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

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 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.

Audience
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.

Hardbound, 533 Pages

Published: November 1998

Imprint: Academic Press

ISBN: 978-0-12-221440-0

Reviews

  • 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

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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