2.4：
Some Non-Galerkin Results / 2.5：
Dispersion, Dissipation, Phase Speed, Group Velocity, Mesh Design, and Wiggles / 2.6：
Time Integration / 2.7：
Additional Numerical Examples / 2.8：
Advection Diffusion Matrices / Appendix 1 Some Element Matrices：
One-Dimensional Element Matrices / A.1.2：
Two-Dimensional Element Matrices / A.1.3：
Two Dimensional Control Volume Finite Element Matrices / A.1.4：
Viewpoint One / Appendix 2 Further Comparison of Finite Elements and Finite Volumes：
Viewpoint Two / A.2.3：
Scalar Projections / Appendix 3 Scalar Projections, Orthogonal and Not and Projection Methods：
References
Author Index
Subject Index
Preface
Glossary of Abbreviations
Introduction / 1：
19.
図書
J.N. Reddy
20.
図書
Achintya Haldar, Sankaran Mahadevan
出版情報:
New York : John Wiley & Sons, c2000 xvi, 328 p. ; 26 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Basic Concept of Reliability
Commonly Used Probability Distributions
Fundamentals of Reliability Analysis
Simulation Techniques
Implicit Performance Functions: Introduction to SFEM
SFEM for Linear Static Problems
SFEM for Spatial Variability Problems
SFEM-Based Reliability Evaluation of Nonlinear Two- and Three-Dimensional Structures
Structures under Dynamic Loading
Appendices
References
Index
Basic Concept of Reliability
Commonly Used Probability Distributions
Fundamentals of Reliability Analysis
21.
図書
by Suong Van Hoa and Wei Feng
出版情報:
Boston : Kluwer Academic Publishers, c1998 x, 298 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
22.
図書
by E.S. Mistakidis and G.E. Stavroulakis
23.
図書
Vidar Thomée
24.
図書
P. M. Gresho, R. L. Sani in collaboration with M. S. Engelman
出版情報:
Chichester : Wiley, c1998 xx, 1021p ; 25cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Preface
Glossary of Abbreviations
Introduction / 1：
Incompressible Flow / 1.1：
The Finite Element Method / 1.3：
Incompressible Flow and the Finite Element Method / 1.4：
Overview of this Book; Some Subjective Discussion / 1.5：
Why Finite Elements? Why not Finite Volume? / 1.6：
The Advection-Diffusion Equation / 2：
The Continuum Equation / 2.1：
The Advective (Convective) Form / 2.1.1：
Dimensionless Forms and Limiting Cases of the Equation / 2.1.2：
The Divergence (Conservation) Form / 2.1.3：
Conservation Laws / 2.1.4：
Weak forms of PDE's/Natural Boundary Conditions / 2.1.5：
The Finite Element Equations/Discretization of the Weak Form / 2.2：
Advective Form / 2.2.1：
Divergence Form / 2.2.2：
An Absolutely Conserving Form / 2.2.3：
A Finite Difference Interpretation / 2.2.5：
A Control Volume FEM... / 2.2.6：
Some Semi-Discrete Equations / 2.3：
One Dimension / 2.3.1：
Two Dimensions with Bilinear Elements / 2.3.2：
Two Dimension with Biquadratic Elements / 2.3.3：
Two Dimensions with Serendipity Elements / 2.3.4：
Open Boundary Conditions (OBC's) / 2.4：
Two Dimensions / 2.4.1：
Some Non-Galerkin Results / 2.5：
The Lumped Mass Approximation / 2.5.1：
One-point Quadrature / 2.5.2：
Control Volume Finite Element (CVFEM) / 2.5.3：
The Group FEM/Product Approximation / 2.5.4：
The Petrov-Galerkin FEM / 2.5.5：
Dispersion, Dissipation, Phase Speed, Group Velocity, Mesh Design, and - Wiggles / 2.6：
Qualitative Discussion / 2.6.1：
Qualitative Discussion for some 1D Problems / 2.6.2：
Extension to 2D / 2.6.3：
Time Integration / 2.7：
Some Explicit ODE Methods / 2.7.1：
Application to Advection Diffusion (Scalar Transport) / 2.7.2：
Some Implicit ODE Methods / 2.7.3：
A Variable-Step Implicit Method for Advection-Diffusion / 2.7.4：
A Semi-Implicit Method / 2.7.5：
Dispersion (et al.) Errors for some Fully Discrete Methods / 2.7.6：
Concluding remarks and Suggestions / 2.7.8：
Additional Numerical Examples / 2.8：
Unstable ODE Examples / 2.8.1：
Advection-Diffusion of a Puff (Point Source) / 2.8.2：
The Rotating Cone - A Pure Advection Test Problem / 2.8.3：
The Navier-Stokes Equations / 3：
Notational Introduction / 3.1：
The Continuum, Equations (PDE's) / 3.2：
Alternate Forms of the Viscous Term / 3.3：
Stress-Divergence Form / 3.3.1：
Div-Curl Form / 3.3.2：
Curl Form / 3.3.3：
Alternate Forms of the Non-Linear Term / 3.4：
Rotational Form / 3.4.1：
Skew-Symmetric Form / 3.4.3：
A Symmetric Form / 3.4.4：
Derived Equations / 3.5：
The Pressure Poisson Equation (PPE) / 3.5.1：
The Vorticity Transport Equation / 3.5.2：
The Penalized Momentum Equation / 3.5.3：
Alternate Statements of the NS Equations / 3.6：
Velocity-Pressure in Divergence Form / 3.6.1：
Velocity-Pressure in Rotational Form / 3.6.2：
PPE Form / 3.6.3：
The Stream Function-Vorticity (-) / 3.6.4：
The Velocity-Vorticity Formulation / 3.6.5：
Other Formulations / 3.6.6：
Special Cases of Interest / 3.7：
Stokes Flow / 3.7.1：
Inviscid Flow / 3.7.2：
Potential Flow / 3.7.3：
Axisymmetric Flow / 3.7.4：
Boundary Conditions / 3.8：
u-P Equations / 3.8.1：
The Pressure Poisson Equation and Pressure Boundary Conditions / 3.8.2：
The Vorticity Transport Equation and Boundary Conditions on the Vorticity / 3.8.3：
Initial Conditions (and Well-Posedness) / 3.9：
The u-P Formulation / 3.9.1：
The PPE Formulation / 3.9.2：
Vorticity-Based Methods / 3.9.3：
Interim Summary / 3.10：
A Well-Posed IBVP for Incompressible Flow, and the Equivalence Theorem / 3.10.1：
Some Ill-Posed Problems / 3.10.2：
The Simplified PPE is also Ill-Posed / 3.10.3：
Fixing the SPPE and PPE Paradox / 3.10.4：
PPE Solutions that are not NSE Solutions / 3.10.5：
A Remark on the Penalty Method / 3.10.6：
Key Features of Incompressible Flow / 3.10.7：
Global Conservation Laws / 3.11：
Preface
Glossary of Abbreviations
Introduction / 1：
25.
図書
Frank Ihlenburg
26.
図書
edited by R. Glowinski, E.Y. Rodin, O.C. Zienkiewicz
27.
図書
V. Girault, P.-A. Raviart
28.
図書
V.V. Shaidurov
29.
図書
R.W. Lewis ... [et al.]
出版情報:
Chichester ; New York : Wiley, c1996 x, 279 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Conduction Heat Transfer and Formulation
Linear Steady State Problems
Time Stepping Methods for Heat Transfer
Non-Linear Heat Conduction Analysis
Phase Change Problems--Solidification and Melting
Convective Heat Transfer
Nomenclature
Index
Conduction Heat Transfer and Formulation
Linear Steady State Problems
Time Stepping Methods for Heat Transfer
30.
図書
K.C. Rockey ... [et al.]
出版情報:
London : Granada, 1983 x, 239 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
31.
図書
K. C. Rockey ... [et al.]
出版情報:
London : Crosby Lockwood Staples, 1975 x, 239 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
32.
図書
Roger T. Fenner
出版情報:
London : Imperial College Press , Singapore : distributed by World Scientific Publishing, c1996 xvii, 171 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
33.
図書
M.D. Kotsovos and M.N. Pavlović
出版情報:
London : Thomas Telford, 1995 x, 550 p. ; 26 cm
子書誌情報:
loading…
所蔵情報:
loading…
34.
図書
J.T. Marti ; translation editor, J.R. Whiteman
目次情報:
続きを見る
(Chapter Titles): Convolutions and Mollifiers
Sobolev Spaces on One-Dimensional Intervals
Sobolev Spaces Hm(G) on Domains G in Rn
The Inequalities of Poincar, and Friedrichs
Extension Theorems
Imbeddings of Hm(G)
Elliptic Boundary Value Problems
The Finite Element Method for the Solution of Elliptic Boundary Value Problems
References
Subject Index
(Chapter Titles): Convolutions and Mollifiers
Sobolev Spaces on One-Dimensional Intervals
Sobolev Spaces Hm(G) on Domains G in Rn
35.
図書
Larry J. Segerlind
出版情報:
New York : Wiley, c1984 xiv, 427 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Basic Concepts
One-Dimensional Linear Element
A Finite Element Example
Element Matrices: Galerkin Formulation
Two-Dimensional Elements
Coordinate Systems
Field Problems
Two-Dimensional Field Equation
Torsion of Noncircular Sections
Derivative Boundary Conditions: Point Sources and Sinks
Irrotational Flow
Heat Transfer by Conduction and Convection
Acoustical Vibrations
Axisymmetric Field Problems
Time-Dependent Field Problems: Theoretical Considerations
Time-Dependent Field Problems: Practical Considerations
Computer Program for Two-Dimensional Field Problems
Structural And Solid Mechanics
The Axial Force Member
Element Matrices: Potential Energy Formulations
The Truss Element
A Beam Element
A Plane Frame Element
Theory of Elasticity
Two-Dimensional Elasticity
Axisymmetric Elasticity
Computer Programs for Structural and Solid Mechanics
Linear And Quadratic Elements
Element Shape Functions
Element Matrices
Isoparametric Computer Programs
References
Appendices
Basic Concepts
One-Dimensional Linear Element
A Finite Element Example
36.
