A Finite Element Primer for Beginners The Basics
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model
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Tarek I. Zohdi
A Finite Element Primer for Beginners The Basics 123
SpringerBriefs in Applied Sciences and Technology
More information about this series at http://www.springer.com/series/8884
Tarek I. Zohdi
A Finite Element Primer for Beginners The Basics
123
Tarek I. Zohdi University of California Berkeley, CA USA
ISSN 2191-530X ISBN 978-3-319-09035-1 DOI 10.1007/978-3-319-09036-8
ISSN 2191-5318 (electronic) ISBN 978-3-319-09036-8 (eBook)
Library of Congress Control Number: 2014946399 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The purpose of this primer is to provide the reader with the basics of the Finite Element Method (FEM), primarily illustrated through a classical model problem, linearized elasticity. The topics covered are: • • • • • • • • • • • • • •
Weighted residual methods and Galerkin approximations; A model problem for one-dimensional linear elastostatics; Weak formulations in one dimension; Minimum principles in one dimension; Error estimation in one dimension; Construction of Finite Element basis functions in one dimension; Gaussian quadrature; Iterative solvers and element-by-element data structures; A model problem for three-dimensional linear ela
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