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The finite element method : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
| The finite element method : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu |
| Autore | Zienkiewicz O. C |
| Edizione | [Seventh edition.] |
| Pubbl/distr/stampa | Oxford, UK : , : Butterworth-Heinemann, , [2013] |
| Descrizione fisica | 1 online resource (xxxviii, 714 p.) |
| Disciplina | 620/.00151825 |
| Altri autori (Persone) |
TaylorR. L
ZhuJ. Z |
| Soggetto topico |
Structural analysis (Engineering)
Continuum mechanics Finite element method |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-85617-630-4
0-08-095135-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Half Title; Author Biography; Title Page; Copyright; Dedication; Contents; List of Figures; List of Tables; Preface; 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; References; 2 Problems in Linear Elasticity and Fields; 2.1 Introduction; 2.2 Elasticity equations
2.2.1 Displacement function2.2.2 Strain matrix; 2.2.2.1 Strain-displacement matrix; 2.2.2.2 Volume change and deviatoric strain; 2.2.3 Stress matrix; 2.2.3.1 Mean stress and deviatoric stress; 2.2.4 Equilibrium equations; 2.2.4.1 Plane stress and plane strain problems; 2.2.4.2 Axisymmetric problems; 2.2.5 Boundary conditions; 2.2.5.1 Boundary conditions on inclined coordinates; 2.2.5.2 Normal pressure loading; 2.2.5.3 Symmetry and repeatability; 2.2.6 Initial conditions; 2.2.7 Transformation of stress and strain; 2.2.7.1 Energy; 2.2.8 Stress-strain relations: Elasticity matrix 2.2.8.1 Isotropic materials2.2.8.2 Deviatoric and pressure-volume relations; 2.2.8.3 Anisotropic materials; 2.2.8.4 Initial strain-thermal effects; 2.3 General quasi-harmonic equation; 2.3.1 Governing equations: Flux and continuity; 2.3.2 Boundary conditions; 2.3.3 Initial condition; 2.3.4 Constitutive behavior; 2.3.5 Irreducible form in φ; 2.3.6 Anisotropic and isotropic forms for k: Transformations; 2.3.7 Two-dimensional problems; 2.4 Concluding remarks; 2.5 Problems; References; 3 Weak Forms and Finite Element Approximation: 1-D Problems; 3.1 Weak forms 3.2 One-dimensional form of elasticity3.2.1 Weak form of equilibrium equation; 3.2.1.1 Adjoint forms; 3.3 Approximation to integral and weak forms: The weighted residual (Galerkin) method; 3.3.1 Galerkin solution of elasticity equation; 3.4 Finite element solution; 3.4.1 Requirements for finite element approximations; 3.5 Isoparametric form; 3.5.1 Higher order elements: Lagrange interpolation; 3.5.1.1 Linear shape functions; 3.5.1.2 Quadratic shape functions; 3.5.2 Integrals on the parent element: Numerical integration; 3.6 Hierarchical interpolation; 3.7 Axisymmetric one-dimensional problem 3.7.1 Weak form for axisymmetric problem3.7.2 A variational notation; 3.7.3 Irreducible form for axisymmetric problem; 3.7.4 Finite element solution; 3.8 Transient problems; 3.8.1 Discrete time methods; 3.8.1.1 Stability and dissipation; 3.8.2 Semi-discretization of the problem; 3.8.2.1 Stability of modes; 3.9 Weak form for one-dimensional quasi-harmonic equation; 3.9.1 Weak form; 3.9.2 Finite element solution of quasi-harmonic problem; 3.9.3 Transient problems; 3.9.3.1 Stability; 3.10 Concluding remarks; 3.11 Problems; References 4 Variational Forms and Finite Element Approximation: 1-D Problems |
| Record Nr. | UNISA-996426332003316 |
Zienkiewicz O. C
|
||
| Oxford, UK : , : Butterworth-Heinemann, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