図書
Irving H. Shames, Clive L. Dym
出版情報:
Washington : Hemisphere Pub. Corp , New York : McGraw-Hill, c1985 xviii, 757 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
37.
図書
R.E. White
出版情報:
New York : Wiley, c1985 x, 354 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
38.
図書
T.Y. Yang
39.
図書
edited by I. Babuška ... [et al.]
40.
図書
Noboru Kikuchi
出版情報:
New Rochelle, NY : Cambridge University Press, 1986 xiii, 418 p. ; 26 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Preface
Review of background materials / 1：
Finite element analysis of heat conduction problems / 2：
Generalisation of the finite element methods for heat conduction problems / 3：
Simple elastic structures and their free vibration problems / 4：
Finite element approximations for problems in linear elasticity / 5：
Plate-bending problems / 6：
Appendixes
Bibliography
List of notation
Index
Preface
Review of background materials / 1：
Finite element analysis of heat conduction problems / 2：
41.
図書
R. Wait and A.R. Mitchell
出版情報:
Chichester [West Sussex] ; New York : J. Wiley, c1985 xii, 260 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
42.
図書
by M.H. Aliabadi and D.P. Rooke
出版情報:
Southampton, U.K. ; Boston : Computational Mechanics Publications , Dordrecht ; Boston : Kluwer Academic Publishers, 1991 276 p. ; 24 cm
シリーズ名:
Solid mechanics and its applications ; v. 8
子書誌情報:
loading…
所蔵情報:
loading…
43.
図書
C.T.F. Ross
出版情報:
Chichester : Horwood, 1985 319p ; 24cm
子書誌情報:
loading…
所蔵情報:
loading…
44.
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
45.
図書
by O.O. Ochoa and J.N. Reddy
46.
図書
Harold C. Martin, Graham F. Carey
出版情報:
New York : McGraw-Hill, c1973 xiii, 386 p. ; 23 cm
子書誌情報:
loading…
所蔵情報:
loading…
47.
図書
Jean-Pierre Aubin
目次情報:
続きを見る
Introduction
Aim and Scope / 1：
Neumann Problems / 2：
Introduction of Internal Approximations / 3：
Properties of Internal Approximations / 4：
Stability, Optimal Stability, and Regularity of the Convergence / 5：
The Case of Operators Mapping a Hilbert Space onto Its Dual / 6：
Finite-Element Approximations of Sobolev Spaces / 7：
Approximation of Nonhomogeneous Neumann Problems / 8：
Approximations of Nonhomogeneous Dirichlet Problems / 9：
A Posteriori Error Estimates / 10：
External and Partial Approximations / 11：
General Outline / 12：
Approximation of Solutions of Neumann Problems for Second-Order Linear Differential Equations
Weak Solutions of Neumann Problems for Second-Order Linear Differential Operators
The Neumann Boundary-Value Problem / 1-1：
Definition of Distributions / 1-2：
Weak Derivatives of a Distribution / 1-3：
Variational Formulation of the Problem / 1-4：
Weak Solutions of the Neumann Boundary-Value Problem / 1-5：
Sobolev Spaces / 1-6：
The Lax-Milgram Theorem / 1-7：
Approximation of an Abstract Variational Problem
The Galerkin Approximation of a Separable Hilbert Space / 2-1：
Approximation of a Hilbert Space / 2-2：
Internal Approximation of a Variational Equation / 2-3：
Existence, Uniqueness, and Convergence Properties / 2-4：
Estimates of Global Error / 2-5：
What Kind of Approximations Should Be Chosen? / 2-6：
Examples of Approximations of Sobolev Spaces
Piecewise-Linear Approximations of the Sobolev Space H[superscript 1] (I) / 3-1：
Estimates of Error Functions of Piecewise-Linear Approximations / 3-2：
Examples of Approximate Equations
Construction of a Finite-Difference Scheme / 4-1：
A Simpler Finite-Difference Scheme / 4-2：
Approximations of Hilbert Spaces
Hilbert Spaces and Their Duals
Dual of a Hilbert Space and Canonical Isometry
Example: Finite-Dimensional Hilbert Spaces
Hahn-Banach Theorem
Dual of a Dense Subspace
Imbedding of a Space into Its Dual
Example: Imbedding of Spaces of Functions into Spaces of Distributions
Dual of Closed Subspaces and Factor Spaces
Applications to Error Estimates / 1-8：
Dual of a Product / 1-9：
Dual of Domains of Operators / 1-10：
Examples: Dual of Sobolev Spaces H[subscript 0 superscript m](I) / 1-11：
Properties of Bounded Sets of Operators; Uniform Boundedness / 1-12：
Banach Theorem / 1-13：
Dual of Sobolev Spaces H[superscript m](I) / 1-14：
The Riesz-Fredholm Alternative / 1-15：
V-Elliptic and Coercive Operators / 1-16：
Quasi-Optimal Approximations
Stability Functions
Duality Relations between Error and Stability Functions
Estimates of the Stability Functions
Quasi-Optimal Approximations; Estimate of the Error Function
Truncation Errors and Error Functions
Optimal Approximations
Eigenvalues and Eigenvectors of Symmetric Compact Operators
Optimal Galerkin Approximations
Convergence and Optimality Properties / 3-3：
Spaces H[subscript Theta] / 3-4：
Optimal Restrictions and Prolongations; Applications
Optimal Restrictions and Prolongations
Dual Approximations
Construction of Optimal Prolongations and Restrictions / 4-3：
Miscellaneous Remarks / 4-4：
Characterization of Error and Stability Functions / 4-5：
Spaces of Order [Theta] / 4-6：
Approximation of Operators
Internal Approximations
Construction of an Internal Approximate Equation
The Case of Finite-Dimensional Discrete Spaces
The Case of Operators from V onto V[prime]
Stability of Internal Approximations of Operators
Convergence and Error Estimates
Approximation of a Sum of an Isomorphism and a Compact Operator
Approximation of Coercive and V-Elliptic Operators
Optimal and Quasi-Optimal Stability
Regularity of the Convergence and Estimates of Error in Terms of n-Width
Stability and Convergence in Smaller Spaces
Stability and Convergence in Larger Spaces
Approximation of the Value of a Functional at a Solution
Discrete Convergence, Consistency, and Optimal Approximation of Linear Operators
Discrete Convergence and Consistency
Optimal Approximation of Operators and Internal Approximations
Estimates of Error and Discrete Errors
Finite-Element Approximation of Functions of One Variable
Approximation of Functions of L[superscript 2] by Step Functions and by Convolution
The Space L[superscript 2] and the Discrete Space L[subscript h superscript 2]]
The Prolongations P[subscript h superscript 0]
The Restrictions r[subscript h]
The Theorem of Convergence
Convolution of Functions and Measures
Approximation by Convolution
Piecewise-Polynomial Approximations of Sobolev Spaces H[superscript m]
Finite-Difference Operators
Construction of Approximations of the Space H[superscript m]
Convergence Theorem
Explicit Form of Functions [Pi subscript m]
Properties of the Prolongations p[subscript h superscript m]
Optimal Properties of Prolongations p[subscript h superscript m] / 2-7：
Finite-Element Approximations of Sobolev Spaces H[superscript m]
Finite-Element Approximations
The Criterion of m-Convergence
Characterization of Convergent Finite-Element Approximations
Stability Properties of Finite-Element Approximations
Finite-Element Approximation of Functions of Several Variables
Approximations of the Sobolev Spaces H[superscript m](R[superscript n])
Notations
(2m + 1)[superscript n]-Level Piecewise-Polynomial Approximations
[2(2m)[superscript n] - (2m - 1)[superscript n]]-Level Piecewise-Polynomial Approximations
Approximations of the Sobolev Spaces H[superscript m]([Omega])
Sobolev Spaces H[superscript m]([Omega])
Finite-Element Approximations of H[superscript m]([Omega])
Quasi-Optimal Finite-Element Approximations of H[superscript m]([Omega])
Piecewise-Polynomial Approximations of H[superscript m]([Omega])
Approximation of the Sobolev Spaces H[subscript 0 superscript m]([Omega])
Sobolev Spaces H[subscript 0 superscript m]([Omega])
Finite-Element Approximations of H[subscript 0 superscript m]([Omega])
Convergent Finite-Element Approximations of H[subscript 0 superscript m]([Omega])
Boundary-Value Problems and the Trace Theorem
Some Variational Boundary-Value Problems for the Laplacian
The Laplacian
Characterization of Sobolev Spaces H[subscript 0 superscript 1]([Omega])
The Green Formula
The Dirichlet Problem for the Laplacian
The Neumann Problem for the Laplacian
A Mixed Problem for the Laplacian
An Oblique Problem for the Laplacian
Existence and Uniqueness of the Solutions
Variational Boundary-Value Problems and Their Adjoints
Spaces V, H and Operator [gamma]
Formal Operator [Lambda] Associated with a(u, v)
Abstract Neumann and Dirichlet Problems Associated with a(u, v)
Mixed Type Boundary-Value Problems Associated with a(u, v)
Existence and Uniqueness of the Solutions of Boundary-Value Problems
Formal Adjoint of an Operator and Green's Formula
Theorems of Regularity / 2-8：
The Trace Theorem and Properties of Sobolev Spaces
Statement of the Trace Theorem
Change of Coordinates
Sobolev Spaces H[superscript s](R[superscript n]) for Real Numbers s
Sobolev Spaces H[superscript s]([Gamma] and H[superscript s]([Omega])
Trace Operators and Operators of Extension: Theorems of Density / 3-5：
Properties of the Spaces H[superscript m](R[subscript + superscript n]) / 3-6：
Proof of the Trace Theorem / 3-7：
Sobolev Inequalities and the Trace Theorem in Space H[superscript s]([Omega]) / 3-8：
Theorem of Compactness / 3-9：
Examples of Boundary-Value Problems
