The finite element method :: its basis and fundamentals /
Annotation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford ; Boston :
Elsevier Butterworth-Heinemann,
2005.
|
| Ausgabe: | 6th ed. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Annotation |
| Beschreibung: | "In the present edition we have decided not to pursue the course of having three contiguous volumes but rather we treat the whole work as an assembly of three separate works, each one capable of being used without the others ... The two further volumes form again separate books ... The first of these is entitled The Finite Element Method in Solid and Structural Mechanics and the second is a text entitled The Finite Element Method in Fluid Dynamics."--Preface |
| Beschreibung: | 1 online resource (xiv, 733 pages, 4 unnumbered pages of plates) : illustrations (some color) |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9780080472775 008047277X |
Internformat
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| 100 | 1 | |a Zienkiewicz, O. C. |0 http://id.loc.gov/authorities/names/n80028072 | |
| 245 | 1 | 4 | |a The finite element method : |b its basis and fundamentals / |c O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. |
| 250 | |a 6th ed. | ||
| 260 | |a Oxford ; |a Boston : |b Elsevier Butterworth-Heinemann, |c 2005. | ||
| 300 | |a 1 online resource (xiv, 733 pages, 4 unnumbered pages of plates) : |b illustrations (some color) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 500 | |a "In the present edition we have decided not to pursue the course of having three contiguous volumes but rather we treat the whole work as an assembly of three separate works, each one capable of being used without the others ... The two further volumes form again separate books ... The first of these is entitled The Finite Element Method in Solid and Structural Mechanics and the second is a text entitled The Finite Element Method in Fluid Dynamics."--Preface | ||
| 504 | |a Includes bibliographical references and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover -- Title page -- Copyright page -- Table of contents -- 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 -- 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 -- 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 -- 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity -- 4.1 Introduction -- 4.2 Standard and hierarchical concepts -- Part 1. 'Standard' shape functions -- Two-dimensional elements -- One-dimensional elements -- Three-dimensional elements -- Part 2. Hierarchical shape functions -- 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 -- 4.17 Global and local finite element approximation -- 4.18 Elimination of internal parameters before assembly -- substructures -- 4.19 Concluding remarks -- 4.20 Problems -- 5. Mapped elements and numerical integration -- 'infinite' and 'singularity elements' -- 5.1 Introduction -- 5.2 Use of 'shape functions' in the establishment of coordinate tran. | |
| 520 | 8 | |a Annotation |b The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.<br /><br />. The classic FEM text, written by the subject's leading authors<br />. Enhancements include more worked examples and exercises, plus a companion website with a solutions manual and downloadable algorithms<br />. With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems<br /><br />Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations.<br /><br />Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics.<br /><br />* The classic introduction to the finite element method, by two of the subject's leading authors<br />* Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text<br />* Enhancements include more worked examples, exercises, plus a companion website with a worked solutions manual for tutors and downloadable algorithms. | |
| 650 | 0 | |a Finite element method. |0 http://id.loc.gov/authorities/subjects/sh85048349 | |
| 650 | 0 | |a Engineering mathematics. |0 http://id.loc.gov/authorities/subjects/sh85043235 | |
| 650 | 0 | |a Engineering mathematics |x Data processing. | |
| 650 | 6 | |a Méthode des éléments finis. | |
| 650 | 6 | |a Mathématiques de l'ingénieur |x Informatique. | |
| 650 | 6 | |a Mathématiques de l'ingénieur. | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Engineering (General) |2 bisacsh | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Reference. |2 bisacsh | |
| 650 | 7 | |a Engineering mathematics |x Data processing |2 fast | |
| 650 | 7 | |a Engineering mathematics |2 fast | |
| 650 | 7 | |a Finite element method |2 fast | |
| 700 | 1 | |a Taylor, Robert L. |q (Robert Leroy), |d 1934- |1 https://id.oclc.org/worldcat/entity/E39PCjyh39hqXDGXvhwgyHyw4q |0 http://id.loc.gov/authorities/names/n94023604 | |
| 700 | 1 | |a Zhu, J. Z. |0 http://id.loc.gov/authorities/names/no2005055265 | |
| 700 | 1 | |a Zienkiewicz, O. C. |t Finite element method in solid and structural mechanics. | |
| 700 | 1 | |a Zienkiewicz, O. C. |t Finite element method in fluid dynamics. | |
| 776 | 0 | 8 | |i Print version: |a Zienkiewicz, O.C. |t Finite element method. |b 6th ed. |d Oxford ; Boston : Elsevier Butterworth-Heinemann, 2005 |z 0750663200 |z 9780750663205 |w (OCoLC)60592819 |
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| contents | Cover -- Title page -- Copyright page -- Table of contents -- 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 -- 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 -- 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 -- 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity -- 4.1 Introduction -- 4.2 Standard and hierarchical concepts -- Part 1. 'Standard' shape functions -- Two-dimensional elements -- One-dimensional elements -- Three-dimensional elements -- Part 2. Hierarchical shape functions -- 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 -- 4.17 Global and local finite element approximation -- 4.18 Elimination of internal parameters before assembly -- substructures -- 4.19 Concluding remarks -- 4.20 Problems -- 5. Mapped elements and numerical integration -- 'infinite' and 'singularity elements' -- 5.1 Introduction -- 5.2 Use of 'shape functions' in the establishment of coordinate tran. |
