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The finite element method [[electronic resource] ] : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
The finite element method [[electronic resource] ] : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
Autore Zienkiewicz O. C
Edizione [6th ed.]
Pubbl/distr/stampa Amsterdam ; ; London, : Elsevier Butterworth-Heinemann, 2005
Descrizione fisica 1 online resource (753 p.)
Disciplina 620.00151825
Altri autori (Persone) TaylorRobert L <1934-> (Robert Leroy)
ZhuJ. Z
ZienkiewiczO. C
Soggetto topico Finite element method
Engineering mathematics
Soggetto genere / forma Electronic books.
ISBN 1-281-01652-7
9786611016524
0-08-047277-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; The Finite Element Method: Its Basis and Fundamentals; Copyright Page; Contents; Preface; Chapter 1. The standard discrete system and origins of the finite element method; 1.1 Introduction; 1.2 The structural element and the structural system; 1.3 Assembly and analysis of a structure; 1.4 The boundary conditions; 1.5 Electrical and fluid networks; 1.6 The general pattern; 1.7 The standard discrete system; 1.8 Transformation of coordinates; 1.9 Problems; Chapter 2. A direct physical approach to problems in elasticity: plane stress; 2.1 Introduction
2.2 Direct formulation of finite element characteristics 2.3 Generalization to the whole region- internal nodal force concept abandoned; 2.4 Displacement approach as a minimization of total potential energy; 2.5 Convergence criteria; 2.6 Discretization error and convergence rate; 2.7 Displacement functions with discontinuity between elements - non-conforming elements and the patch test; 2.8 Finite element solution process; 2.9 Numerical examples; 2.10 Concluding remarks; 2.11 Problems
Chapter 3. Generalization of the finite element concepts. Galerkin-weighted residual and variational approaches 3.1 Introduction; 3.2 Integral or 'weak' statements equivalent to the differential equations; 3.3 Approximation to integral formulations: the weighted residual-Galerkin method; 3.4 Virtual work as the 'weak form' of equilibrium equations for analysis of solids or fluids; 3.5 Partial discretization; 3.6 Convergence; 3.7 What are 'variational principles'?; 3.8 'Natural' variational principles and their relation to governing differential equations
3.9 Establishment of natural variational principles for linear, self-adjoint, differential equations 3.10 Maximum, minimum, or a saddle point?; 3.11 Constrained variational principles. Lagrange multipliers; 3.12 Constrained variational principles. Penalty function and perturbed lagrangian methods; 3.13 Least squares approximations; 3.14 Concluding remarks - finite difference and boundary methods; 3.15 Problems; Chapter 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity; 4.1 Introduction; 4.2 Standard and hierarchical concepts
4.3 Rectangular elements- some preliminary considerations 4.4 Completeness of polynomials; 4.5 Rectangular elements- Lagrange family; 4.6 Rectangular elements- 'serendipity' family; 4.7 Triangular element family; 4.8 Line elements; 4.9 Rectangular prisms - Lagrange family; 4.10 Rectangular prisms - 'serendipity' family; 4.11 Tetrahedral elements; 4.12 Other simple three-dimensional elements; 4.13 Hierarchic polynomials in one dimension; 4.14 Two- and three-dimensional, hierarchical elements of the 'rectangle' or 'brick' type; 4.15 Triangle and tetrahedron family
4.16 Improvement of conditioning with hierarchical forms
Record Nr. UNINA-9910457665903321
Zienkiewicz O. C  
Amsterdam ; ; London, : Elsevier Butterworth-Heinemann, 2005
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The finite element method [[electronic resource] ] : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
The finite element method [[electronic resource] ] : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
Autore Zienkiewicz O. C
Edizione [6th ed.]
Pubbl/distr/stampa Amsterdam ; ; London, : Elsevier Butterworth-Heinemann, 2005
Descrizione fisica 1 online resource (753 p.)
