Variational Methods in the Mechanics of Solids. Proceedings of the IUTAM Symposium on Variational Methods in the Mechanics of Solids Held at Northwestern University, Evanston, Illinois, U.S.A., 11–13 September 1978 PDF
Preview Variational Methods in the Mechanics of Solids. Proceedings of the IUTAM Symposium on Variational Methods in the Mechanics of Solids Held at Northwestern University, Evanston, Illinois, U.S.A., 11–13 September 1978
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NEMAT-NASSER Sponsored by International Union of Theoretical and Applied Mechanics Solid Mechanics Division of the National Science Foundation U. S. Army Research Office PERGAMON PRESS OXFORD · NEW YORK ■ TORONTO ■ SYDNEY · PARIS · FRANKFURT U.K. Pergamon Press Ltd., Headington Hill Hall, Oxford 0X3 OBW, England U.S.A. Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523, U.S.A. CANADA Pergamon of Canada, Suite 104, 150 Consumers Road, Willowdale, Ontario M2J 1P9, Canada AUSTRALIA Pergamon Press (Aust.) Pty. Ltd., P.O. Box 544, Potts Point, N.S.W. 2011, Australia FRANCE Pergamon Press SARL, 24 rue des Ecoles, 75240 Paris, Cedex 05, France FEDERAL REPUBLIC Pergamon Press GmbH, 6242 Kronberg-Taunus, OF GERMANY Hammerweg 6, Federal Republic of Germany Copyright © 1980 Pergamon Press Ltd. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. First edition 1980 British Library Cataloguing in Publication Data IUTAM Symposium on Variational Methods in the Mechanics of Solids, Illinois, 1978 Variational methods in the mechanics of solids. 1. Mechanics, Analytic - Congresses 2. Calculus of variations - Congresses I. Title II. Nemat-Nasser, Siavouche 531 QA801 80-41529 ISBN 0-08-024728-8 In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method has its typographical limitations but it is hoped that they in no way distract the reader. Printed and bound in Great Britain by William Clowes (Beccles) Limited, Becc/es and London PREFACE Considerable technical activities and progress in the application of variational methods to a variety of mathematically and technically significant problems in solid mechanics have resulted in a huge body of literature in recent years. In an effort to coordinate and bring together diverse applications of variational principles, an international symposium on the subject was held at Northwestern University during September 11-13, 1978, under the sponsorship of the International Union of Theoretical and Applied Mechanics, with the financial support of the Solid Mechanics Division of the National Science Foundation and the U.S. Army Research Office. The objectives of the Symposium on Variational Methods in the Mechanics of Solids were to address with equal emphasis the following three basic areas: a) Characterization of global parameters defining thermomechanical behavior of composites. b) Development of effective computational schemes for the calculation of elastic and inelastic boundary-value problems. c) Development of effective computational schemes for solutions of elastic and inelastic dynamic problems. These areas were extensively examined, covering both small and finite deformation problems, by the participation and contributions of 120 active researchers from 22 countries (Australia, Austria, Belgium, Bulgaria, Canada, Czechoslovakia, Denmark, France, German Federal Republic, Iran, Italy, Japan, Mexico, Netherlands, Norway, Poland, Saudi Arabia, South Africa, Sweden, Switzerland, United Kingdom, and United States of America). The scientific program included three General Lectures and twelve Sessions. The general lec- turers were J. L. Lions (France) who spoke on "Remarks on Some Asymptotic Problems in Composite and in Perforated Materials," G. Strang (United States of America) who spoke on "Mathematical and Computational Methods in Plasticity," and M. A. Biot (Belgium) who addressed "New Varia- tional Irreversible Thermodynamics of-Open Physical-Chemical Continua." The scientific program, the list of participants, and all the scientific contributions are con- tained in this Proceedings, Included here are summaries by chairpersons of various sessions, which bring into focus significant points covered by various participants. The editorial assistance provided by several chairpersons is gratefully acknowledged. The scientific committee appointed by the Bureau of the International Union of Theoretical and Applied Mechanics consisted of: S. Nemat-Nasser Northwestern University (USA) Co-Chairman and Local Coordinator K. Washizu University of Tokyo (Japan) Co-Chairman G. Duvaut Universite Pierre et Marie Curie (France) W. Prager Savognin, Switzerland L. I. Sedov USSR Academy of Sciences (USSR) The local arrangements were made through the efforts of