Boundary-Value Problems for Second-Order Differential Operators
Second-Order Linear Differential Operators
Elliptic Second-Order Partial Differential Operators
The Dirichlet Problem
The Neumann Problem
Mixed Problems
Oblique Problems
Interface Problems
The Regularity Theorem
Theorems of Isomorphism
Value of the Solution at a Point of the Boundary
Problems with Elliptic Differential Boundary Conditions
Boundary-Value Problems for Differential Operators of Higher Order
Linear Differential Operators of Order 2k
Regularity and Theorems of Isomorphism
Other Boundary-Value Problems
Boundary Value Problems for [Delta][superscript 2] + [lambda]
Approximation of Neumann-Type Problems
Theorems of Convergence and Error Estimates
Internal Approximation of a Neumann-type Problem
Convergence and Estimates of Error in Larger Spaces
Approximation of Neumann Problems for Elliptic Operators of Order 2k
Approximation of Neumann Problems for Elliptic Differential Operators
Convergence Properties of Finite Element Approximations of Neumann Problems
The (2m + 1)[superscript n]-Level Approximations of the Neumann Problem
The [2(2m)[superscript n] - (2m - 1)[superscript n]]-Level Approximations of the Neumann Problem
Approximations of the Spaces H[superscript k]([Omega], [Lambda] and H([Omega], [Lambda]
Approximation of Other Neumann-Type Problems
Approximation of the Value of the Solution at a Point of the Boundary
Approximation of Oblique Boundary-Value Problems
Approximation of a Problem with Elliptic Boundary Conditions
Approximation of Interface Problems
Approximation of the Neumann Problem for [Delta][superscript 2] + [gamma]
Perturbed Approximations and Least-Squares Approximations
Perturbed Approximations
Internal Approximation of a Variational Boundary-Value Problem
Perturbed Approximation of a Variational Boundary-Value Problem
Convergence in the Initial Space
Estimates of Error
Convergence in Smaller Spaces
Convergence in Larger Spaces
Perturbed Approximations of Boundary-Value Problems
Perturbed Approximations by Finite-Element Approximations
Error Estimates and Regularity of the Convergence
The 3[superscript n]-level Perturbed Approximation of the Dirichlet Problem
Least-Squares Approximations
Least-Squares Approximation Schemes
Error Estimates (I)
Error Estimates (II)
Least-Squares Approximations of Dirichlet Problems
Conjugate Problems and A Posteriori Error Estimates
Conjugate Problems of Boundary-Value Problems
First Example of a Conjugate Problem
Second Example of a Conjugate Problem
Construction of Conjugate Problems
Applications to the Approximation of Dirichlet Problems
Approximation of the Dirichlet Problem (I)
Approximation of the Dirichlet Problem (II)
The Case of Second-Order Differential Operators
Finite-Element Approximations of the Spaces H[superscript k]([Omega], D*)
Spaces H[superscript k]([Omega], D*)
Approximations of the Space H[superscript k]([Omega], D*)
Approximation of the Second Example of a Conjugate Problem
Approximation of the Conjugate Dirichlet Problem
Properties of the Discrete Conjugate Problem
External Approximations; Stability, Convergence, and Error Estimates
Definition of External Approximations
Example: Partial Approximations of a Finite Intersection of Spaces
Stability and Convergence of External Approximations of Operators
Estimates of Error and Regularity of the Convergence
Properties of the External Error Functions
External and Partial Approximations of Variational Equations
Partial Approximation of a Split Variational Equation
External Approximation of Variational Equations
Partial Approximation of Neumann Problems
Perturbed Partial Approximation of Boundary-Value Problems
Partial Approximations of Sobolev Spaces
Spaces H([Omega], D[subscript i])
Partial Approximations of the Sobolev Space H[superscript 1]([Omega])
Estimates of Truncation Errors and External Error Functions
Partial Approximations of the Sobolev Spaces H[superscript m]([Omega]) and H[subscript 0 superscript m]([Omega])
Partial Approximation of Boundary-Value Problems
Partial Approximation of Second-Order Linear Operators
Partial Approximation of the Neumann Problem
Perturbed Partial Approximation of Mixed Boundary-Value Problems
Estimates of Error in the Interior
Partial Approximations of Higher-Order Differential Operators
Comments
References
Index
Introduction
Aim and Scope / 1：
Neumann Problems / 2：
48.
図書
S. Amini, P.J. Harris, D.T. Wilton
49.
図書
A. Ženišek ; translation editor, J.R. Whiteman
50.
図書
P. M. Prenter
51.
図書
by Josef Henrych
出版情報:
Amsterdam ; Tokyo : Elsevier, 1990 , New York : Distributor for the U.S.A. and Canada, Elsevier Science Pub. Co.[m] 541 p. ; 25 cm
シリーズ名:
Developments in civil engineering ; 28
子書誌情報:
loading…
所蔵情報:
loading…
52.
図書
by Ivo Kazda ; [translation Zdeňka Jeniková]
53.
図書
G.G.A. Bäuerle, E.A. de Kerf
54.
図書
D.J. Dawe
55.
図書
[by] Richard H. Gallagher
56.
図書
Douglas H. Norrie, Gerard de Vries
出版情報:
New York : Academic Press, 1973 xiii, 322 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
57.
図書
[by] J.T. Oden
58.
図書
edited by E. Stein, W. Wendland
59.
図書
[by] Robert D. Cook
出版情報:
New York : Wiley, c1974 xvii, 402 p. ; 23 cm
子書誌情報:
loading…
所蔵情報:
loading…
60.
図書
J.N. Reddy
出版情報:
New York : McGraw-Hill, c1984 xiii, 495 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
61.
図書
edited by J.R. Whiteman
出版情報:
London ; Tokyo : Academic Press, 1988 xviii, 622 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
62.
図書
O. C. Zienkiewicz in collaboration with Y. K. Cheung
63.
図書
Eugene L. Wachspress
64.
図書
Roger Valid
65.
図書
A.J. Baker
目次情報:
続きを見る
The finite-element method
an introduction
inviscid potential flow
initial- value problems
convection/diffusion
viscous incompressible two- dimensional flow
two-dimensional and three-dimensional parabolic flow
general three-dimensional flow
The finite-element method
an introduction
inviscid potential flow
66.
図書
T.H. Richards
67.
図書
Gouri Dhatt and Gilbert Touzot ; translated by Gilles Cantin
出版情報:
Chichester [West Sussex] ; New York : Wiley, c1984 xv, 509 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
68.
図書
O.C. Zienkiewicz and R.L. Taylor
69.
図書
A. R. Mitchell and R. Wait
出版情報:
London ; New York : Wiley, c1977 x, 198 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
70.
図書
Kenneth H. Huebner
出版情報:
New York : Wiley, c1975 xix, 500 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
71.
図書
editor, C. A. Brebbia
出版情報:
Berlin ; Tokyo : Springer-Verlag, c1985 767 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
72.
図書
Vivette Girault, Pierre-Arnaud Raviart
73.
図書
William Weaver, Jr., Paul R. Johnston
74.
図書
O. Axelsson, V.A. Barker
75.
図書
N. Kikuchi and J.T. Oden
目次情報:
続きを見る
Introduction
Signorini's problem
Minimization methods and their variants
Finite element approximations
Orderings, Trace Theorems, Green's Formulas and korn's Inequalities
Signorini's problem revisited
Signorini's problem for incompressible materials
Alternate variational principles for Signorini's problem
Contact problems for large deflections of elastic plates
Some special contact problems with friction
Contact problems with nonclassical friction laws
Contact problems involving deformations and nonlinear materials
Dynamic friction problems
Rolling contact problems
Concluding comments
Introduction
Signorini's problem
Minimization methods and their variants
76.
図書
M.J. Baines
出版情報:
Oxford : Clarendon Press , Oxford ; Tokyo : Oxford University Press, 1994 xi, 226 p. ; 25 cm
シリーズ名:
Monographs on numerical analysis
子書誌情報:
loading…
所蔵情報:
loading…
77.
図書
Frank L. Stasa
目次情報:
続きを見る
Preface
General Concepts / 1：
Mathematical Preliminaries / 2：
Two Dimensional Truss Analysis / 3：
Variational and Weighted Residual Formulations / 4：
General Approach to Structural Analysis / 5：
Parameter Functions; C-Continuous Shape Functions; Simple Integration Formulas; Active Zone Equation Solvers / 6：
Stress Analysis / 7：
Steady-State Thermal and Fluid Flow Analysis / 8：
Higher-Order Isoparametric Elements and Quadrature / 9：
Transient and Dynamic Analyses / 10：
Appendices
Preface
General Concepts / 1：
Mathematical Preliminaries / 2：
78.
図書
Ronald L. Huston, Chris E. Passerello
79.
図書
M.J. Fagan
出版情報:
Harlow, Essex, England : Longman Scientific & Technical, 1992 , New York, NY : Wiley, 1992 xx, 315 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Background and Application / 1：
Introduction to the Method / 2：
Practical Aspects of the Finite Element Method / 3：
Interpolation Functions and Simplex Elements / 4：
Formulation of the Element Characteristic Matrices and Vectors for Elasticity Problems / 5：
Formulation of the Element Characteristics Matrices and Vectors for Field Problems / 6：
Assembly and Solution of the Finite Element Equations / 7：
Higher Order Element Formulations / 8：
Further Applications of the Finite Element Method / 9：
Commercial Finite Element Programs / 11：
Background and Application / 1：
Introduction to the Method / 2：
Practical Aspects of the Finite Element Method / 3：
80.