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| edition | 6th ed. |
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The two further volumes form again separate books ... The first of these is entitled The Finite Element Method in Solid and Structural Mechanics and the second is a text entitled The Finite Element Method in Fluid Dynamics."--Preface</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and indexes.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover -- Title page -- Copyright page -- Table of contents -- 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 -- 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 -- 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 -- 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity -- 4.1 Introduction -- 4.2 Standard and hierarchical concepts -- Part 1. 'Standard' shape functions -- Two-dimensional elements -- One-dimensional elements -- Three-dimensional elements -- Part 2. Hierarchical shape functions -- 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 -- 4.17 Global and local finite element approximation -- 4.18 Elimination of internal parameters before assembly -- substructures -- 4.19 Concluding remarks -- 4.20 Problems -- 5. Mapped elements and numerical integration -- 'infinite' and 'singularity elements' -- 5.1 Introduction -- 5.2 Use of 'shape functions' in the establishment of coordinate tran.</subfield></datafield><datafield tag="520" ind1="8" ind2=" "><subfield code="a">Annotation</subfield><subfield code="b">The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.<br /><br />. The classic FEM text, written by the subject's leading authors<br />. Enhancements include more worked examples and exercises, plus a companion website with a solutions manual and downloadable algorithms<br />. With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems<br /><br />Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations.<br /><br />Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics.<br /><br />* The classic introduction to the finite element method, by two of the subject's leading authors<br />* Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text<br />* Enhancements include more worked examples, exercises, plus a companion website with a worked solutions manual for tutors and downloadable algorithms.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Finite element method.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85048349</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Engineering mathematics.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85043235</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Engineering mathematics</subfield><subfield code="x">Data processing.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Méthode des éléments finis.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Mathématiques de l'ingénieur</subfield><subfield code="x">Informatique.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Mathématiques de l'ingénieur.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">TECHNOLOGY & ENGINEERING</subfield><subfield code="x">Engineering (General)</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">TECHNOLOGY & ENGINEERING</subfield><subfield code="x">Reference.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Engineering mathematics</subfield><subfield code="x">Data processing</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Engineering mathematics</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Finite element method</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Taylor, Robert L.</subfield><subfield code="q">(Robert Leroy),</subfield><subfield code="d">1934-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjyh39hqXDGXvhwgyHyw4q</subfield><subfield code="0">http://id.loc.gov/authorities/names/n94023604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhu, J. 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| id | ZDB-4-EBA-ocn123984678 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:02Z |
| institution | BVB |
| isbn | 9780080472775 008047277X |
| language | English |
| oclc_num | 123984678 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 733 pages, 4 unnumbered pages of plates) : illustrations (some color) |
| psigel | ZDB-4-EBA |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Elsevier Butterworth-Heinemann, |
| record_format | marc |
| spelling | Zienkiewicz, O. C. http://id.loc.gov/authorities/names/n80028072 The finite element method : its basis and fundamentals / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. 6th ed. Oxford ; Boston : Elsevier Butterworth-Heinemann, 2005. 1 online resource (xiv, 733 pages, 4 unnumbered pages of plates) : illustrations (some color) text txt rdacontent computer c rdamedia online resource cr rdacarrier "In the present edition we have decided not to pursue the course of having three contiguous volumes but rather we treat the whole work as an assembly of three separate works, each one capable of being used without the others ... The two further volumes form again separate books ... The first of these is entitled The Finite Element Method in Solid and Structural Mechanics and the second is a text entitled The Finite Element Method in Fluid Dynamics."--Preface Includes bibliographical references and indexes. Print version record. Cover -- Title page -- Copyright page -- Table of contents -- 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 -- 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 -- 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 -- 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity -- 4.1 Introduction -- 4.2 Standard and hierarchical concepts -- Part 1. 