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1.

図書

図書
R.H. Wagoner, J.-L. Chenot
出版情報: Cambridge : Cambridge University Press, 2001  xiii, 376 p. ; 27 cm
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2.

図書

図書
A.J. Davies
出版情報: New York : Oxford University Press, 2011  ix, 297 p. ; 25 cm
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目次情報: 続きを見る
Historical introduction / 1:
Weighted residual and variational methods / 2:
Classification of differential operators / 2.1:
Self-adjoint positive definite operators / 2.2:
Weighted residual methods / 2.3:
Extremum formulation: homogeneous boundary conditions / 2.4:
Non-homogeneous boundary conditions / 2.5:
Partial differential equations: natural boundary conditions / 2.6:
The Rayleigh-Ritz method / 2.7:
The 'elastic analogy' for Poisson's equation / 2.8:
Variational methods for time-dependent problems / 2.9:
Exercises and solutions / 2.10:
The finite element method for elliptic problems / 3:
Difficulties associated with the application of weighted residual methods / 3.1:
Piecewise application of the Galerkin method / 3.2:
Terminology / 3.3:
Finite element idealization / 3.4:
Illustrative problem involving one independent variable / 3.5:
Finite element equations for Poisson's equation / 3.6:
A rectangular element for Poisson's equation / 3.7:
A triangular element for Poisson's equation / 3.8:
Higher-order elements: the isoparametric concept / 3.9:
A two-point boundary-value problem / 4.1:
Higher-order rectangular elements / 4.2:
Higher-order triangular elements / 4.3:
Two degrees of freedom at each node / 4.4:
Condensation of internal nodal freedoms / 4.5:
Curved boundaries and higher-order elements: isoparametric elements / 4.6:
Further topics in the finite element method / 4.7:
The variational approach / 5.1:
Collocation and least squares methods / 5.2:
Use of Galerkin's method for time-dependent and non-linear problems / 5.3:
Time-dependent problems using variational principles which are not extremal / 5.4:
The Laplace transform / 5.5:
Convergence of the finite element method / 5.6:
A one-dimensional example / 6.1:
Two-dimensional problems involving Poisson's equation / 6.2:
Isoparametric elements: numerical integration / 6.3:
Non-conforming elements: the patch test / 6.4:
Comparison with the finite difference method: stability / 6.5:
The boundary element method / 6.6:
Integral formulation of boundary-value problems / 7.1:
Boundary element idealization for Laplace's equation / 7.2:
A constant boundary element for Laplace's equation / 7.3:
A linear element for Laplace's equation / 7.4:
Time-dependent problems / 7.5:
Computational aspects / 7.6:
Pre-processor / 8.1:
Solution phase / 8.2:
Post-processor / 8.3:
Finite element method (FEM) or boundary element method (BEM)? / 8.4:
Partial differential equation models in the physical sciences / Appendix A:
Parabolic problems / A.l:
Elliptic problems / A.2:
Hyperbolic problems / A.3:
Initial and boundary conditions / A.4:
Some integral theorems of the vector calculus / Appendix B:
A formula for integrating products of area coordinates over a triangle / Appendix C:
Numerical integration formulae / Appendix D:
One-dimensional Gauss quadrature / D.l:
Two-dimensional Gauss quadrature / D.2:
Logarithmic Gauss quadrature / D.3:
Stehfest's formula and weights for numerical Laplace transform inversion / Appendix E:
References
Index
Historical introduction / 1:
Weighted residual and variational methods / 2:
Classification of differential operators / 2.1:
3.

図書

図書
by E.S. Mistakidis and G.E. Stavroulakis
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1998  xx, 285 p. ; 25 cm
シリーズ名: Nonconvex optimization and its applications ; v. 21
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4.

図書

図書
John O. Dow
出版情報: San Diego : Academic Press, 1998  xxiv, 533 p. ; 26 cm
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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
5.

