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A unified approach to the finite element method and error analysis procedures

紀錄類型:	書目-電子資源 : 單行本
正題名/作者:	A unified approach to the finite element method and error analysis procedures/ John O. Dow.
其他題名:	Finite element method and error analysis procedures
作者:	Dow, John O.,
出版者:	San Diego :Academic Press, : c1999.,
面頁冊數:	xxiv, 533 p. :ill. ; : 26 cm.;
標題:	Finite element method. -
電子資源:	An electronic book accessible through the World Wide Web; click for information
ISBN:	9780122214400

A unified approach to the finite element method and error analysis procedures
Dow, John O.,1941-

A unified approach to the finite element method and error analysis procedures[electronic resource] /Finite element method and error analysis proceduresJohn O. Dow. - San Diego :Academic Press,c1999. - xxiv, 533 p. :ill. ;26 cm.

Includes bibliographical references and index.

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.

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.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780122214400

Source: 80514:80514Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

122483
Finite element method.
Index Terms--Genre/Form:

96803
Electronic books.

LC Class. No.: TA347.F5 / D69 1999eb

Dewey Class. No.: 620/.001/51535

A unified approach to the finite element method and error analysis procedures
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245 1 2 $a A unified approach to the finite element method and error analysis procedures $h [electronic resource] / $c John O. Dow.
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300 $a xxiv, 533 p. : $b ill. ; $c 26 cm.
504 $a Includes bibliographical references and index.
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.
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.
533 $a Electronic reproduction. $b Amsterdam : $c Elsevier Science & Technology, $d 2007. $n Mode of access: World Wide Web. $n System requirements: Web browser. $n Title from title screen (viewed on Aug. 2, 2007). $n Access may be restricted to users at subscribing institutions.
650 0 $a Finite element method. $3 122483
650 0 $a Error analysis (Mathematics) $3 134363
655 7 $a Electronic books. $2 local. $3 96803
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856 4 1 $3 Table of contents $u http://www.loc.gov/catdir/toc/els032/98022147.html
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