The finite element method : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
| The finite element method : its basis and fundamentals / / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu |
| Autore | Zienkiewicz O. C |
| Edizione | [Seventh edition.] |
| Pubbl/distr/stampa | Oxford, UK : , : Butterworth-Heinemann, , [2013] |
| Descrizione fisica | 1 online resource (xxxviii, 714 p.) |
| Disciplina | 620/.00151825 |
| Altri autori (Persone) |
TaylorR. L
ZhuJ. Z |
| Soggetto topico |
Structural analysis (Engineering)
Continuum mechanics Finite element method |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-85617-630-4
0-08-095135-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Half Title; Author Biography; Title Page; Copyright; Dedication; Contents; List of Figures; List of Tables; Preface; 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; References; 2 Problems in Linear Elasticity and Fields; 2.1 Introduction; 2.2 Elasticity equations
2.2.1 Displacement function2.2.2 Strain matrix; 2.2.2.1 Strain-displacement matrix; 2.2.2.2 Volume change and deviatoric strain; 2.2.3 Stress matrix; 2.2.3.1 Mean stress and deviatoric stress; 2.2.4 Equilibrium equations; 2.2.4.1 Plane stress and plane strain problems; 2.2.4.2 Axisymmetric problems; 2.2.5 Boundary conditions; 2.2.5.1 Boundary conditions on inclined coordinates; 2.2.5.2 Normal pressure loading; 2.2.5.3 Symmetry and repeatability; 2.2.6 Initial conditions; 2.2.7 Transformation of stress and strain; 2.2.7.1 Energy; 2.2.8 Stress-strain relations: Elasticity matrix 2.2.8.1 Isotropic materials2.2.8.2 Deviatoric and pressure-volume relations; 2.2.8.3 Anisotropic materials; 2.2.8.4 Initial strain-thermal effects; 2.3 General quasi-harmonic equation; 2.3.1 Governing equations: Flux and continuity; 2.3.2 Boundary conditions; 2.3.3 Initial condition; 2.3.4 Constitutive behavior; 2.3.5 Irreducible form in φ; 2.3.6 Anisotropic and isotropic forms for k: Transformations; 2.3.7 Two-dimensional problems; 2.4 Concluding remarks; 2.5 Problems; References; 3 Weak Forms and Finite Element Approximation: 1-D Problems; 3.1 Weak forms 3.2 One-dimensional form of elasticity3.2.1 Weak form of equilibrium equation; 3.2.1.1 Adjoint forms; 3.3 Approximation to integral and weak forms: The weighted residual (Galerkin) method; 3.3.1 Galerkin solution of elasticity equation; 3.4 Finite element solution; 3.4.1 Requirements for finite element approximations; 3.5 Isoparametric form; 3.5.1 Higher order elements: Lagrange interpolation; 3.5.1.1 Linear shape functions; 3.5.1.2 Quadratic shape functions; 3.5.2 Integrals on the parent element: Numerical integration; 3.6 Hierarchical interpolation; 3.7 Axisymmetric one-dimensional problem 3.7.1 Weak form for axisymmetric problem3.7.2 A variational notation; 3.7.3 Irreducible form for axisymmetric problem; 3.7.4 Finite element solution; 3.8 Transient problems; 3.8.1 Discrete time methods; 3.8.1.1 Stability and dissipation; 3.8.2 Semi-discretization of the problem; 3.8.2.1 Stability of modes; 3.9 Weak form for one-dimensional quasi-harmonic equation; 3.9.1 Weak form; 3.9.2 Finite element solution of quasi-harmonic problem; 3.9.3 Transient problems; 3.9.3.1 Stability; 3.10 Concluding remarks; 3.11 Problems; References 4 Variational Forms and Finite Element Approximation: 1-D Problems |
| Record Nr. | UNINA-9910452742803321 |
|
Zienkiewicz O. C
|
||
| Oxford, UK : , : Butterworth-Heinemann, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 | ||
| ||