図書

図書
Vidar Thomée
出版情報: Berlin ; New York : Springer-Verlag, 1997  x, 302 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 25
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6.

図書

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

図書

図書
Mark Ainsworth and J. Tinsley Oden
出版情報: New York : John Wiley & Sons, c2000  xvii, 240 p. ; 25 cm
シリーズ名: Pure and applied mathematics
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Preface
Acknowledgments
Introduction / 1:
A Posteriori Error Estimation: The Setting / 1.1:
Status and Scope / 1.2:
Finite Element Nomenclature / 1.3:
Sobolev Spaces / 1.3.1:
Inverse Estimates / 1.3.2:
Finite Element Partitions / 1.3.3:
Finite Element Spaces on Triangles / 1.3.4:
Finite Element Spaces on Quadrilaterals / 1.3.5:
Properties of Lagrange Basis Functions / 1.3.6:
Finite Element Interpolation / 1.3.7:
Patches of Elements / 1.3.8:
Regularized Approximation Operators / 1.3.9:
Model Problem / 1.4:
Properties of A Posteriori Error Estimators / 1.5:
Bibliographical Remarks / 1.6:
Explicit A Posteriori Estimators / 2:
A Simple A Posteriori Error Estimate / 2.1:
Efficiency of Estimator / 2.3:
Bubble Functions / 2.3.1:
Bounds on the Residuals / 2.3.2:
Proof of Two-Sided Bounds on the Error / 2.3.3:
A Simple Explicit Least Squares Error Estimator / 2.4:
Estimates for the Pointwise Error / 2.5:
Regularized Point Load / 2.5.1:
Regularized Green's Function / 2.5.2:
Two-Sided Bounds on the Pointwise Error / 2.5.3:
Implicit A Posteriori Estimators / 2.6:
The Subdomain Residual Method / 3.1:
Formulation of Subdomain Residual Problem / 3.2.1:
Preliminaries / 3.2.2:
Equivalence of Estimator / 3.2.3:
Treatment of Residual Problems / 3.2.4:
The Element Residual Method / 3.3:
Formulation of Local Residual Problem / 3.3.1:
Solvability of the Local Problems / 3.3.2:
The Classical Element Residual Method / 3.3.3:
Relationship with Explicit Error Estimators / 3.3.4:
Efficiency and Reliability of the Estimator / 3.3.5:
The Influence and Selection of Subspaces / 3.4:
Exact Solution of Element Residual Problem / 3.4.1:
Analysis and Selection of Approximate Subspaces / 3.4.2:
Conclusions / 3.4.3:
Recovery-Based Error Estimators / 3.5:
Examples of Recovery-Based Estimators / 4.1:
An Error Estimator for a Model Problem in One Dimension / 4.1.1:
An Error Estimator for Bilinear Finite Element Approximation / 4.1.2:
Recovery Operators / 4.2:
Approximation Properties of Recovery Operators / 4.2.1:
The Superconvergence Property / 4.3:
Application to A Posteriori Error Estimation / 4.4:
Construction of Recovery Operators / 4.5:
The Zienkiewicz-Zhu Patch Recovery Technique / 4.6:
Linear Approximation on Triangular Elements / 4.6.1:
Quadratic Approximation on Triangular Elements / 4.6.2:
Patch Recovery for Quadrilateral Elements / 4.6.3:
A Cautionary Tale / 4.7:
Estimators, Indicators, and Hierarchic Bases / 4.8:
Saturation Assumption / 5.1:
Analysis of Estimator / 5.3:
Error Estimation Using a Reduced Subspace / 5.4:
The Strengthened Cauchy-Schwarz Inequality / 5.5:
Examples / 5.6:
Multilevel Error Indicators / 5.7:
The Equilibrated Residual Method / 5.8:
The Equilibrated Flux Conditions / 6.1:
Equilibrated Fluxes on Regular Partitions / 6.4:
First-Order Equilibration Condition / 6.4.1:
The Form of the Boundary Fluxes / 6.4.2:
