Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods PDF
Preview Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods
Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods Civil and Environmental Engineering A Series of Reference Books and Textbooks Editor Michael D. Meyer Department of Gvil and Environmental Engineering Georgia Institute of Technology Atlanta, Georgia 1. Preliminary Design of Bridges for Architects and Engineers Michele Melaragno 2. Concrete Formwork Systems Awad S. Hanna 3. Multilayered Aquifer Systems: Fundamentals and Applica- tions Alexander H.-D. Cheng 4. Matrix Analysis of Structural Dynamics: Applications and Earthquake Engineering Franklin Y. Cheng 5. Hazardous Gases Underground: Applications to Tunnel Engineering Barry R. Doyle 6. Cold-Formed Steel Structures to the AISI Specification Gregory J. Hancock, TJiomas M. Murray, Duane S. Ellifritt 1. Fundamentals of Infrastructure Engineering: Civil Engi- neering Systems: Second Edition, Revised and Expanded Patrick H. McDonald 8. Handbook of Pollution Control and Waste Minimization edited by Abbas Ghassemi 9. Introduction to Approximate Solution Techniques, Numer- ical Modeling, and Finite Element Methods Victor N. Kaliakin Additional Volumes in Production Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods Victor N. Kaliakin University of Delaware Newark, Delaware MARCEL DEKKER, INC. NEW YORK • BASEL 0 E K K E R lSB(\:0-8247-0679-X This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AC Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more infor- mation, write to Special Sales/Professional Marketing at the headquarters address above. Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 21 PRINTED IN THE UNITED STATES OF AMERICA Publisher’s Note The publisher has gone to great lengths to ensure the quality of this book but points out that some imperfections from the original may be apparent. To Leeza, Yanni, Dimitri & Maria Preface This book has evolved from notes compiled while teaching the senior/first- year graduate level course CIEG 401/601 (Introduction to the Finite El- ement Method) offered at the University of Delaware. The goals of this course are to: (1) Introduce students to the general subject of approximate solutions; (2) Introduce and emphasize the finite element method; (3) Help students understand the strengths and limitations of various approximation solution techniques; and (4) Develop in the students the ability to assess the correctness of approximate solutions. Quite often in the past, introductory finite element texts were written on the assumption that students possessed a background in structural mechan- ics. This is evidenced by the common use of simple bar and beam examples to illustrate the development of element equations. The present reality is, however, that a wider range of students is striving to learn the finite el- ement method. For example, here at the University of Delaware, CIEG 401/601, though populated largely by students from Mechanical and Civil Engineering, is also taken by students from the College of Marine Studies. Water Resources, and Health and Exercise Sciences. Consequently, struc- tural mechanics concepts, though well understood by engineers, represent potential stumbling blocks for students with non-engineering backgrounds. In order to address the changing make-up of the student body enrolled in introductory finite element classes, this book emphasizes fairly generic forms of differential equations. The approximate solution techniques stud- ied are applied to these generic problems; once introduced and "digested," these techniques are then applied to specific physical problems such as heat conduction, elastostatics, flow through porous media, etc. Many of the chapters have been designed to be quite modular. As such. certain sections or chapters can be omitted from a course plan without detrimentally affecting the understanding of material in subsequent chap- ters. A brief overview of the respective chapters is presented at the end of Chapter 1. Victor N.Kaliakin Acknowledgements Very rarely do individuals work successfully in a vacuum. The prepara- tion and refinement of this book over the past ten years have been greatly aided by the comments of students who have taken the introductory course in approximate solution techniques. Their help is thankfully acknowledged. The author is very fortunate to have studied under H L. Taylor (Uni- versity of California, Berkeley) and L. R. Herrmann (University of Califor- nia, Davis). These pioneers in the finite element method have significantly influenced the structure and content of these notes. The author's philosophy towards programming, however peculiar, has been influenced by past collaborations with Dr. K. J. Perano. If one phrase is chosen to host summarize approximate solution tech- niques, it would be: "When considering a specific numerical procedure, you don't get something for nothing." cheers, V.N.K. VI Glossary of Notations and Units Units E : denotes units of energy (e.g., Joules, cal, BTU, ft-lb) F : denotes units of force (e.g., Newtons, dynes, pounds, etc.) L : denotes units of length (e.g., meters, centimeters, inches, etc.) m : denotes units of mass (e.g., kilograms, grams, slugs, etc.) Q : denotes units of charge (e.g., Coulombs) t : denotes units of time (e.g., seconds, minutes, etc.) T : denotes units of temperature (e.g., degrees Kelvin, Fahrenheit, etc. Sets U : union (.OR.) n : intersection (.AND.) 0 : empty set £ : is member of (a set) £ : is not a member of (a set) C : is subset of (contained in) <£_ : is not a subset of (not contained in) => : implies <=X if and only if V : for all 3 : there exists B : such that Miscellaneous Integers Neddoj = number of element displacement degrees of freedom. -\ n — total number of nodes in an element. N t = total number of points used to describe the element geometry. p Nrowb = number of rows in the strain-displacement matrix B. Nsdim = spatial dimension of the analysis (1, 2 or 3).
Description:The list of books you might like
