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A Unified Approach to the Finite Element Method and Error Analysis Procedures,

Edition 1

Editors: By Julian A. T. Dow

Publication Date: 02 Nov 1998

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A Unified Approach to the Finite Element Method and Error Analysis Procedures 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.

Key Features

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

About the author

By Julian A. T. Dow, University of Colorado, Boulder, U.S.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.

ISBN: 9780122214400

Page Count: 533

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