Equilibration Conditions in Terms of the Moments / 6.4.3:
Local Patch Problems for the Flux Moments / 6.4.4:
Procedure for Resolution of Patch Problems / 6.4.5:
Summary / 6.4.6:
Efficiency of the Estimator / 6.5:
Stability of the Equilibrated Fluxes / 6.5.1:
Proof of Efficiency of the Estimator / 6.5.2:
Equilibrated Fluxes on Partitions Containing Hanging Nodes / 6.6:
First-Order Equilibration / 6.6.1:
Flux Moments for Unconstrained Nodes / 6.6.2:
Flux Moments with Respect to Constrained Nodes / 6.6.3:
Recovery of Actual Fluxes / 6.6.4:
Equilibrated Fluxes for Higher-Order Elements / 6.7:
Determination of the Flux Moments / 6.7.1:
Methodology for the Comparison of Estimators / 6.8:
Overview of the Technique / 7.1:
Approximation over an Interior Subdomain / 7.3:
Translation Invariant Meshes / 7.3.1:
Lower Bounds on the Error / 7.3.2:
Interior Estimates / 7.3.3:
Asymptotic Finite Element Approximation / 7.4:
Periodic Finite Element Projection on Reference Cell / 7.4.1:
Periodic Finite Element Projection on a Physical Cell / 7.4.2:
Periodic Extension on a Subdomain / 7.4.3:
Stability of Estimators / 7.4.4:
Verification of Stability Condition for Explicit Estimator / 7.5.1:
Verification of Stability Condition for Implicit Estimators / 7.5.2:
Verification of Stability Condition for Recovery-Based Estimator / 7.5.3:
Elementary Consequences of the Stability Condition / 7.5.4:
Evaluation of Effectivity Index in the Asymptotic Limit / 7.5.5:
An Application of the Theory / 7.6:
Computation of Asymptotic Finite Element Solution / 7.6.1:
Evaluation of the Error in Asymptotic Finite Element Approximation / 7.6.2:
Computation of Limits on the Asymptotic Effectivity Index for Zienkiewicz-Zhu Patch Recovery Estimator / 7.6.3:
Application to Equilibrated Residual Method / 7.6.4:
Application to Implicit Element Residual Method / 7.6.5:
Estimation of the Errors in Quantities of Interest / 7.7:
Estimates for the Error in Quantities of Interest / 8.1:
Upper and Lower Bounds on the Errors / 8.3:
Goal-Oriented Adaptive Refinement / 8.4:
Example of Goal-Oriented Adaptivity / 8.5:
Adaptivity Based on Control of Global Error in Energy / 8.5.1:
Goal-Oriented Adaptivity Based on Pointwise Quantities of Interest / 8.5.2:
Local and Pollution Errors / 8.6:
Some Extensions / 8.7:
Stokes and Oseen's Equations / 9.1:
A Posteriori Error Analysis / 9.2.1:
Incompressible Navier-Stokes Equations / 9.2.2:
Extensions to Nonlinear Problems / 9.4:
A Class of Nonlinear Problems / 9.4.1:
A Posteriori Error Estimation / 9.4.2:
Estimation of the Residual / 9.4.3:
References / 9.5:
Index
Preface
Acknowledgments
Introduction / 1:
8.

図書

図書
Achintya Haldar, Sankaran Mahadevan
出版情報: New York : John Wiley & Sons, c2000  xvi, 328 p. ; 26 cm
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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
9.

図書

図書
P.M. Gresho, R.L. Sani ; in collaboration with M.S. Engelman
出版情報: Chichester : Wiley, 2000  xx, 445 p. ; 25 cm
シリーズ名: Incompressible flow and the finite element method ; v. 1
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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:
10.

図書

図書
K.C. Rockey ... [et al.]
出版情報: London : Granada, 1983  x, 239 p. ; 24 cm
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