Barbara Fabian, Erika Ivansons, Use Dundurs, and James F. Dorris. It is with pleasure that their superb work is being gratefully acknowledged. Thanks are also due Dr. Clifford J. Astill and Dr. Edward A. Saibel for their ceaseless encouragement and support. The manuscript of these Proceedings was typed by Cathy Schonberg; Barbara Fabian, Katherine Condit and Michaela Condit helped in various editorial tasks. S. Nemat-Nasser K. Washizu SCIENTIFIC PROGRAM Monday, September 11 Opening Session Chairman: K. Washizu J. L. Lions: "Remarks on Some Asymptotic Problems in Composite and in Perforated Materials" (General Lecture). Session A: Composites; Eigenvalue Problems Chairman: G. M. L. Gladwell F. Lene: "Macroscopic Behavior of Elastic Material with Periodically Spaced Rigid Inclusions." C. O. Horgan and S. Nemat-Nasser: "Variational Methods for Eigenvalue Problems in Composites." J. R. Willis: "Relationships Between Derivations of the Overall Properties of Composites by Perturbation Expansions and Variational Principles." Short Presentations: M. Geradin; R. E. Nickell. Discussions. Session B: General Methods Chairman: P. G. Bergan I. Herrera: "Theory of Connectivity. A Unified Approach to Boundary Methods." Short Presentations: E. J. Haug; H. Stolarski; M. K. Duszek. Discussions. Session C: Elasticity Chairman: W. Wunderlich S. Nair: "Bounds for the Shear Center Coordinates of Prismatic Beams." P. M. Pinsky, R. L. Taylor, and K. S. Pister: "Finite Deformation of Elastic Beams." H. Stumpf: "Generalization of the Hypercircle Method and Pointwise Error Bounds in Nonlinear Elasticity." G. Wempner: "Complementary Theorems of Solid Mechanics." Short Presentations: M. Como and A. Grimaldi; B. Tabarrok. Discussions. xiii xiv Scientific Program Session D: General Principles Chairman: B. Storakers G. Herrmann: "Some Applications of Invariant Variational Principles in Mechanics of Solids." H. H. E. Leipholz: "On Variational Principles for Non-Conservative Mechanical Systems with Follower Forces." M. Inokuti, H. Sekine, and T. Mura: "General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics." M. J. Sewell: "Complementary Energy and Catastrophes." Short Presentations: D. Karamanlidis, K. Knothe, and O. Tsuzuki; L. H. N. Lee; K. Washizu Discussions. Tuesday, September 12 Chairman: E. Reissner G. Strang, H. Matthies, and R. Temam: "Mathematical and Computational Methods in Plasticity" (General Lecture). Session E: Finite Elements Chairman: T. H. H. Pian T. Kawai: "A New Discrete Element and Its Variational Formulation." E. Haugeneder and H. A. Mang: "Admissible and Inadmissible Simplifications of Variational Methods in Finite Element Analysis." K.-D. Klee and E. Stein: "Incremental Finite Element Methods for Geometrically Nonlinear Elasto-Visco-Plastic Solids." Short Presentations: S. Athel and M. S. El Naschie; Nguyen Dang Hung; Y. Yamamoto and H. Ohtsubo. Discussions. Session F: Homogenization; Computational Methods Chairman: L. Tartar H. Lanchon, D. Cioranescu, and J. Saint Jean Paulin: "Elastic-Plastic Torsion of Heterogeneous Cylindrical Bars." M. Artola and G. Duvaut: "Homogenization Results for a Class of Nonlinear Stationary Diffusion Problems." Short Presentation: J. F. Besseling. Discussions. Session G: Fracture, Contact, and Variational Inequalities Chairman: E. A. Saibel C. Do: "On the Dynamic Deformation of a Bar Against an Obstacle." Scientific Program xv J. J. Kalken "Numerical Contact Elastostatics." S. Nemat-Nasser: "Variational Methods for Analysis of Stability of Interacting Cracks." Nguyen Quoc Son: "Normal Dissipativity and Energy Criteria in Fracture." J. T. Oden and N. Kikuchi: "Use of Variational Methods for the Analysis of Contact Problems in Solid Mechanics." Short Presentations: L. Ascione and A. Grimaldi; J. R. Turner. Discussions. Session H: Plasticity I Chairman: J. Chandra B. Halphen: "Periodic Solutions in Plasticity and Viscoplasticity." J. B. Martin: "Variational Methods for Problems in Rigid-Plastic Structural Dynamics." C. Johnson, B. Mercier, and J. C. Nedelec: "Convergence to a Periodic Solution in Elastic Perfectly Plastic Structures." S. Minagawa: "A Geometrical Facet of the Theory of Dislocations and Disclinations in a Cosserat Continuum." B. J. P. Nayroles: "Minimum Theorems Concerning Cauchy and Periodic Problems for Maxwell Body." P.