Disciplina 620.00151825
Altri autori (Persone) TaylorRobert L <1934-> (Robert Leroy)
ZhuJ. Z
ZienkiewiczO. C
Soggetto topico Finite element method
Engineering mathematics
ISBN 1-281-01652-7
9786611016524
0-08-047277-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; The Finite Element Method: Its Basis and Fundamentals; Copyright Page; Contents; Preface; Chapter 1. The standard discrete system and origins of the finite element method; 1.1 Introduction; 1.2 The structural element and the structural system; 1.3 Assembly and analysis of a structure; 1.4 The boundary conditions; 1.5 Electrical and fluid networks; 1.6 The general pattern; 1.7 The standard discrete system; 1.8 Transformation of coordinates; 1.9 Problems; Chapter 2. A direct physical approach to problems in elasticity: plane stress; 2.1 Introduction
2.2 Direct formulation of finite element characteristics 2.3 Generalization to the whole region- internal nodal force concept abandoned; 2.4 Displacement approach as a minimization of total potential energy; 2.5 Convergence criteria; 2.6 Discretization error and convergence rate; 2.7 Displacement functions with discontinuity between elements - non-conforming elements and the patch test; 2.8 Finite element solution process; 2.9 Numerical examples; 2.10 Concluding remarks; 2.11 Problems
Chapter 3. Generalization of the finite element concepts. Galerkin-weighted residual and variational approaches 3.1 Introduction; 3.2 Integral or 'weak' statements equivalent to the differential equations; 3.3 Approximation to integral formulations: the weighted residual-Galerkin method; 3.4 Virtual work as the 'weak form' of equilibrium equations for analysis of solids or fluids; 3.5 Partial discretization; 3.6 Convergence; 3.7 What are 'variational principles'?; 3.8 'Natural' variational principles and their relation to governing differential equations
3.9 Establishment of natural variational principles for linear, self-adjoint, differential equations 3.10 Maximum, minimum, or a saddle point?; 3.11 Constrained variational principles. Lagrange multipliers; 3.12 Constrained variational principles. Penalty function and perturbed lagrangian methods; 3.13 Least squares approximations; 3.14 Concluding remarks - finite difference and boundary methods; 3.15 Problems; Chapter 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity; 4.1 Introduction; 4.2 Standard and hierarchical concepts
4.3 Rectangular elements- some preliminary considerations 4.4 Completeness of polynomials; 4.5 Rectangular elements- Lagrange family; 4.6 Rectangular elements- 'serendipity' family; 4.7 Triangular element family; 4.8 Line elements; 4.9 Rectangular prisms - Lagrange family; 4.10 Rectangular prisms - 'serendipity' family; 4.11 Tetrahedral elements; 4.12 Other simple three-dimensional elements; 4.13 Hierarchic polynomials in one dimension; 4.14 Two- and three-dimensional, hierarchical elements of the 'rectangle' or 'brick' type; 4.15 Triangle and tetrahedron family
4.16 Improvement of conditioning with hierarchical forms
Record Nr. UNINA-9910784446703321
Zienkiewicz O. C  
Amsterdam ; ; London, : Elsevier Butterworth-Heinemann, 2005
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The finite element method [[electronic resource] ] : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
The finite element method [[electronic resource] ] : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
Autore Zienkiewicz O. C
Edizione [6th ed.]
Pubbl/distr/stampa Amsterdam ; ; London, : Elsevier Butterworth-Heinemann, 2005
Descrizione fisica 1 online resource (753 p.)
Disciplina 620.00151825
Altri autori (Persone) TaylorRobert L <1934-> (Robert Leroy)
ZhuJ. Z
ZienkiewiczO. C
Soggetto topico Finite element method
Engineering mathematics
ISBN 1-281-01652-7
9786611016524
0-08-047277-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; The Finite Element Method: Its Basis and Fundamentals; Copyright Page; Contents; Preface; Chapter 1. The standard discrete system and origins of the finite element method; 1.1 Introduction; 1.2 The structural element and the structural system; 1.3 Assembly and analysis of a structure; 1.4 The boundary conditions; 1.5 Electrical and fluid networks; 1.6 The general pattern; 1.7 The standard discrete system; 1.8 Transformation of coordinates; 1.9 Problems; Chapter 2. A direct physical approach to problems in elasticity: plane stress; 2.1 Introduction
2.2 Direct formulation of finite element characteristics 2.3 Generalization to the whole region- internal nodal force concept abandoned; 2.4 Displacement approach as a minimization of total potential energy; 2.5 Convergence criteria; 2.6 Discretization error and convergence rate; 2.7 Displacement functions with discontinuity between elements - non-conforming elements and the patch test; 2.8 Finite element solution process; 2.9 Numerical examples; 2.10 Concluding remarks; 2.11 Problems