図書
Soheil Mohammadi
出版情報:
Chichester, West Sussex : John Wiley & Sons, 2012 xxvii, 371 p. ; 26 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Preface
Nomenclature
Introduction / 1：
Composite Structures / 1.1：
Failures of Composites / 1.2：
Matrix Cracking / 1.2.1：
Delamination / 1.2.2：
Fibre/Matrix Debonding / 1.2.3：
Fibre Breakage / 1.2.4：
Macro Models of Cracking in Composites / 1.2.5：
Crack Analysis / 1.3：
Local and Non-Local Formulations / 1.3.1：
Theoretical Methods for Failure Analysis / 1.3.2：
Analytical Solutions for Composites / 1.4：
Continuum Models / 1.4.1：
Fracture Mechanics of Composites / 1.4.2：
Numerical Techniques / 1.5：
Boundary Element Method / 1.5.1：
Finite Element Method / 1.5.2：
Adaptive Finite/Discrete Element Method / 1.5.3：
Meshless Methods / 1.5.4：
Extended Finite Element Method / 1.5.5：
Extended Isogeometric Analysis / 1.5.6：
Multiscale Analysis / 1.5.7：
Scope of the Book / 1.6：
Fracture Mechanics, A Review / 2：
Basics of Elasticity / 2.1：
Stress-Strain Relations / 2.2.1：
Airy Stress Function / 2.2.2：
Complex Stress Functions / 2.2.3：
Basics of LEFM / 2.3：
Fracture Mechanics / 2.3.1：
Infinite Tensile Plate with a Circular Hole / 2.3.2：
Infinite Tensile Plate with an Elliptical Hole / 2.3.3：
Westergaard Analysis of a Line Crack / 2.3.4：
Williams Solution of a Wedge Corner / 2.3.5：
Stress Intensity Factor, K / 2.4：
Definition of the Stress Intensity Factor / 2.4.1：
Examples of Stress Intensity Factors for LEFM / 2.4.2：
Griffith Energy Theories / 2.4.3：
Mixed Mode Crack Propagation / 2.4.4：
Classical Solution Procedures for K and G / 2.5：
Displacement Extrapolation/Correlation Method / 2.5.1：
Mode I Energy Release Rate / 2.5.2：
Mode I Stiffness Derivative/Virtual Crack Model / 2.5.3：
Two Virtual Crack Extensions for Mixed Mode Cases / 2.5.4：
Single Virtual Crack Extension Based on Displacement Decomposition / 2.5.5：
Quarter Point Singular Elements / 2.6：
J Integral / 2.7：
Generalization of J / 2.7.1：
Effect of Crack Surface Traction / 2.7.2：
Effect of Body Force / 2.7.3：
Equivalent Domain Integral (EDI) Method / 2.7.4：
Interaction Integral Method / 2.7.5：
Elastoplastic Fracture Mechanics (EPFM) / 2.8：
Plastic Zone / 2.8.1：
Crack-Tip Opening Displacements (CTOD) / 2.8.2：
J Integral for EPFM / 2.8.3：
Historic Development of XFEM / 3：
A Review of XFEM Development / 3.2.1：
A Review of XFEM Composite Analysis / 3.2.2：
Enriched Approximations / 3.3：
Partition of Unity / 3.3.1：
Intrinsic and Extrinsic Enrichments / 3.3.2：
Partition of Unity Finite Element Method / 3.3.3：
MLS Enrichment / 3.3.4：
Generalized Finite Element Method / 3.3.5：
Generalized PU Enrichment / 3.3.6：
XFEM Formulation / 3.4：
Basic XFEM Approximation / 3.4.1：
Signed Distance Function / 3.4.2：
Modelling the Crack / 3.4.3：
Governing Equation / 3.4.4：
XFEM Discretization / 3.4.5：
Evaluation of Derivatives of Enrichment Functions / 3.4.6：
Selection of Nodes for Discontinuity Enrichment / 3.4.7：
Numerical Integration / 3.4.8：
XFEM Strong Discontinuity Enrichments / 3.5：
A Modified FE Shape Function / 3.5.1：
The Heaviside Function / 3.5.2：
The Sign Function / 3.5.3：
Strong Tangential Discontinuity / 3.5.4：
Crack Intersection / 3.5.5：
XFEM Weak Discontinuity Enrichments / 3.6：
XFEM Crack-Tip Enrichments / 3.7：
Isotropic Enrichment / 3.7.1：
Orthotropic Enrichment Functions / 3.7.2：
Bimaterial Enrichments / 3.7.3：
Orthotropic Bimaterial Enrichments / 3.7.4：
Dynamic Enrichment / 3.7.5：
Orthotropic Dynamic Enrichments for Moving Cracks / 3.7.6：
Bending Plates / 3.7.7：
Crack-Tip Enrichments in Shells / 3.7.8：
Electro-Mechanical Enrichment / 3.7.9：
Dislocation Enrichment / 3.7.10：
Hydraulic Fracture Enrichment / 3.7.11：
Plastic Enrichment / 3.7.12：
Viscoelastic Enrichment / 3.7.13：
Contact Corner Enrichment / 3.7.14：
Modification for Large Deformation Problems / 3.7.15：
Automatic Enrichment / 3.7.16：
Transition from Standard to Enriched Approximation / 3.8：
Linear Blending / 3.8.1：
Hierarchical Transition Domain / 3.8.2：
Tracking Moving Boundaries / 3.9：
Level Set Method / 3.9.1：
Alternative Methods / 3.9.2：
Numerical Simulations / 3.10：
A Central Crack in an Infinite Tensile Plate / 3.10.1：
An Edge Crack in a Finite Plate / 3.10.2：
Tensile Plate with a Central Inclined Crack / 3.10.3：
A Bending Plate in Fracture Mode III / 3.10.4：
Crack Propagation in a Shell / 3.10.5：
Shear Band Simulation / 3.10.6：
Fault Simulation / 3.10.7：
Sliding Contact Stress Singularity by PUFEM / 3.10.8：
Hydraulic Fracture / 3.10.9：
Dislocation Dynamics / 3.10.10：
Static Fracture Analysis of Composites / 4：
Anisotropic Elasticity / 4.1：
Elasticity Solution / 4.2.1：
Anisotropic Stress Functions / 4.2.2：
Analytical Solutions for Near Crack Tip / 4.3：
The General Solution / 4.3.1：
Special Solutions for Different Types of Composites / 4.3.2：
Orthotropic Mixed Mode Fracture / 4.4：
Energy Release Rate for Anisotropic Materials / 4.4.1：
Anisotropic Singular Elements / 4.4.2：
SIF Calculation by Interaction Integral / 4.4.3：
Orthotropic Crack Propagation Criteria / 4.4.4：
Anisotropic XFEM / 4.5：
Plate with a Crack Parallel to the Material Axis of Orthotropy / 4.5.1：
Edge Crack with Several Orientations of the Axes of Orthotropy / 4.6.2：
Inclined Edge Notched Tensile Specimen / 4.6.3：
Central Slanted Crack / 4.6.4：
An Inclined Centre Crack in a Disk Subjected to Point Loads / 4.6.5：
Crack Propagation in an Orthotropic Beam / 4.6.6：
Dynamic Fracture Analysis of Composites / 5：
Dynamic Fracture Mechanics / 5.1：
Dynamic Fracture Mechanics of Composites / 5.1.2：
Dynamic Fracture by XFEM / 5.1.3：
Analytical Solutions for Near Crack Tips in Dynamic States / 5.2：
Analytical Solution for a Propagating Crack in Isotropic Material / 5.2.1：
Asymptotic Solution for a Stationary Crack in Orthotropic Media / 5.2.2：
Analytical Solution for Near Crack Tip of a Propagating Crack in Orthotropic Material / 5.2.3：
Dynamic Stress Intensity Factors / 5.3：
Stationary and Moving Crack Dynamic Stress Intensity Factors / 5.3.1：
Dynamic Fracture Criteria / 5.3.2：
J Integral for Dynamic Problems / 5.3.3：
Domain Integral for Orthotropic Media / 5.3.4：
Interaction Integral / 5.3.5：
Crack-Axis Component of the Dynamic J Integral / 5.3.6：
Field Decomposition Technique / 5.3.7：
Dynamic XFEM / 5.4：
Dynamic Equations of Motion / 5.4.1：
XFEM Enrichment Functions / 5.4.2：
Time Integration Schemes / 5.4.4：
Plate with a Stationary Central Crack / 5.5：
Mode I Plate with an Edge Crack / 5.5.2：
Mixed Mode Edge Crack in Composite Plates / 5.5.3：
A Composite Plate with Double Edge Cracks under Impulsive Loading / 5.5.4：
Pre-Cracked Three Point Bending Beam under Impact Loading / 5.5.5：
Propagating Central Inclined Crack in a Circular Orthotropic Plate / 5.5.6：
Fracture Analysis of Functionally Graded Materials (FGMs) / 6：
Analytical Solution for Near a Crack Tip / 6.1：
Average Material Properties / 6.2.1：
Mode I Near Tip Fields in FGM Composites / 6.2.2：
Stress and Displacement Field (Similar to Homogeneous Orthotropic Composites) / 6.2.3：
Stress Intensity Factor / 6.3：
FGM Auxillary Fields / 6.3.1：
Isoparametric FGM / 6.3.4：
Crack Propagation in FGM Composites / 6.4：
Inhomogeneous XFEM / 6.5：
XFEM Approximation / 6.5.1：
Numerical Examples / 6.5.3：
Plate with a Centre Crack Parallel to the Material Gradient / 6.6.1：
Proportional FGM Plate with an Inclined Central Crack / 6.6.2：
Non-Proportional FGM Plate with a Fixed Inclined Central Crack / 6.6.3：
Rectangular Plate with an Inclined Crack (Non-Proportional Distribution) / 6.6.4：
Crack Propagation in a Four-Point FGM Beam / 6.6.5：
Delamination/Interlaminar Crack Analysis / 7：
Fracture Mechanics for Bimaterial Interface Cracks / 7.1：
Isotropic Bimaterial Interfaces / 7.2.1：
Orthotropic Bimaterial Interface Cracks / 7.2.2：
Stress Contours for a Crack between Two Dissimilar Orthotropic Materials / 7.2.3：
Stress Intensity Factors for Interlaminar Cracks / 7.3：
Delamination Propagation / 7.4：
Fracture Energy-Based Criteria / 7.4.1：
Stress-Based Criteria / 7.4.2：
Contact-Based Criteria / 7.4.3：
Bimaterial XFEM / 7.5：
XFEM Enrichment Functions for Bimaterial Problems / 7.5.1：
Discretization and Integration / 7.5.4：
Central Crack in an Infinite Bimaterial Plate / 7.6：
Isotropic-Orthotropic Bimaterial Crack / 7.6.2：
Orthotopic Double Cantilever Beam / 7.6.3：
Concrete Beams Strengthened with Fully Bonded GFRP / 7.6.4：
FRP Reinforced Concrete Cantilever Beam Subjected to Edge Loadings / 7.6.5：
Delamination of Metallic I Beams Strengthened by FRP Strips / 7.6.6：
Variable Section Beam Reinforced by FRP / 7.6.7：
New Orthotropic Frontiers / 8：
Orthotropic XIGA / 8.1：
NURBS Basis Function / 8.2.1：
XIGA Simulations / 8.2.2：
Orthotropic Dislocation Dynamics / 8.3：
Straight Dislocations in Anisotropic Materials / 8.3.1：
Edge Dislocations in Anisotropic Materials / 8.3.2：
Curve Dislocations in Anisotropic Materials / 8.3.3：
Anisotropic Dislocation XFEM / 8.3.4：
Plane Strain Anisotropic Solution / 8.3.5：
Individual Sliding Systems s1 and s2 in an Infinite Domain / 8.3.6：
Simultaneous Sliding Systems in an Infinite Domain / 8.3.7：
Other Anisotropic Applications / 8.4：
Biomechanics / 8.4.1：
Piezoelectric / 8.4.2：
References
Index
Preface
Nomenclature
Introduction / 1：
81.
