A unified approach to the finite element method and error analysis procedures /:
This book provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are sys...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
San Diego :
Academic Press,
©1999.
|
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | This book provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. * New, simpler element formulation techniques, model-independent results, and error measures * New polynomial-based methods for identifying critical points * New procedures for evaluating sheer/strain accuracy * Accessible to undergraduates, insightful to researchers, and useful to practitioners * Taylor series (polynomial) based * Intuitive elemental and point-wise error measures * Essential background information provided in 12 appendices. |
| Beschreibung: | 1 online resource (xxiv, 533 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9780122214400 0122214404 9780080543420 0080543421 1281046426 9781281046420 9786611046422 6611046429 |
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| 520 | |a This book provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. * New, simpler element formulation techniques, model-independent results, and error measures * New polynomial-based methods for identifying critical points * New procedures for evaluating sheer/strain accuracy * Accessible to undergraduates, insightful to researchers, and useful to practitioners * Taylor series (polynomial) based * Intuitive elemental and point-wise error measures * Essential background information provided in 12 appendices. | ||
| 505 | 0 | |a General Introduction. Problem Definition and Development: Introduction. Principle of Minimum Potential Energy. Elements of the Calculus of Variations. Derivation of the Plane Stress Problem. Rayleigh-Ritz Variational Solution Technique. Physically Interpretable Displacement Polynomials: Strain Gradient Notation: Introduction. Strain Gradient Notation. Strain Gradient Representation of Discrete Structures. Strain Transformations. A-Priori Error Analysis Procedures: Introduction. The Development of Strain Gradient Based Finite Elements. Four Node Quadrilateral Element. Six Node Linear Strain Element. Eight and Nine Node Elements. Shear Locking and Aspect Ratio Stiffening. The Strain Gradient Reformation of the Finite Differences Method: Introduction. Elements of the Finite Difference Method. Finite Difference Boundary Condition Models. Extensions to the Finite Difference Method. A-Posteriori Error Analysis Procedures: Introduction. The Zienkiewicz/Zhu Error Estimation Procedure. Error Estimation Based on Finite Difference Smoothing. Point-Wise Error Estimates. Super-Convergence of the Augmented Finite Element Results. Adaptive Refinement of Finite Difference Models. Subject Index. | |
| 504 | |a Includes bibliographical references and index. | ||
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| contents | General Introduction. Problem Definition and Development: Introduction. Principle of Minimum Potential Energy. Elements of the Calculus of Variations. Derivation of the Plane Stress Problem. Rayleigh-Ritz Variational Solution Technique. Physically Interpretable Displacement Polynomials: Strain Gradient Notation: Introduction. Strain Gradient Notation. Strain Gradient Representation of Discrete Structures. Strain Transformations. A-Priori Error Analysis Procedures: Introduction. The Development of Strain Gradient Based Finite Elements. Four Node Quadrilateral Element. Six Node Linear Strain Element. Eight and Nine Node Elements. Shear Locking and Aspect Ratio Stiffening. The Strain Gradient Reformation of the Finite Differences Method: Introduction. Elements of the Finite Difference Method. Finite Difference Boundary Condition Models. Extensions to the Finite Difference Method. A-Posteriori Error Analysis Procedures: Introduction. The Zienkiewicz/Zhu Error Estimation Procedure. Error Estimation Based on Finite Difference Smoothing. Point-Wise Error Estimates. Super-Convergence of the Augmented Finite Element Results. Adaptive Refinement of Finite Difference Models. Subject Index. |
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| indexdate | 2024-11-27T13:16:06Z |
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| publisher | Academic Press, |
| record_format | marc |
| spelling | Dow, John O., 1941- https://id.oclc.org/worldcat/entity/E39PCjGTjqJPG8gMpwwy3fc7H3 http://id.loc.gov/authorities/names/n98067079 A unified approach to the finite element method and error analysis procedures / John O. Dow. Finite element method and error analysis procedures San Diego : Academic Press, ©1999. 1 online resource (xxiv, 533 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier text file rdaft http://rdaregistry.info/termList/fileType/1002. This book provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. * New, simpler element formulation techniques, model-independent results, and error measures * New polynomial-based methods for identifying critical points * New procedures for evaluating sheer/strain accuracy * Accessible to undergraduates, insightful to researchers, and useful to practitioners * Taylor series (polynomial) based * Intuitive elemental and point-wise error measures * Essential background information provided in 12 appendices. General Introduction. Problem Definition and Development: Introduction. Principle of Minimum Potential Energy. Elements of the Calculus of Variations. Derivation of the Plane Stress Problem. Rayleigh-Ritz Variational Solution Technique. Physically Interpretable Displacement Polynomials: Strain Gradient Notation: Introduction. Strain Gradient Notation. Strain Gradient Representation of Discrete Structures. Strain Transformations. A-Priori Error Analysis Procedures: Introduction. The Development of Strain Gradient Based Finite Elements. Four Node Quadrilateral Element. Six Node Linear Strain Element. Eight and Nine Node Elements. Shear Locking and Aspect Ratio Stiffening. The Strain Gradient Reformation of the Finite Differences Method: Introduction. Elements of the Finite Difference Method. Finite Difference Boundary Condition Models. Extensions to the Finite Difference Method. A-Posteriori Error Analysis Procedures: Introduction. The Zienkiewicz/Zhu Error Estimation Procedure. Error Estimation Based on Finite Difference Smoothing. Point-Wise Error Estimates. Super-Convergence of the Augmented Finite Element Results. Adaptive Refinement of Finite Difference Models. Subject Index. Includes bibliographical references and index. Print version record. English. Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Error analysis (Mathematics) http://id.loc.gov/authorities/subjects/sh85044724 Méthode des éléments finis. Théorie des erreurs. TECHNOLOGY & ENGINEERING Engineering (General) bisacsh TECHNOLOGY & ENGINEERING Reference. bisacsh Error analysis (Mathematics) fast Finite element method fast Print version: Dow, John O., 1941- Unified approach to the finite element method and error analysis procedures. San Diego : Academic Press, ©1999 0122214404 9780122214400 (DLC) 98022147 (OCoLC)39627440 FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/book/9780122214400 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=207386 Volltext |
| spellingShingle | Dow, John O., 1941- A unified approach to the finite element method and error analysis procedures / General Introduction. Problem Definition and Development: Introduction. Principle of Minimum Potential Energy. Elements of the Calculus of Variations. Derivation of the Plane Stress Problem. Rayleigh-Ritz Variational Solution Technique. Physically Interpretable Displacement Polynomials: Strain Gradient Notation: Introduction. Strain Gradient Notation. Strain Gradient Representation of Discrete Structures. Strain Transformations. A-Priori Error Analysis Procedures: Introduction. The Development of Strain Gradient Based Finite Elements. Four Node Quadrilateral Element. Six Node Linear Strain Element. Eight and Nine Node Elements. Shear Locking and Aspect Ratio Stiffening. The Strain Gradient Reformation of the Finite Differences Method: Introduction. Elements of the Finite Difference Method. Finite Difference Boundary Condition Models. Extensions to the Finite Difference Method. A-Posteriori Error Analysis Procedures: Introduction. The Zienkiewicz/Zhu Error Estimation Procedure. Error Estimation Based on Finite Difference Smoothing. Point-Wise Error Estimates. Super-Convergence of the Augmented Finite Element Results. Adaptive Refinement of Finite Difference Models. Subject Index. Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Error analysis (Mathematics) http://id.loc.gov/authorities/subjects/sh85044724 Méthode des éléments finis. Théorie des erreurs. TECHNOLOGY & ENGINEERING Engineering (General) bisacsh TECHNOLOGY & ENGINEERING Reference. bisacsh Error analysis (Mathematics) fast Finite element method fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048349 http://id.loc.gov/authorities/subjects/sh85044724 |
| title | A unified approach to the finite element method and error analysis procedures / |
| title_alt | Finite element method and error analysis procedures |
| title_auth | A unified approach to the finite element method and error analysis procedures / |
| title_exact_search | A unified approach to the finite element method and error analysis procedures / |
| title_full | A unified approach to the finite element method and error analysis procedures / John O. Dow. |
| title_fullStr | A unified approach to the finite element method and error analysis procedures / John O. Dow. |
| title_full_unstemmed | A unified approach to the finite element method and error analysis procedures / John O. Dow. |
| title_short | A unified approach to the finite element method and error analysis procedures / |
| title_sort | unified approach to the finite element method and error analysis procedures |
| topic | Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Error analysis (Mathematics) http://id.loc.gov/authorities/subjects/sh85044724 Méthode des éléments finis. Théorie des erreurs. TECHNOLOGY & ENGINEERING Engineering (General) bisacsh TECHNOLOGY & ENGINEERING Reference. bisacsh Error analysis (Mathematics) fast Finite element method fast |
| topic_facet | Finite element method. Error analysis (Mathematics) Méthode des éléments finis. Théorie des erreurs. TECHNOLOGY & ENGINEERING Engineering (General) TECHNOLOGY & ENGINEERING Reference. Finite element method |
| url | https://www.sciencedirect.com/science/book/9780122214400 https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=207386 |
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