Chapter 3. Generalization of the finite element concepts. Galerkin-weighted residual and variational approaches 3.1 Introduction; 3.2 Integral or 'weak' statements equivalent to the differential equations; 3.3 Approximation to integral formulations: the weighted residual-Galerkin method; 3.4 Virtual work as the 'weak form' of equilibrium equations for analysis of solids or fluids; 3.5 Partial discretization; 3.6 Convergence; 3.7 What are 'variational principles'?; 3.8 'Natural' variational principles and their relation to governing differential equations
3.9 Establishment of natural variational principles for linear, self-adjoint, differential equations 3.10 Maximum, minimum, or a saddle point?; 3.11 Constrained variational principles. Lagrange multipliers; 3.12 Constrained variational principles. Penalty function and perturbed lagrangian methods; 3.13 Least squares approximations; 3.14 Concluding remarks - finite difference and boundary methods; 3.15 Problems; Chapter 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity; 4.1 Introduction; 4.2 Standard and hierarchical concepts
4.3 Rectangular elements- some preliminary considerations 4.4 Completeness of polynomials; 4.5 Rectangular elements- Lagrange family; 4.6 Rectangular elements- 'serendipity' family; 4.7 Triangular element family; 4.8 Line elements; 4.9 Rectangular prisms - Lagrange family; 4.10 Rectangular prisms - 'serendipity' family; 4.11 Tetrahedral elements; 4.12 Other simple three-dimensional elements; 4.13 Hierarchic polynomials in one dimension; 4.14 Two- and three-dimensional, hierarchical elements of the 'rectangle' or 'brick' type; 4.15 Triangle and tetrahedron family
4.16 Improvement of conditioning with hierarchical forms
Record Nr. UNINA-9910825026503321
Zienkiewicz O. C  
Amsterdam ; ; London, : Elsevier Butterworth-Heinemann, 2005
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The finite element method for fluid dynamics [[electronic resource] /] / O.C. Zienkiewicz, R.L. Taylor, P. Nithiarasu
The finite element method for fluid dynamics [[electronic resource] /] / O.C. Zienkiewicz, R.L. Taylor, P. Nithiarasu
Autore Zienkiewicz O. C
Edizione [6th ed.]
Pubbl/distr/stampa Amsterdam ; ; Boston, : Elsevier Butterworth-Heinemann, c2005
Descrizione fisica 1 online resource (457 p.)
Disciplina 620.10601515353
Altri autori (Persone) TaylorRobert L <1934-> (Robert Leroy)
NithiarasuPerumal
ZienkiewiczO. C
Soggetto topico Finite element method
Mechanics, Applied
Fluid dynamics
Soggetto genere / forma Electronic books.
ISBN 1-280-63895-8
9786610638956
0-08-045559-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; The Finite Element Method for Fluid Dynamics; Copyright Page; Contents; Preface; Acknowledgements; Chapter 1. Introduction to the equations of fluid dynamics and the finite element approximation; 1.1 General remarks and classification of fluid dynamics problems discussed in this book; 1.2 The governing equations of fluid dynamics; 1.3 Inviscid, incompressible flow; 1.4 Incompressible (or nearly incompressible) flows; 1.5 Numerical solutions: weak forms, weighted residual and finite element approximation; 1.6 Concluding remarks; References
Chapter 2. Convection dominated problems- finite element approximations to the convection-diffusion-reaction equation2.1 Introduction; 2.2 The steady-state problem in one dimension; 2.3 The steady-state problem in two (or three) dimensions; 2.4 Steady state - concluding remarks; 2.5 Transients - introductory remarks; 2.6 Characteristic-based methods; 2.7 Taylor-Galerkin procedures for scalar variables; 2.8 Steady-state condition; 2.9 Non-linear waves and shocks; 2.10 Treatment of pure convection; 2.11 Boundary conditions for convection-diffusion; 2.12 Summary and concluding remarks
ReferencesChapter 3. The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow; 3.1 Introduction; 3.2 Non-dimensional form of the governing equations; 3.3 Characteristic-based split (CBS) algorithm; 3.4 Explicit, semi-implicit and nearly implicit forms; 3.5 Artificial compressibility and dual time stepping; 3.6 'Circumvention' of the Babuška-Brezzi (BB)restrictions; 3.7 A single-step version; 3.8 Boundary conditions; 3.9 The performance of two-step and one-step algorithms on an inviscid problem; 3.10 Concluding remarks; References
Chapter 4. Incompressible Newtonian laminar flows4.1 Introduction and the basic equations; 4.2 Use of the CBS algorithm for incompressible flows; 4.3 Adaptive mesh refinement; 4.4 Adaptive mesh generation for transient problems; 4.5 Slow flows - mixed and penalty formulations; 4.6 Concluding remarks; References; Chapter 5. Incompressible non-Newtonian flows; 5.1 Introduction; 5.2 Non-Newtonian flows - metal and polymer forming; 5.3 Viscoelastic flows; 5.4 Direct displacement approach to transient metal forming; 5.5 Concluding remarks; References
