Finite Elements A Gentle Introduction
The finite element method is popular among engineers and scientists as a numerical technique for solving practical problems. At the same time, the links with classical variational methods make the technique of interest to mathematicians. This book introdu
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A Gentle Introduction
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Finite Elements A Gentle Introduction David Henwood Department of Mathematics University of Zimbabwe Javier Bonet Department of Civil Engineering University of Wales, Swansea
pal grave macmillan
© David Henwood and Javier Bonet 1996
All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provision of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London WlP 9HE. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The authors have asserted their rights to be identified as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 1996 by MACMILLAN PRESS LTD Houndmills, Basingstoke, Hampshire RG21 6XS and London Companies and representatives throughout the world ISBN 978-333-64626-7 ISBN 978-1-349-13898-2 (eBook) I DO 10.1007/978-1-349-13898-2
A catalogue record for this book is available from the British Library. This book is printed on paper suitable for recycling and made from fully managed and sustained forests sources. Logging, pulping and manufacruring processes are expected to conform to the environmental regulations of the country of origin.
Contents
xi
Preface
1
2
3
Finite elements introduced as bars forming a truss 1.1 Introduction 1.2 Definition of a truss, and the model problem 1.3 Discretisation: nodes, elements and a numbering system 1.4 Global and local coordinates 1.5 Equations representing the mechanics of an element 1.6 Changing from local to global variables 1.7 Local and global variables 1.8 Combining the equations 1.9 Applying the boundary conditions 1.10 Obtaining the solution General exercises for chapter I
1
2 4 5 7 9 12 15 16 17
Some mathematical aspects 2.1 Introduction 2.2 The simple problem 2.3 Mathematical formulations 2.4 Exploring the idea of a functional 2.5 The finite element method revealed 2.5.
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