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…
82.
図書
Peter Monk
目次情報:
続きを見る
Mathematical models of electromagnetism / 1：
Introduction / 1.1：
Maxwell's equations / 1.2：
Constitutive equations for linear media / 1.2.1：
Interface and boundary conditions / 1.2.2：
Scattering problems and the radiation condition / 1.3：
Boundary value problems / 1.4：
Time-harmonic problem in a cavity / 1.4.1：
Cavity resonator / 1.4.2：
Scattering from a bounded object / 1.4.3：
Scattering from a buried object / 1.4.4：
Functional analysis and abstract error estimates / 2：
Basic functional analysis and the Fredholm alternative / 2.1：
Hilbert space / 2.2.1：
Linear operators and duality / 2.2.2：
Variational problems / 2.2.3：
Compactness and the Fredholm alternative / 2.2.4：
Hilbert-Schmidt theory of eigenvalues / 2.2.5：
Abstract finite element convergence theory / 2.3：
Cea's lemma / 2.3.1：
Discrete mixed problems / 2.3.2：
Convergence of collectively compact operators / 2.3.3：
Eigenvalue estimates / 2.3.4：
Sobolev spaces, vector function spaces and regularity / 3：
Standard Sobolev spaces / 3.1：
Trace spaces / 3.2.1：
Regularity results for elliptic equations / 3.3：
Differential operators on a surface / 3.4：
Vector functions with well-defined curl or divergence / 3.5：
Integral identities / 3.5.1：
Properties of H(div; [Omega]) / 3.5.2：
Properties of H(curl; [Omega]) / 3.5.3：
Scalar and vector potentials / 3.6：
The Helmholtz decomposition / 3.7：
A function space for the impedance problem / 3.8：
Curl or divergence conserving transformations / 3.9：
Variational theory for the cavity problem / 4：
Assumptions on the coefficients and data / 4.1：
The space X and the nullspace of the curl / 4.3：
Helmholtz decomposition / 4.4：
Compactness properties of X[subscript 0] / 4.4.1：
The variational problem as an operator equation / 4.5：
Uniqueness of the solution / 4.6：
Cavity eigenvalues and resonances / 4.7：
Finite elements on tetrahedra / 5：
Introduction to finite elements / 5.1：
Sets of polynomials / 5.2.1：
Meshes and affine maps / 5.3：
Divergence conforming elements / 5.4：
The curl conforming edge elements of Nedelec / 5.5：
Linear edge element / 5.5.1：
Quadratic edge elements / 5.5.2：
H[superscript 1]([Omega]) conforming finite elements / 5.6：
The Clement interpolant / 5.6.1：
An L[superscript 2]([Omega]) conforming space / 5.7：
Boundary spaces / 5.8：
Finite elements on hexahedra / 6：
Divergence conforming elements on hexahedra / 6.1：
Curl conforming hexahedral elements / 6.3：
H[superscript 1]([Omega]) conforming elements on hexahedra / 6.4：
An L[superscript 2]([Omega]) conforming space and a boundary space / 6.5：
Finite element methods for the cavity problem / 7：
Error analysis via duality / 7.1：
The discrete Helmholtz decomposition / 7.2.1：
Preliminary error analysis / 7.2.2：
Duality estimate / 7.2.3：
Error analysis via collective compactness / 7.3：
Pointwise convergence / 7.3.1：
Collective compactness / 7.3.2：
Numerical results for the cavity problem / 7.3.3：
The ellipticized Maxwell system / 7.4：
Discrete ellipticized variational problem / 7.4.1：
The discrete eigenvalue problem / 7.5：
Topics concerning finite elements / 8：
The second family of elements on tetrahedra / 8.1：
Divergence conforming element / 8.2.1：
Curl conforming element / 8.2.2：
Scalar functions and the de Rham diagram / 8.2.3：
Curved domains / 8.3：
Locally mapped tetrahedral meshes / 8.3.1：
Large-element fitting of domains / 8.3.2：
hp finite elements / 8.4：
H[superscript 1]([Omega]) conforming hp element / 8.4.1：
hp curl conforming elements / 8.4.2：
hp divergence conforming space / 8.4.3：
de Rham diagram for hp elements / 8.4.4：
Classical scattering theory / 9：
Basic integral identities / 9.1：
Scattering by a sphere / 9.3：
Spherical harmonics / 9.3.1：
Spherical Bessel functions / 9.3.2：
Series solution of the exterior Maxwell problem / 9.3.3：
Electromagnetic Calderon operators / 9.4：
The electric-to-magnetic Calderon operator / 9.4.1：
The magnetic-to-electric Calderon operator / 9.4.2：
Scattering of a plane wave by a sphere / 9.5：
Uniqueness and Rellich's lemma / 9.5.1：
Series solution / 9.5.2：
The scattering problem using Calderon maps / 10：
Reduction to a bounded domain / 10.1：
Analysis of the reduced problem / 10.3：
Extended Helmholtz decomposition / 10.3.1：
An operator equation on X[subscript 0] / 10.3.2：
The discrete problem / 10.4：
Scattering by a bounded inhomogeneity / 11：
Derivation of the domain-decomposed problem / 11.1：
The finite-dimensional problem / 11.3：
Analysis of the interior finite element problem / 11.4：
Error estimates for the fully discrete problem / 11.5：
Scattering by a buried object / 12：
Homogeneous isotropic background / 12.1：
Analysis of the scheme / 12.2.1：
The fully discrete problem / 12.2.2：
Computational considerations / 12.2.3：
Perfectly conducting half space / 12.3：
Layered medium / 12.4：
Incident plane waves / 12.4.1：
The dyadic Green's function / 12.4.2：
Algorithmic development / 12.4.3：
Solution of the linear system / 13.1：
Phase error in finite element methods / 13.3：
Wavenumber dependent error estimates / 13.3.1：
Phase error in three dimensional edge elements / 13.3.2：
A posteriori error estimation / 13.4：
A residual-based error estimator / 13.4.1：
Numerical experiments / 13.4.2：
Absorbing boundary conditions / 13.5：
Silver-Muller absorbing boundary condition / 13.5.1：
Infinite element method / 13.5.2：
The perfectly matched layer / 13.5.3：
Far field recovery / 13.6：
Inverse problems / 14：
The linear sampling method / 14.1：
Implementing the LSM / 14.2.1：
Numerical results with the LSM / 14.2.2：
Mathematical aspects of inverse scattering / 14.3：
Uniqueness for the inverse problem / 14.3.1：
Herglotz wave functions / 14.3.2：
The far field operators F and B / 14.3.3：
Mathematical justification of the LSM / 14.3.4：
Appendices
Coordinate systems / A：
Cartesian coordinates / A.1：
Spherical coordinates / A.2：
Vector and differential identities / B：
Vector identities / B.1：
Differential identities / B.2：
Differential identities on a surface / B.3：
References
Index
Mathematical models of electromagnetism / 1：
Introduction / 1.1：
Maxwell's equations / 1.2：
83.
図書
Pavel Šolín, Karel Segeth, Ivo Doležel
84.