Chapter 6. Free surface and buoyancy driven flows6.1 Introduction; 6.2 Free surface flows; 6.3 Buoyancy driven flows; 6.4 Concluding remarks; References; Chapter 7. Compressible high-speed gas flow; 7.1 Introduction; 7.2 The governing equations; 7.3 Boundary conditions - subsonic and supersonic flow; 7.4 Numerical approximations and the CBS algorithm; 7.5 Shock capture; 7.6 Variable smoothing; 7.7 Some preliminary examples for the Euler equation; 7.8 Adaptive refinement and shock capture in Euler problems; 7.9 Three-dimensional inviscid examples in steady state
7.10 Transient two- and three-dimensional problems
Record Nr. UNINA-9910457669703321
Zienkiewicz O. C  
Amsterdam ; ; Boston, : Elsevier Butterworth-Heinemann, c2005
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The finite element method for fluid dynamics [[electronic resource] /] / O.C. Zienkiewicz, R.L. Taylor, P. Nithiarasu
The finite element method for fluid dynamics [[electronic resource] /] / O.C. Zienkiewicz, R.L. Taylor, P. Nithiarasu
Autore Zienkiewicz O. C
Edizione [6th ed.]
Pubbl/distr/stampa Amsterdam ; ; Boston, : Elsevier Butterworth-Heinemann, c2005
Descrizione fisica 1 online resource (457 p.)
Disciplina 620.10601515353
Altri autori (Persone) TaylorRobert L <1934-> (Robert Leroy)
NithiarasuPerumal
ZienkiewiczO. C
Soggetto topico Finite element method
Mechanics, Applied
Fluid dynamics
ISBN 1-280-63895-8
9786610638956
0-08-045559-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; The Finite Element Method for Fluid Dynamics; Copyright Page; Contents; Preface; Acknowledgements; Chapter 1. Introduction to the equations of fluid dynamics and the finite element approximation; 1.1 General remarks and classification of fluid dynamics problems discussed in this book; 1.2 The governing equations of fluid dynamics; 1.3 Inviscid, incompressible flow; 1.4 Incompressible (or nearly incompressible) flows; 1.5 Numerical solutions: weak forms, weighted residual and finite element approximation; 1.6 Concluding remarks; References
Chapter 2. Convection dominated problems- finite element approximations to the convection-diffusion-reaction equation2.1 Introduction; 2.2 The steady-state problem in one dimension; 2.3 The steady-state problem in two (or three) dimensions; 2.4 Steady state - concluding remarks; 2.5 Transients - introductory remarks; 2.6 Characteristic-based methods; 2.7 Taylor-Galerkin procedures for scalar variables; 2.8 Steady-state condition; 2.9 Non-linear waves and shocks; 2.10 Treatment of pure convection; 2.11 Boundary conditions for convection-diffusion; 2.12 Summary and concluding remarks
ReferencesChapter 3. The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow; 3.1 Introduction; 3.2 Non-dimensional form of the governing equations; 3.3 Characteristic-based split (CBS) algorithm; 3.4 Explicit, semi-implicit and nearly implicit forms; 3.5 Artificial compressibility and dual time stepping; 3.6 'Circumvention' of the Babuška-Brezzi (BB)restrictions; 3.7 A single-step version; 3.8 Boundary conditions; 3.9 The performance of two-step and one-step algorithms on an inviscid problem; 3.10 Concluding remarks; References
Chapter 4. Incompressible Newtonian laminar flows4.1 Introduction and the basic equations; 4.2 Use of the CBS algorithm for incompressible flows; 4.3 Adaptive mesh refinement; 4.4 Adaptive mesh generation for transient problems; 4.5 Slow flows - mixed and penalty formulations; 4.6 Concluding remarks; References; Chapter 5. Incompressible non-Newtonian flows; 5.1 Introduction; 5.2 Non-Newtonian flows - metal and polymer forming; 5.3 Viscoelastic flows; 5.4 Direct displacement approach to transient metal forming; 5.5 Concluding remarks; References
Chapter 6. Free surface and buoyancy driven flows6.1 Introduction; 6.2 Free surface flows; 6.3 Buoyancy driven flows; 6.4 Concluding remarks; References; Chapter 7. Compressible high-speed gas flow; 7.1 Introduction; 7.2 The governing equations; 7.3 Boundary conditions - subsonic and supersonic flow; 7.4 Numerical approximations and the CBS algorithm; 7.5 Shock capture; 7.6 Variable smoothing; 7.7 Some preliminary examples for the Euler equation; 7.8 Adaptive refinement and shock capture in Euler problems; 7.9 Three-dimensional inviscid examples in steady state
7.10 Transient two- and three-dimensional problems
Record Nr. UNINA-9910784446803321
Zienkiewicz O. C  
Amsterdam ; ; Boston, : Elsevier Butterworth-Heinemann, c2005
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The finite element method for fluid dynamics [[electronic resource] /] / O.C. Zienkiewicz, R.L. Taylor, P. Nithiarasu
The finite element method for fluid dynamics [[electronic resource] /] / O.C. Zienkiewicz, R.L. Taylor, P. Nithiarasu
Autore Zienkiewicz O. C
Edizione [6th ed.]
