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THE MATHEMATICS OF FINITE ELEMENTS AND APPLICATIONS Proceedings of the Brunei University conference of the Institute of Mathematics and Its Applications held in April 1972 Edited by J. R. WHITEMAN Department of Mathematics Brunei University Oxbridge, Middlesex, England 1973 @ ACADEMIC PRESS · LONDON AND NEW YORK A subsidiary of Harcourt Brace Jooanovich, publishers ACADEMIC PRESS INC. (LONDON) LTD. 24/28 Oval Road London NW1 United States Edition published by ACADEMIC PRESS INC. Ill Fifth Avenue New York, New York 10003 Copyright © 1973 by The Institute of Mathematics and Its Applications All Rights Reserved No part of this book may be reproduced in any form by photostat, microfilm, or any other means, without written permission from the publishers Library of Congress Catalog Card Number: 72-7713 ISBN: 0-12-747250-9 PRINTED IN GREAT BRITAIN BY ROYSTAN PRINTERS LIMITED Spencer Court, 7 Chalcot Road London NW1 Contributors J. E. AKIN; Department of Engineering Mechanics, Tennessee, Knoxville, Tennessee 37916, U.S.A. University of A. ALUJEVIC; Nuclear Power Section, Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London, S.W.7, England. A. J. BARNARD; Department of Transport Technology, Loughborough University of Technology, Loughborough, Leicestershire LEU 3 TU, England. R. E. BARNHILL; Department of Mathematics, Universtiy of Utah, Salt Lake City, Utah 84112, U.S.A. W. S. BLACKBURN; International Research and Development Co., Fossway, Newcastle Upon Tyne 6, England. G. B. BOLLAND; Department of Mechanical Engineering, Lanchester Polytechnic, Priory Street, Coventry CV1 5FB, England. J. C. BRUCH; Department of Mechanical Engineering, University of California, Santa Barbara, California 93106. U.S.A. I. G. CAMERON; United Kingdom Atomic Energy Authority, Atomic Weapons Research Establishment, Aldermaston, Reading RG7 4PR, England. W. C. CARPENTER; Department of Engineering Science, University of Durham, Durham, England. P. G. CIARLET; Laboratoire Central des Ponts et Chaussées, 58, Boulevard Lefebvre, 75 Paris 15, France. Z. CSENDES; Department of Electrical Engineering, McGill University, P.O. Box 6070, Montreal 101, Quebec, Canada. P. DALY; Department of Electrical and Electronic Engineering, University of Leeds, Leeds LS2 9JT, England. D. J. EVANS; Department of Mathematics, Loughborough University of Technology, Loughborough, Leicestershire LEU 3 TU, England. C. C. FLEISCHER; Institute of Sound and Vibration Research, University of Southampton, Southampton S09 5NH, England. v VI CONTRIBUTORS P. W. FRANCE; Department of Civil Engineering, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, Wales. M. FREMOND; Laboratoire Central des Ponts et Chaussées, 58, Boulevard Lefebvre, 75 Paris 15, France. I. FRIED; Department of Mathematics, Boston University, Boston, Massachusetts 02215, U.S.A. P. A. T. GILL; Department of Engineering Science, University of Durham, Durham, England. A. GOPINATH; Department of Electronics, University College of North Wales, Bangor, Wales. 3. L. HEAD; Nuclear Power Section, Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London, S.W.7., England. U.HEISE; Lehrstuhl für Technische Mechanik, Technische Hochschule Aachen, 51 Aachen, Templergraben 55, West Germany. R. D. HENSHELL; Department of Mechanical Engineering, University of Nottingham, Nottingham NG7 2RD, England. V. HOPPE; Burmeister and Wain's Motor-og Maskinfabrik, Torvegade 2, DK 1449y Copenhagen K, Denmark. A. JEZERNIK; Central Electricity Generating Board, Computing Bureau, 85, Park Street, London, S.E.I., England. A. V. KRISHNA MURTY; Department of Aeronautical Engineering, Indian Institute of Science, Bangalore 1