図書
Victor N. Kaliakin
目次情報:
続きを見る
Preface
Acknowledgements
Glossary of Notations and Units
Governing Equations and Their Approximate Solution / 1：
Introductory Remarks / 1.1：
Some Simple Governing Equations / 1.2：
Mathematical Preliminaries / 1.3：
General Comments / 1.3.1：
Classification of Physical Problems / 1.3.2：
The Solution Domain and its Boundary / 1.3.3：
General Form of Governing Equations / 1.3.4：
General Form of Boundary Conditions / 1.3.5：
Defining a Well-Posed Problem / 1.3.6：
Comments on Approximate Solutions / 1.4：
The Role of Mathematical Modeling in Design / 1.5：
Concluding Remarks / 1.6：
Computer Storage and Manipulation of Numbers / 2：
Storage of Character / 2.1：
Storage of Numbers / 2.3：
Bytes / 2.3.1：
Integers (Fixed-Point Numbers) / 2.3.2：
Floating-Point Numbers / 2.3.3：
Roundoff Error / 2.3.4：
Approximation Error / 2.4：
Algorithmic Stability and Error Growth / 2.5：
Exercises / 2.6：
The Finite Difference Method / 3：
Historical Note / 3.1：
General Steps / 3.3：
Ordinary Differential Equations / 3.4：
Partial Differential Equations / 3.5：
Elliptic Partial Differential Equations / 3.5.1：
Parabolic Partial Differential Equations / 3.5.2：
Hyperbolic Partial Differential Equations / 3.5.3：
The Method of Weighted Residuals / 3.6：
Residuals / 4.1：
General Considerations / 4.3：
Interior Methods / 4.3.1：
Boundary Methods / 4.3.2：
Mixed Methods / 4.3.3：
Choice of Trial Functions / 4.4：
Specific Weighting Functions / 4.5：
Collocation Method / 4.5.1：
Subdomain Method / 4.5.2：
Method of Least Squares / 4.5.3：
The Bubnov-Galerkin Method / 4.5.4：
Method of Moments / 4.5.5：
Comparison of Results / 4.5.6：
Continuity Requirements / 4.6：
Weak Form / 4.7：
Variational Methods / 4.8：
Admissible Functions / 5.1：
Functionals / 5.3：
Existence of Functionals / 5.3.1：
Derivation of Differential Equations / 5.4：
Stationary Functional Method / 5.5：
Relation to Weighted Residual Method / 5.6：
Related Methods / 5.7：
Kantorovich Method / 5.7.1：
Introduction to the Finite Element Method / 5.8：
The Notion of Nodes / 6.1：
The Notion of Elements / 6.3：
Piecewise Defined Approximations / 6.4：
Some Specifics / 6.5：
A Historical Note / 6.6：
Early Contributions of Applied Mathematicians / 6.6.1：
Early Contributions of Mathematical Physicists / 6.6.2：
Early Contributions of Engineers / 6.6.3：
Synthesis / 6.6.4：
Growth / 6.6.5：
Present State of the Method / 6.6.6：
Development of Finite Element Equations / 6.7：
Selection of Primary Dependent Variables / 7.1：
Definition of Constitutive Relations / 7.3：
Identification of the Element Equations / 7.4：
Selection of Element Interpolation Functions / 7.5：
Convergence Criteria / 7.5.1：
Spatial Isotropy / 7.5.2：
Rate of Convergence / 7.5.3：
Information Regarding Element Nodes / 7.5.4：
Specialization of Element Equations / 7.6：
Illustrative Examples / 7.7：
Steps in Performing Finite Element Analyses / 7.8：
Discretization of the Domain / 8.1：
Domain Discretization Error / 8.2.1：
Common Element Types / 8.2.2：
Element Characteristics / 8.2.3：
Placement of Elements / 8.2.4：
Element Shapes / 8.2.5：
Mesh Generation / 8.2.6：
Meshless Methods / 8.2.7：
Computer Implementation Issues / 8.2.8：
Assembly of Element Equations / 8.3：
Insight Into Node and Element Numbering / 8.3.1：
Errors Associated with Formation and Assembly of Element Arrays / 8.3.2：
Nodal Specifications / 8.4：
Elimination Approach at the Global Level / 8.4.1：
Elimination Approach at the Element Level / 8.4.2：
Penalty Approach at the Global Level / 8.4.3：
Penalty Approach at the Element Level / 8.4.4：
Solution of Global Equations / 8.4.5：
Mesh Renumbering Schemes / 8.5.1：
Secondary Dependent Variables / 8.6：
Postprocessing of Results / 8.7：
Interpretation of Results / 8.8：
Validity of Finite Element Analyses / 8.8.1：
Refinement of the Finite Element Solution / 8.8.2：
Element Interpolation Functions / 8.9：
Lagrangian Elements / 9.1：
One-Dimensional Lagrangian Elements / 9.2.1：
Two-Dimensional Lagrangian Elements / 9.2.2：
Three-Dimensional Lagrangian Elements / 9.2.3：
Lagrangian Elements: A Summary / 9.2.4：
Serendipity Elements / 9.3：
Two-Dimensional Serendipity Elements / 9.3.1：
Three-Dimensional Serendipity Elements / 9.3.2：
Triangular and Tetrahedral Elements / 9.4：
Element "Degeneration" / 9.4.1：
Triangular Elements / 9.4.2：
Tetrahedral Elements / 9.4.3：
Triangular Prism Elements / 9.5：
Transition Elements / 9.6：
Nodal Condensation / 9.7：
Element Mapping / 9.8：
General Aspects of Mapping / 10.1：
Treatment of Derivatives / 10.3：
Treatment of Integrals / 10.4：
Parametric Mapping / 10.5：
Isoparametric Elements / 10.5.1：
Evaluation of Element Arrays / 10.5.2：
Element Distortions / 10.6：
Linear Triangular Elements / 10.6.1：
Quadratic Triangular Elements / 10.6.2：
Higher-Order Triangular Elements / 10.6.3：
Bilinear Quadrilateral Elements / 10.6.4：
Biquadratic Quadrilateral Elements / 10.6.6：
Hexahedral Elements / 10.6.7：
Further Insight Into Element Distortion / 10.6.8：
Finite Element Analysis of Scalar Field Problems / 10.7：
General Governing Equations / 11.1：
Development of General Finite Element Equations / 11.3：
Torsion of Straight, Prismatic Bars / 11.5：
The Solution of Saint-Venant / 11.5.1：
The Solution of Prandtl / 11.5.2：
Finite Element Equations / 11.5.3：
Flow Through Porous Geologic Media / 11.6：
Finite Element Analysis in Linear Elastostatics / 11.7：
Three-Dimensional Idealizations / 12.1：
Plane Stress Idealizations / 12.4：
Generalized Plane Strain Idealizations / 12.5：
Axisymmetric Idealizations / 12.6：
Computation of Equivalent Nodal Loads / 12.7：
Plane Stress and Plane Strain Idealizations / 12.7.1：
Potential Errors Along Curved Boundaries / 12.7.2：
Relations Between Moduli / 12.8：
Implementation, Modeling, and Related Issues / 12.9：
Role of Modeling and Analysis in Engineering Design / 13.1：
Phases of a Finite Element Analysis / 13.3：
Outline of a Finite Element Program / 13.4：
Meshing Guidelines Revisited / 13.5：
Element Types / 13.5.1：
Individual Element Shapes / 13.5.2：
Element Combinations / 13.5.4：
Changes in Mesh Density / 13.5.5：
Types of Meshes / 13.6：
Overview of Structured Meshing Schemes / 13.6.2：
Overview of Unstructured Meshing Schemes / 13.6.3：
Overview of General Meshing Schemes / 13.6.4：
Sources of Error / 13.7：
Programming Errors / 13.8.1：
Errors in Input Data / 13.8.2：
Mathematical Potpourri / 13.9：
Indicial Notation / A.1：
Classification of PDEs / A.2：
Some Finite Difference Formulas / A.3：
Forward Differences in One Dimension / A.3.1：
Backward Differences in One Dimension / A.3.2：
Central Differences in One Dimension / A.3.3：
Self-Adjoint Operators / A.4：
Some Notes on Heat Flow / B：
Fourier's Law of Heat Conduction / B.1：
Heat Conduction Equations / B.3：
Three-Dimensional Heat Conduction / B.3.1：
Two-Dimensional Heat Conduction / B.3.2：
One-Dimensional Heat Conduction / B.3.3：
Boundary and Initial Conditions / B.4：
Local and Natural Coordinate Systems / C：
Local Coordinate Systems / C.1：
Natural Coordinate Systems / C.3：
One-Dimensional Natural Coordinate Systems / C.3.1：
Natural Coordinates for Triangular Elements / C.3.2：
Natural Coordinates for Tetrahedral Elements / C.3.3：
Natural Coordinates for Rectangular Elements / C.3.4：
Natural Coordinates for Rectangular Prisms / C.3.5：
The Patch Test / C.4：
Test A / D.1：
Test B / D.3：
Test C / D.4：
Solution of Linear Systems of Equations / D.5：
Direct Methods / E.1：
Basic Gauss Elimination / E.1.1：
Formal Statement of Basic Gauss Elimination / E.1.2：
Triangular Decomposition / E.1.3：
Operation Counts and Storage Requirements / E.1.4：
Constant Bandwidth Solvers / E.1.5：
Skyline Solvers / E.1.6：
Frontal Solvers / E.1.7：
Iterative Methods / E.2：
Stationary Methods / E.2.1：
Non-Stationary Methods / E.2.2：
Preconditioning / E.2.3：
Solution Errors / E.3：
Sources of Ill-Conditioning / E.3.1：
Notes on Integration of Finite Elements / F：
Interpolatory Quadrature / F.1：
Closed Newton-Cotes Formulae / F.2.1：
Open Newton-Cotes Formulae / F.2.2：
Gaussian Quadrature / F.3：
Gauss-Legendre Quadrature / F.3.1：
Modifications to Gaussian Quadrature / F.3.2：
Numerical Integration of Lines / F.4：
Numerical Integration of Rectangles / F.5：
Numerical Integration of Prisms / F.6：
Right Prisms / F.6.1：
Triangular Prisms / F.6.2：
Integration of Triangles and Tetrahedra / F.7：
Exact Integration / F.7.1：
Numerical Integration / F.7.2：
Order of Numerical Integration / F.8：
General Observations / F.8.1：
Minimum and Optimal Order of Integration / F.8.2：
Reduced Integration / F.8.3：
Evaluating Fluxes / F.8.4：
Flux Recovery / F.8.5：
References
Index
Preface
Acknowledgements
Glossary of Notations and Units
85.
図書
A.A. Becker
86.