Pubbl/distr/stampa Amsterdam ; ; Boston, : Elsevier Butterworth-Heinemann, c2005
Descrizione fisica 1 online resource (457 p.)
Disciplina 620.10601515353
Altri autori (Persone) TaylorRobert L <1934-> (Robert Leroy)
NithiarasuPerumal
ZienkiewiczO. C
Soggetto topico Finite element method
Mechanics, Applied
Fluid dynamics
ISBN 1-280-63895-8
9786610638956
0-08-045559-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; The Finite Element Method for Fluid Dynamics; Copyright Page; Contents; Preface; Acknowledgements; Chapter 1. Introduction to the equations of fluid dynamics and the finite element approximation; 1.1 General remarks and classification of fluid dynamics problems discussed in this book; 1.2 The governing equations of fluid dynamics; 1.3 Inviscid, incompressible flow; 1.4 Incompressible (or nearly incompressible) flows; 1.5 Numerical solutions: weak forms, weighted residual and finite element approximation; 1.6 Concluding remarks; References
Chapter 2. Convection dominated problems- finite element approximations to the convection-diffusion-reaction equation2.1 Introduction; 2.2 The steady-state problem in one dimension; 2.3 The steady-state problem in two (or three) dimensions; 2.4 Steady state - concluding remarks; 2.5 Transients - introductory remarks; 2.6 Characteristic-based methods; 2.7 Taylor-Galerkin procedures for scalar variables; 2.8 Steady-state condition; 2.9 Non-linear waves and shocks; 2.10 Treatment of pure convection; 2.11 Boundary conditions for convection-diffusion; 2.12 Summary and concluding remarks
ReferencesChapter 3. The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow; 3.1 Introduction; 3.2 Non-dimensional form of the governing equations; 3.3 Characteristic-based split (CBS) algorithm; 3.4 Explicit, semi-implicit and nearly implicit forms; 3.5 Artificial compressibility and dual time stepping; 3.6 'Circumvention' of the Babuška-Brezzi (BB)restrictions; 3.7 A single-step version; 3.8 Boundary conditions; 3.9 The performance of two-step and one-step algorithms on an inviscid problem; 3.10 Concluding remarks; References
Chapter 4. Incompressible Newtonian laminar flows4.1 Introduction and the basic equations; 4.2 Use of the CBS algorithm for incompressible flows; 4.3 Adaptive mesh refinement; 4.4 Adaptive mesh generation for transient problems; 4.5 Slow flows - mixed and penalty formulations; 4.6 Concluding remarks; References; Chapter 5. Incompressible non-Newtonian flows; 5.1 Introduction; 5.2 Non-Newtonian flows - metal and polymer forming; 5.3 Viscoelastic flows; 5.4 Direct displacement approach to transient metal forming; 5.5 Concluding remarks; References
Chapter 6. Free surface and buoyancy driven flows6.1 Introduction; 6.2 Free surface flows; 6.3 Buoyancy driven flows; 6.4 Concluding remarks; References; Chapter 7. Compressible high-speed gas flow; 7.1 Introduction; 7.2 The governing equations; 7.3 Boundary conditions - subsonic and supersonic flow; 7.4 Numerical approximations and the CBS algorithm; 7.5 Shock capture; 7.6 Variable smoothing; 7.7 Some preliminary examples for the Euler equation; 7.8 Adaptive refinement and shock capture in Euler problems; 7.9 Three-dimensional inviscid examples in steady state
7.10 Transient two- and three-dimensional problems
Record Nr. UNINA-9910815968403321
Zienkiewicz O. C  
Amsterdam ; ; Boston, : Elsevier Butterworth-Heinemann, c2005
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui