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1.

図書
図書
1. The finite element method. 5th ed.
Zienkiewicz, O. C. ; Taylor, R. L.
出版情報: Oxford : Butterworth-Heinemann, 2000  3 v. ; 26 cm
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2.

図書
図書
2. The basis. 5th ed
O.C. Zienkiewicz, R.L. Taylor
出版情報: Oxford : Butterworth-Heinemann, 2000  xvi, 689 p., [4] p. of plates ; 26 cm
シリーズ名: The finite element method ; v. 1
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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
3.

図書
図書
3. Solid mechanics. 5th ed
O.C. Zienkiewicz, R.L. Taylor
出版情報: Oxford : Butterworth-Heinemann, 2000  xiv, 459 p., [4] p. of plates ; 26 cm
シリーズ名: The finite element method ; v. 2
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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
4.

図書
図書
4. Fluid dynamics. 5th ed
O.C. Zienkiewicz, R.L. Taylor
出版情報: Oxford : Butterworth-Heinemann, 2000  xiv, 334 p., [4] p. of plates ; 26 cm
シリーズ名: The finite element method ; v. 3
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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
5.

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

図書
図書
6. The finite element method : its basis and fundamentals. 6th ed
O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
出版情報: Amsterdam ; Oxford ; Tokyo : Elsevier Butterworth-Heinemann, 2005  xiv, 733 p., [4] p. of plates ; 26 cm
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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
7.

図書
図書
7. The finite element method for fluid dynamics. 6th ed
O.C. Zienkiewicz, R.L. Taylor, P. Nithiarasu
出版情報: Amsterdam ; Oxford ; Tokyo : Elsevier Butterworth-Heinemann, 2005  xii, 435 p., 6 p. of plates ; 26 cm
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目次情報: 続きを見る
Preface
Acknowledgements
Introduction to the equations of fluid dynamics and the finite element approximation / 1：
General remarks and classification of fluid dynamics problems discussed in this book / 1.1：
The governing equations of fluid dynamics / 1.2：
Inviscid, incompressible flow / 1.3：
Incompressible (or nearly incompressible) flows / 1.4：
Numerical solutions: weak forms, weighted residual and finite element approximation / 1.5：
Concluding remarks / 1.6：
References
Convection dominated problems - finite element approximations to the convection-diffusion-reaction equation / 2：
Introduction / 2.1：
The steady-state problem in one dimension / 2.2：
The steady-state problem in two (or three) dimensions / 2.3：
Steady state - concluding remarks / 2.4：
Transients - introductory remarks / 2.5：
Characteristic-based methods / 2.6：
Taylor-Galerkin procedures for scalar variables / 2.7：
Steady-state condition / 2.8：
Non-linear waves and shocks / 2.9：
Treatment of pure convection / 2.10：
Boundary conditions for convection-diffusion / 2.11：
Summary and concluding remarks / 2.12：
The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow / 3：
Non-dimensional form of the governing equations / 3.1：
Characteristic-based split (CBS) algorithm / 3.3：
Explicit, semi-implicit and nearly implicit forms / 3.4：
Artificial compressibility and dual time stepping / 3.5：
'Circumvention' of the Babuska-Brezzi (BB) restrictions / 3.6：
A single-step version / 3.7：
Boundary conditions / 3.8：
The performance of two-step and one-step algorithms on an inviscid problem / 3.9：
Incompressible Newtonian laminar flows / 3.10：
Introduction and the basic equations / 4.1：
Use of the CBS algorithm for incompressible flows / 4.2：
Adaptive mesh refinement / 4.3：
Adaptive mesh generation for transient problems / 4.4：
Slow flows - mixed and penalty formulations / 4.5：
Incompressible non-Newtonian flows / 4.6：
Non-Newtonian flows - metal and polymer forming / 5.1：
Viscoelastic flows / 5.3：
Direct displacement approach to transient metal forming / 5.4：
Free surface and buoyancy driven flows / 5.5：
Free surface flows / 6.1：
Buoyancy driven flows / 6.3：
Compressible high-speed gas flow / 6.4：
The governing equations / 7.1：
Boundary conditions - subsonic and supersonic flow / 7.3：
Numerical approximations and the CBS algorithm / 7.4：
Shock capture / 7.5：
Variable smoothing / 7.6：
Some preliminary examples for the Euler equation / 7.7：
Adaptive refinement and shock capture in Euler problems / 7.8：
Three-dimensional inviscid examples in steady state / 7.9：
Transient two- and three-dimensional problems / 7.10：
Viscous problems in two dimensions / 7.11：
Three-dimensional viscous problems / 7.12：
Boundary layer-inviscid Euler solution coupling / 7.13：
Turbulent flows / 7.14：
Treatment of incompressible turbulent flows / 8.1：
Treatment of compressible flows / 8.3：
Large eddy simulation / 8.4：
Detached Eddy Simulation (DES) / 8.5：
Direct Numerical Simulation (DNS) / 8.6：
Generalized flow through porous media / 8.7：
A generalized porous medium flow approach / 9.1：
Discretization procedure / 9.3：
Non-isothermal flows / 9.4：
Forced convection / 9.5：
Natural convection / 9.6：
Shallow water problems / 9.7：
The basis of the shallow water equations / 10.1：
Numerical approximation / 10.3：
Examples of application / 10.4：
Drying areas / 10.5：
Shallow water transport / 10.6：
Long and medium waves / 10.7：
Introduction and equations / 11.1：
Waves in closed domains - finite element models / 11.2：
Difficulties in modelling surface waves / 11.3：
Bed friction and other effects / 11.4：
The short-wave problem / 11.5：
Waves in unbounded domains (exterior surface wave problems) / 11.6：
Unbounded problems / 11.7：
Local Non-Reflecting Boundary Conditions (NRBCs) / 11.8：
Infinite elements / 11.9：
Mapped periodic (unconjugated) infinite elements / 11.10：
Ellipsoidal type infinite elements of Burnett and Holford / 11.11：
Wave envelope (or conjugated) infinite elements / 11.12：
Accuracy of infinite elements / 11.13：
Trefftz type infinite elements / 11.14：
Convection and wave refraction / 11.15：
Transient problems / 11.16：
Linking to exterior solutions (or DtN mapping) / 11.17：
Three-dimensional effects in surface waves / 11.18：
Short waves / 11.19：
Background / 12.1：
Errors in wave modelling / 12.3：
Recent developments in short wave modelling / 12.4：
Transient solution of electromagnetic scattering problems / 12.5：
Finite elements incorporating wave shapes / 12.6：
Refraction / 12.7：
Spectral finite elements for waves / 12.8：
Discontinuous Galerkin finite elements (DGFE) / 12.9：
Computer implementation of the CBS algorithm / 12.10：
The data input module / 13.1：
Solution module / 13.3：
Output module / 13.4：
Non-conservative form of Navier-Stokes equations / Appendix A：
Self-adjoint differential equations / Appendix B：
Postprocessing / Appendix C：
Integration formulae / Appendix D：
Convection-diffusion equations: vector-valued variables / Appendix E：
Edge-based finite element formulation / Appendix F：
Multigrid method / Appendix G：
Boundary layer-inviscid flow coupling / Appendix H：
Mass-weighted averaged turbulence transport equations / Appendix I：
Author index
Subject index
Preface
Acknowledgements
Introduction to the equations of fluid dynamics and the finite element approximation / 1：
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