図書
David Hutton
目次情報:
続きを見る
Preface
Basic Concepts of the Finite Element Method / Chapter 1：
Introduction / 1.1：
How does the Finite Element Method Work? / 1.2：
Comparison of Finite Element and Exact Solutions / 1.2.1：
Comparison of Finite Element and Finite Difference Methods / 1.2.2：
A General Procedure for Finite Element Analysis / 1.3：
Preprocessing / 1.3.1：
Solution / 1.3.2：
Postprocessing / 1.3.3：
Brief History of the Finite Element Method / 1.4：
Examples of Finite Element Analysis / 1.5：
Objectives of the Text / 1.6：
Stiffness Matrices, Spring and Bar Elements / Chapter 2：
Linear Spring as a Finite Element / 2.1：
System Assembly in Global Coordinates / 2.2.1：
Elastic Bar, Spar/Link/Truss Element / 2.3：
Strain Energy, Castigliano's First Theorem / 2.4：
Minimum Potential Energy / 2.5：
Summary / 2.6：
Truss Structures: The Direct Stiffness Method / Chapter 3：
Nodal Equilibrium Equations / 3.1：
Element Transformation / 3.3：
Direction Cosines / 3.3.1：
Direct Assembly of Global Stiffness Matrix / 3.4：
Boundary Conditions, Constraint Forces / 3.5：
Element Strain and Stress / 3.6：
Comprehensive Example / 3.7：
Three-Dimensional Trusses / 3.8：
Flexure Elements / 3.9：
Elementary Beam Theory / 4.1：
Flexure Element / 4.3：
Flexure Element Stiffness Matrix / 4.4：
Element Load Vector / 4.5：
Work Equivalence for Distributed Loads / 4.6：
Flexure Element with Axial Loading / 4.7：
A General Three-Dimensional Beam Element / 4.8：
Closing Remarks / 4.9：
Method of Weighted Residuals / Chapter 5：
The Galerkin Finite Element Method / 5.1：
Element Formulation / 5.3.1：
Application of Galerkin's Method to Structural Elements / 5.4：
Spar Element / 5.4.1：
Beam Element / 5.4.2：
One-Dimensional Heat Conduction / 5.5：
Interpolation Functions for General Element Formulation / 5.6：
Compatibility and Completeness Requirements / 6.1：
Compatibility / 6.2.1：
Completeness / 6.2.2：
Polynomial Forms: One-Dimensional Elements / 6.3：
Higher-Order One-Dimensional Elements / 6.3.1：
Polynomial Forms: Geometric Isotropy / 6.4：
Triangular Elements / 6.5：
Area Coordinates / 6.5.1：
Six-Node Triangular Element / 6.5.2：
Integration in Area Coordinates / 6.5.3：
Rectangular Elements / 6.6：
Three-Dimensional Elements / 6.7：
Four-Node Tetrahedral Element / 6.7.1：
Eight-Node Brick Element / 6.7.2：
Isoparametric Formulation / 6.8：
Axisymmetric Elements / 6.9：
Numerical Integration: Gaussian Quadrature / 6.10：
Applications in Heat Transfer / 6.11：
One-Dimensional Conduction: Quadratic Element / 7.1：
One-Dimensional Conduction with Convection / 7.3：
Finite Element Formulation / 7.3.1：
Boundary Conditions / 7.3.2：
Heat Transfer in Two Dimensions / 7.4：
Symmetry Conditions / 7.4.1：
Element Resultants / 7.4.4：
Internal Heat Generation / 7.4.5：
Heat Transfer with Mass Transport / 7.5：
Heat Transfer in Three Dimensions / 7.6：
System Assembly and Boundary Conditions / 7.6.1：
Axisymmetric Heat Transfer / 7.7：
Time-Dependent Heat Transfer / 7.7.1：
Finite Difference Methods for the Transient Response: Initial Conditions / 7.8.1：
Central Difference and Backward Difference Methods / 7.8.2：
Applications in Fluid Mechanics / 7.9：
Governing Equations for Incompressible Flow / 8.1：
Rotational and Irrotational Flow / 8.2.1：
The Stream Function in Two-Dimensional Flow / 8.3：
The Velocity Potential Function in Two-Dimensional Flow / 8.3.1：
Flow around Multiple Bodies / 8.4.1：
Incompressible Viscous Flow / 8.5：
Stokes Flow / 8.5.1：
Viscous Flow with Inertia / 8.5.2：
Applications in Solid Mechanics / 8.6：
Plane Stress / 9.1：
Finite Element Formulation: Constant Strain Triangle / 9.2.1：
Stiffness Matrix Evaluation / 9.2.2：
Distributed Loads and Body Force / 9.2.3：
Plane Strain: Rectangular Element / 9.3：
Isoparametric Formulation of the Plane Quadrilateral Element / 9.4：
Axisymmetric Stress Analysis / 9.5：
Element Loads / 9.5.1：
General Three-Dimensional Stress Elements / 9.6：
Strain and Stress Computation / 9.6.1：
Practical Considerations / 9.8：
Torsion / 9.9：
Boundary Condition / 9.9.1：
Torque / 9.9.2：
Structural Dynamics / 9.9.3：
The Simple Harmonic Oscillator / 10.1：
Forced Vibration / 10.2.1：
Multiple Degrees-of-Freedom Systems / 10.3：
Many Degrees-of-Freedom Systems / 10.3.1：
Bar Elements: Consistent Mass Matrix / 10.4：
Beam Elements / 10.5：
Mass Matrix for a General Element: Equations of Motion / 10.6：
Orthogonality of the Principal Modes / 10.7：
Harmonic Response Using Mode Superposition / 10.8：
Energy Dissipation: Structural Damping / 10.9：
General Structural Damping / 10.9.1：
Transient Dynamic Response / 10.10：
Bar Element Mass Matrix in Two-Dimensional Truss Structures / 10.11：
Matrix Mathematics / 10.12：
Definitions / A.1：
Algebraic Operations / A.2：
Determinants / A.3：
Matrix Inversion / A.4：
Matrix Partitioning / A.5：
Equations of Elasticity / Appendix B：
Strain-Displacement Relations / B.1：
Stress-Strain Relations / B.2：
Equilibrium Equations / B.3：
Compatibility Equations / B.4：
Solution Techniques for Linear Algebraic Equations / Appendix C：
Cramer's Method / C.1：
Gauss Elimination / C.2：
LU Decomposition / C.3：
Frontal Solution / C.4：
The Finite Element Personal Computer Program / Appendix D：
Problems for Computer Solution / D.1：
Chapter 3 / E.1：
Chapter 4 / E.2：
Chapter 7 / E.3：
Chapter 9 / E.4：
Chapter 10 / E.5：
Index
Preface
Basic Concepts of the Finite Element Method / Chapter 1：
Introduction / 1.1：
87.
図書
S. Mohammadi
出版情報:
Southampton : WIT Press, c2003 308 p. ; 24 cm.
子書誌情報:
loading…
所蔵情報:
loading…
88.
図書
G.R. Liu, S.S. Quek
出版情報:
Oxford : Butterworth-Heinemann, 2003 xv, 384 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
89.
図書
Prem K. Kythe, Dongming Wei
出版情報:
Boston : Birkhäuser, c2004 xxii, 445 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Preface
Notation
Introduction
One-Dimensional Shape Functions
One-Dimensional Second-Order Equations
One-Dimensional Fourth-Order Equations
Two-Dimensional Elements
Two-Dimensional Problems
More Two-Dimensional Problems
Axisymmetric Heat Transfer
Transient Problems
Single Nonlinear One-Dimensional Equations
Plane Elasticity
Stokes Equations and Penalty Method
Vibration Analysis
Computer Codes: Mathematica Codes, Ansys Codes, Mat
Lab Codes, Fortran Codes
Integration Formulas / Appendix A：
Special Cases / Appendix B：
Temporal Approximations / Appendix C：
Isoparametric Elements / Appendix D：
Green's Identities / Appendix E：
Gaussian Quadrature / Appendix F：
Gradient-Based Methods / Appendix G：
Bibliography
Index
Preface
Notation
Introduction
90.
図書
R.H. Wagoner, J.-L. Chenot
出版情報:
Cambridge : Cambridge University Press, 2001 xiii, 376 p. ; 27 cm
子書誌情報:
loading…
所蔵情報:
loading…
91.
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
92.
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
93.
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
94.