'Standard' shape functions -- Two-dimensional elements -- One-dimensional elements -- Three-dimensional elements -- Part 2. Hierarchical shape functions -- 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 -- 4.17 Global and local finite element approximation -- 4.18 Elimination of internal parameters before assembly -- substructures -- 4.19 Concluding remarks -- 4.20 Problems -- 5. Mapped elements and numerical integration -- 'infinite' and 'singularity elements' -- 5.1 Introduction -- 5.2 Use of 'shape functions' in the establishment of coordinate tran. Annotation The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.<br /><br />. The classic FEM text, written by the subject's leading authors<br />. Enhancements include more worked examples and exercises, plus a companion website with a solutions manual and downloadable algorithms<br />. With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems<br /><br />Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations.<br /><br />Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics.<br /><br />* The classic introduction to the finite element method, by two of the subject's leading authors<br />* Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text<br />* Enhancements include more worked examples, exercises, plus a companion website with a worked solutions manual for tutors and downloadable algorithms. Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Engineering mathematics. http://id.loc.gov/authorities/subjects/sh85043235 Engineering mathematics Data processing. Méthode des éléments finis. Mathématiques de l'ingénieur Informatique. Mathématiques de l'ingénieur. TECHNOLOGY & ENGINEERING Engineering (General) bisacsh TECHNOLOGY & ENGINEERING Reference. bisacsh Engineering mathematics Data processing fast Engineering mathematics fast Finite element method fast Taylor, Robert L. (Robert Leroy), 1934- https://id.oclc.org/worldcat/entity/E39PCjyh39hqXDGXvhwgyHyw4q http://id.loc.gov/authorities/names/n94023604 Zhu, J. Z. http://id.loc.gov/authorities/names/no2005055265 Zienkiewicz, O. C. Finite element method in solid and structural mechanics. Zienkiewicz, O. C. Finite element method in fluid dynamics. Print version: Zienkiewicz, O.C. Finite element method. 6th ed. Oxford ; Boston : Elsevier Butterworth-Heinemann, 2005 0750663200 9780750663205 (OCoLC)60592819 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=189602 Volltext |
| spellingShingle | Zienkiewicz, O. C. The finite element method : its basis and fundamentals / Cover -- Title page -- Copyright page -- Table of contents -- 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 -- 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 -- 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 -- 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity -- 4.1 Introduction -- 4.2 Standard and hierarchical concepts -- Part 1. 'Standard' shape functions -- Two-dimensional elements -- One-dimensional elements -- Three-dimensional elements -- Part 2. Hierarchical shape functions -- 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 -- 4.17 Global and local finite element approximation -- 4.18 Elimination of internal parameters before assembly -- substructures -- 4.19 Concluding remarks -- 4.20 Problems -- 5. Mapped elements and numerical integration -- 'infinite' and 'singularity elements' -- 5.1 Introduction -- 5.2 Use of 'shape functions' in the establishment of coordinate tran. Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Engineering mathematics. http://id.loc.gov/authorities/subjects/sh85043235 Engineering mathematics Data processing. Méthode des éléments finis. Mathématiques de l'ingénieur Informatique. Mathématiques de l'ingénieur. TECHNOLOGY & ENGINEERING Engineering (General) bisacsh TECHNOLOGY & ENGINEERING Reference. bisacsh Engineering mathematics Data processing fast Engineering mathematics fast Finite element method fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048349 http://id.loc.gov/authorities/subjects/sh85043235 |
| title | The finite element method : its basis and fundamentals / |
| title_alt | Finite element method in solid and structural mechanics. Finite element method in fluid dynamics. |
| title_auth | The finite element method : its basis and fundamentals / |
| title_exact_search | The finite element method : its basis and fundamentals / |
| title_full | The finite element method : its basis and fundamentals / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. |
| title_fullStr | The finite element method : its basis and fundamentals / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. |
| title_full_unstemmed | The finite element method : its basis and fundamentals / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. |
| title_short | The finite element method : |
| title_sort | finite element method its basis and fundamentals |
| title_sub | its basis and fundamentals / |
| topic | Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Engineering mathematics. http://id.loc.gov/authorities/subjects/sh85043235 Engineering mathematics Data processing. Méthode des éléments finis. Mathématiques de l'ingénieur Informatique. Mathématiques de l'ingénieur. TECHNOLOGY & ENGINEERING Engineering (General) bisacsh TECHNOLOGY & ENGINEERING Reference. bisacsh Engineering mathematics Data processing fast Engineering mathematics fast Finite element method fast |
| topic_facet | Finite element method. Engineering mathematics. Engineering mathematics Data processing. Méthode des éléments finis. Mathématiques de l'ingénieur Informatique. Mathématiques de l'ingénieur. TECHNOLOGY & ENGINEERING Engineering (General) TECHNOLOGY & ENGINEERING Reference. Engineering mathematics Data processing Engineering mathematics Finite element method |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=189602 |
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