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

1st Edition

Authors: Julian Dow
Hardcover ISBN: 9780122214400
eBook ISBN: 9780080543420
Imprint: Academic Press
Published Date: 2nd November 1998
Page Count: 533
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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.

Key Features

@bul:* 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


Students and professional engineers involved in advanced structural mechanics; civil, mechanical, and aeronautical engineers involved in the design of structures that must perform and standup to a wide array of stress.

Table of 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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© Academic Press 1999
Academic Press
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About the Author

Julian Dow

John O. Dow is an Associate Professor at the University of Colorado at Boulder in the Department of Civil, Environmental and Architectural Engineering. He is a specialist in structural mechanics with extensive industrial experience in automotive engineering, aerospace engineering, and civil engineering applications. Professor Dow is an active consultant in the industry of structural mechanics. His graduate students are employed as structural software engineers, bridge designers, offshore structures designers, and aerospace designers and analysts.

Affiliations and Expertise

University of Colorado, Boulder, U.S.A.


Serves as a supplemental text for an undergraduate and a primary textbook for a graduate course, and as a reference for practicing engineers and researchers in computational mechanics. Dow (structural mechanics, U. of Colorado-Boulder) provides background material about finite element results and techniques that can improve their accuracy. From a common theoretical foundation, he develops three error analysis techniques: modeling errors in individual elements, discretization errors in the overall model, and point-wise errors in the final stress or strain results. -- Copyright © 1999 Book News, Inc., Portland, OR All rights reserved