図書
Thomas J.R. Hughes
出版情報:
Mineola : Dover, 2000 xxii, 682 p. ; 24 cm
子書誌情報:
loading…
所蔵情報:
loading…
目次情報:
続きを見る
Preface
A Brief Glossary of Notations
Linear Static Analysis / Part 1：
Fundamental Concepts; A Simple One-Dimensional Boundary-Value Problem / 1：
Introductory Remarks and Preliminaries / 1.1：
Strong, or Classical, Form of the Problem / 1.2：
Weak, or Variational, Form of the Problem / 1.3：
Eqivalence of Strong and Weak Forms; Natural Boundary Conditions / 1.4：
Galerkin's Approximation Method / 1.5：
Matrix Equations; Stiffness Matrix K / 1.6：
Examples: 1 and 2 Degrees of Freedom / 1.7：
Piecewise Linear Finite Element Space / 1.8：
Properties of K / 1.9：
Mathematical Analysis / 1.10：
Interlude: Gauss Elimination; Hand-calculation Version / 1.11：
The Element Point of View / 1.12：
Element Stiffness Matrix and Force Vector / 1.13：
Assembly of Global Stiffness Matrix and Force Vector; LM Array / 1.14：
Explicit Computation of Element Stiffness Matrix and Force Vector / 1.15：
Exercise: Bernoulli-Euler Beam Theory and Hermite Cubics / 1.16：
An Elementary Discussion of Continuity, Differentiability, and Smoothness / Appendix 1.I：
References
Formulation of Two- and Three-Dimensional Boundary-Value Problems / 2：
Introductory Remarks / 2.1：
Preliminaries / 2.2：
Classical Linear Heat Conduction: Strong and Weak Forms; Equivalence / 2.3：
Heat Conduction: Galerkin Formulation; Symmetry and Positive-definiteness of K / 2.4：
Heat Conduction: Element Stiffness Matrix and Force Vector / 2.5：
Heat Conduction: Data Processing Arrays ID, IEN, and LM / 2.6：
Classical Linear Elastostatics: Strong and Weak Forms; Equivalence / 2.7：
Elastostatics: Galerkin Formulation, Symmetry, and Positive-definiteness of K / 2.8：
Elastostatics: Element Stiffness Matrix and Force Vector / 2.9：
Elastostatics: Data Processing Arrays ID, IEN, and LM / 2.10：
Summary of Important Equations for Problems Considered in Chapters 1 and 2 / 2.11：
Axisymmetric Formulations and Additional Exercises / 2.12：
Isoparametric Elements and Elementary Programming Concepts / 3：
Preliminary Concepts / 3.1：
Bilinear Quadrilateral Element / 3.2：
Isoparametric Elements / 3.3：
Linear Triangular Element; An Example of "Degeneration" / 3.4：
Trilinear Hexahedral Element / 3.5：
Higher-order Elements; Lagrange Polynomials / 3.6：
Elements with Variable Numbers of Nodes / 3.7：
Numerical Integration; Gaussian Quadrature / 3.8：
Derivatives of Shape Functions and Shape Function Subroutines / 3.9：
Element Stiffness Formulation / 3.10：
Additional Exercises / 3.11：
Triangular and Tetrahedral Elements / Appendix 3.I：
Methodology for Developing Special Shape Functions with Application to Singularities / Appendix 3.II：
Mixed and Penalty Methods, Reduced and Selective Integration, and Sundry Variational Crimes / 4：
"Best Approximation" and Error Estimates: Why the standard FEM usually works and why sometimes it does not / 4.1：
Incompressible Elasticity and Stokes Flow / 4.2：
Prelude to Mixed and Penalty Methods / 4.2.1：
A Mixed Formulation of Compressible Elasticity Capable of Representing the Incompressible Limit / 4.3：
Strong Form / 4.3.1：
Weak Form / 4.3.2：
Galerkin Formulation / 4.3.3：
Matrix Problem / 4.3.4：
Definition of Element Arrays / 4.3.5：
Illustration of a Fundamental Difficulty / 4.3.6：
Constraint Counts / 4.3.7：
Discontinuous Pressure Elements / 4.3.8：
Continuous Pressure Elements / 4.3.9：
Penalty Formulation: Reduced and Selective Integration Techniques; Equivalence with Mixed Methods / 4.4：
Pressure Smoothing / 4.4.1：
An Extension of Reduced and Selective Integration Techniques / 4.5：
Axisymmetry and Anisotropy: Prelude to Nonlinear Analysis / 4.5.1：
Strain Projection: The B-approach / 4.5.2：
The Patch Test; Rank Deficiency / 4.6：
Nonconforming Elements / 4.7：
Hourglass Stiffness / 4.8：
Additional Exercises and Projects / 4.9：
Mathematical Preliminaries / Appendix 4.I：
Basic Properties of Linear Spaces / 4.I.1：
Sobolev Norms / 4.I.2：
Approximation Properties of Finite Element Spaces in Sobolev Norms / 4.I.3：
Hypotheses on a(.,.) / 4.I.4：
Advanced Topics in the Theory of Mixed and Penalty Methods: Pressure Modes and Error Estimates / David S. MalkusAppendix 4.II：
Pressure Modes, Spurious and Otherwise / 4.II.1：
Existence and Uniqueness of Solutions in the Presence of Modes / 4.II.2：
Two Sides of Pressure Modes / 4.II.3：
Pressure Modes in the Penalty Formulation / 4.II.4：
The Big Picture / 4.II.5：
Error Estimates and Pressure Smoothing / 4.II.6：
The C[superscript 0]-Approach to Plates and Beams / 5：
Introduction / 5.1：
Reissner-Mindlin Plate Theory / 5.2：
Main Assumptions / 5.2.1：
Constitutive Equation / 5.2.2：
Strain-displacement Equations / 5.2.3：
Summary of Plate Theory Notations / 5.2.4：
Variational Equation / 5.2.5：
Matrix Formulation / 5.2.6：
Finite Element Stiffness Matrix and Load Vector / 5.2.9：
Plate-bending Elements / 5.3：
Some Convergence Criteria / 5.3.1：
Shear Constraints and Locking / 5.3.2：
Boundary Conditions / 5.3.3：
Reduced and Selective Integration Lagrange Plate Elements / 5.3.4：
Equivalence with Mixed Methods / 5.3.5：
Rank Deficiency / 5.3.6：
The Heterosis Element / 5.3.7：
T1: A Correct-rank, Four-node Bilinear Element / 5.3.8：
The Linear Triangle / 5.3.9：
The Discrete Kirchhoff Approach / 5.3.10：
Discussion of Some Quadrilateral Bending Elements / 5.3.11：
Beams and Frames / 5.4：
Definitions of Quantities Appearing in the Theory / 5.4.1：
Matrix Formulation of the Variational Equation / 5.4.5：
Representation of Stiffness and Load in Global Coordinates / 5.4.9：
Reduced Integration Beam Elements / 5.5：
The C[superscript 0]-Approach to Curved Structural Elements
Doubly Curved Shells in Three Dimensions / 6.1：
Geometry / 6.2.1：
Lamina Coordinate Systems / 6.2.2：
Fiber Coordinate Systems / 6.2.3：
Kinematics / 6.2.4：
Reduced Constitutive Equation / 6.2.5：
Strain-displacement Matrix / 6.2.6：
Stiffness Matrix / 6.2.7：
External Force Vector / 6.2.8：
Fiber Numerical Integration / 6.2.9：
Stress Resultants / 6.2.10：
Shell Elements / 6.2.11：
Some References to the Recent Literature / 6.2.12：
Simplifications: Shells as an Assembly of Flat Elements / 6.2.13：
Shells of Revolution; Rings and Tubes in Two Dimensions / 6.3：
Geometric and Kinematic Descriptions / 6.3.1：
Reduced Constitutive Equations / 6.3.2：
Linear Dynamic Analysis / 6.3.3：
Formulation of Parabolic, Hyperbolic, and Elliptic-Elgenvalue Problems / 7：
Parabolic Case: Heat Equation / 7.1：
Hyperbolic Case: Elastodynamics and Structural Dynamics / 7.2：
Eigenvalue Problems: Frequency Analysis and Buckling / 7.3：
Standard Error Estimates / 7.3.1：
Alternative Definitions of the Mass Matrix; Lumped and Higher-order Mass / 7.3.2：
Estimation of Eigenvalues / 7.3.3：
Error Estimates for Semidiscrete Galerkin Approximations / Appendix 7.I：
Algorithms for Parabolic Problems / 8：
One-step Algorithms for the Semidiscrete Heat Equation: Generalized Trapezoidal Method / 8.1：
Analysis of the Generalized Trapezoidal Method / 8.2：
Modal Reduction to SDOF Form / 8.2.1：
Stability / 8.2.2：
Convergence / 8.2.3：
An Alternative Approach to Stability: The Energy Method / 8.2.4：
Elementary Finite Difference Equations for the One-dimensional Heat Equation; the von Neumann Method of Stability Analysis / 8.2.5：
Element-by-element (EBE) Implicit Methods / 8.4：
Modal Analysis / 8.5：
Algorithms for Hyperbolic and Parabolic-Hyperbolic Problems / 9：
One-step Algorithms for the Semidiscrete Equation of Motion / 9.1：
The Newmark Method / 9.1.1：
Analysis / 9.1.2：
Measures of Accuracy: Numerical Dissipation and Dispersion / 9.1.3：
Matched Methods / 9.1.4：
Summary of Time-step Estimates for Some Simple Finite Elements / 9.1.5：
Linear Multistep (LMS) Methods / 9.3：
LMS Methods for First-order Equations / 9.3.1：
LMS Methods for Second-order Equations / 9.3.2：
Survey of Some Commonly Used Algorithms in Structural Dynamics / 9.3.3：
Some Recently Developed Algorithms for Structural Dynamics / 9.3.4：
Algorithms Based upon Operator Splitting and Mesh Partitions / 9.4：
Stability via the Energy Method / 9.4.1：
Predictor/Multicorrector Algorithms / 9.4.2：
Mass Matrices for Shell Elements / 9.5：
Solution Techniques for Eigenvalue Problems / 10：
The Generalized Eigenproblem / 10.1：
Static Condensation / 10.2：
Discrete Rayleigh-Ritz Reduction / 10.3：
Irons-Guyan Reduction / 10.4：
Subspace Iteration / 10.5：
Spectrum Slicing / 10.5.1：
Inverse Iteration / 10.5.2：
The Lanczos Algorithm for Solution of Large Generalized Eigenproblems / Bahram Nour-Omid10.6：
Spectral Transformation / 10.6.1：
Conditions for Real Eigenvalues / 10.6.3：
The Rayleigh-Ritz Approximation / 10.6.4：
Derivation of the Lanczos Algorithm / 10.6.5：
Reduction to Tridiagonal Form / 10.6.6：
Convergence Criterion for Eigenvalues / 10.6.7：
Loss of Orthogonality / 10.6.8：
Restoring Orthogonality / 10.6.9：
Dlearn--A Linear Static and Dynamic Finite Element Analysis Program / Thomas J. R. Hughes ; Robert M. Ferencz ; Arthur M. Raefsky11：
Description of Coding Techniques Used in DLEARN / 11.1：
Compacted Column Storage Scheme / 11.2.1：
Crout Elimination / 11.2.2：
Dynamic Storage Allocation / 11.2.3：
Program Structure / 11.3：
Global Control / 11.3.1：
Initialization Phase / 11.3.2：
Solution Phase / 11.3.3：
Adding an Element to DLEARN / 11.4：
DLEARN User's Manual / 11.5：
Remarks for the New User / 11.5.1：
Input Instructions / 11.5.2：
Examples / 11.5.3：
Planar Truss / 1.：
Static Analysis of a Plane Strain Cantilever Beam / 2.：
Dynamic Analysis of a Plane Strain Cantilever Beam / 3.：
Implicit-explicit Dynamic Analysis of a Rod / 4.：
Subroutine Index for Program Listing / 11.5.4：
Index
Preface
A Brief Glossary of Notations
Linear Static Analysis / Part 1：
95.
図書
O. C. Zienkiewicz in collaboration with Y. K. Cheung
96.
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：
97.
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：
98.
図書
Alexandre Ern, Jean-Luc Guermond
目次情報:
続きを見る
Theoretical Fundamentals / Part I：
Finite Element Interpolation
Approximation Theory
Approximation of PDEs / Part II：
Coercive Problems
Mixed problems
First-order PDEs
Time-Dependent Problems
Numerical Implementation / Part III：
Data Structuring and Mesh Generation
Quadratures, Assembling, and Storage
Linear Algebra
A Posteriori Error Estimates
Theoretical Fundamentals / Part I：
Finite Element Interpolation
Approximation Theory
99.
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
100.
図書
J. N. Reddy
出版情報:
Oxford : Oxford University Press, 2004 xv, 463 p. ; 25 cm
子書誌情報:
loading…
所蔵情報:
loading…
図書