-M. Suquet: "Existence and Regularity of Solutions for Plasticity Problems." Wednesday, September 13 Chairman: B. Noble M. A. Biot: "New Variational Irreversible Thermodynamics of Open Physical-Chemical Continua" (General Lecture). Session I: Viscoelasticity Chairman: J. L. Sackman J. Brilla: "Variational Principles and Methods for Viscoelastic Plates and Shells." M. E. Gurtin and L. F. Murphy: "Optimal Strain Paths in Linear Viscoelasticity: The Effect of the Past History." M. M. Kozarov and P. T. Kolev: "Variational Methods in Creep Buckling of a Circular Cylindrical Shell with Varying Wall Thickness." Discussions. Session J: Optimization; Plasticity Chairman: N. Olhoff E. F. Masur and Z. Mroz: "Singular Solutions in Structural Optimization Problems." Short Presentations: O. Debordes; R. M. McMeeking; J. E. Taylor; R. Temam. Discussions. xvi Scientific Program Session K: Plasticity II Chairman: E. H. Lee S. N. Atluri: "Rate Complementary Energy Principles; Finite Strain Plasticity Problems; and Finite Elements." J. Christof fersen: "A Simple Convex Stress Rate-Strain Rate Relation in Plasticity Not Relying on the Yield Surface Concept." K. W. Neale: 'On the Application of a Variational Principle for Large-Displacement Elastic-Plastic Problems." Discussions. Session L: Flow, Viscoelasticity, and Plasticity Chairman: H. Bufler B. Bernstein and D. S. Malkus: "A Variational Principle for Visco-Elastic Memory Fluids and Its Use in Finite Element Analysis of Steady Flows." T. J. R. Hughes and J. D. Atkinson: "A Variational Basis for 'Upwind' Finite Elements." M. Kleiber: "Variational Formulation in Finite Deformation Elasto-Plasticity with Large Increments and Discontinuous Fields." P. Rafalski: "On Minimum Principles in Plasticity." Discussions. Concluding Session Chairman: S. Nemat-Nasser General Discussions. LIST OF PARTICIPANTS Australia Czechoslovakia HILL, James Murray BRILLA, Jozef Department of Mathematics Institute of Applied Mathematics University of Wollongong and Computing Techniques Wollongong N. S.W. Comenius University Mlynska dolina Austria 816 31 Bratislava HAUGENEDER, Ernst Institut für Festigkeitslehre Denmark TU-Wien CHRISTOFFERSEN, Jes Karlsplatz 13 Department of Solid Mechanics A-1040 Vienna Building 404 The Technical University of Denmark Belgium DK-2800 Lyngby BIOT, Maurice A. Royal Academy of Belgium OLHOFF, Niels Avenue Paul Hymans 117 Department of Solid Mechanics Bte. 34 Building 404 B - 1200 Brussels The Technical University of Denmark DK-2800 Lyngby GERADIN, Michel L.T.A.S. England Institut de Mecanique SEWELL, M. J. Universita de Lüge Department of Mathematics 75, Rue du Val Benoit The University of Reading B - 4000 Liege Whiteknights Park Reading, Berks. NGUYEN DANG HUNG Laboratoire de Macanique des Materiaux TURNER, J. Rodney et de Statique des Constructions Department of Engineering Science Institut du Genie Civil University of Oxford Universita de Liege Parks Road 6, Quai Banning Oxford, OX1 3PJ B - 4000 Liege WILLIS, J. R. Bulgaria School of Mathematics KOZAROV, Marin M. University of Bath Technical Institute of Civil Engineering Claverton Down Sofia Bath, BA2 7AY Canada France GLADWELL, G. M. L. DEBORDES, Olivier Department of Civil Engineering Ecole National Superieure de Mecanique University of Waterloo Universite de Nantes Waterloo, Ontario, N2L 3G1 1, rue de la Noe 44072 Nantes Codex LEIPHOLZ, H. H. E. Department of Civil Engineering DO, Claude University of Waterloo Ecole National Superieure de Macanique Waterloo, Ontario, N2L 3G1 Universite de Nantes 1, rue de la Νοέ NEALE, Kenneth W. 44072 Nantes Cedex Department of Civil Engineering Universite de Sherbrooke DUVAUT, Georges Sherbrooke, Quabec, J1K2R1 IM. TA. Universita Pierre et Marie Curie TABARROK, B. Tour 66 - 4, Place Jussieu Department of Mechanical Engineering 75230 Paris Codex 05 University of Toronto Toronto, Ontario, M5S 1A4 HALPHEN, Bernard Laboratoire de Macanique des Solides Ecole Polytechnique 91128 Palaiseau Cudex xvii XVI11 List of Participants LANCHON, Helene STUMPF, Helmut Institut National Polytechnique Lehrstuhl für Mechanik II de Lorraine Ruhr-Universität Bochum L.E.M.TA. Postfach 10 21 48 2, rue de la Citadelle D-4630 Bochum 1 B.P. 850 54011 Nancy Cadex WUNDERLICH, Walter Institut für Konstruktiven Ingenieurbau LENE, Frangoise Lehrstuhl IV Laboratoire de Macanique Thuorique Ruhr-Universität Bochum Universita Pierre et Marie Curie Postfach 10 21 48 Tour 66 - 4> Place Jussieu D-4630 Bochum 1 75230 Paris Codex 05 Iran LIONS, J. L. SHAHINPOOR, Mohsen INRIA Department of Mechanical Engineering Domaine de Voluceau - Rocquencourt University of Shiraz 78150 Le Chesnay Shiraz MERCIER, Bertrand Italy Centre de Mathamatiques Appliqueäs ASCIONE, Luigi Ecole Polytechnique Dipartimento di Strutture 91128 Palaiseau Cadex Universita degli Studi della Calabria Arcavacata di Rende NAYROLES, Bernard J. P. Centre National de la 87030 Cosenza Recherche Scientifique COMO, Mario Laboratoire de Macanique Istituto di Tecnica delle Costruzioni et d'Acoustique Facolta di Ingegneria 31, chemin Joseph-Aiguier Universita di Napoli 13274 Marseille Codex 2 Piazzale V. Tecchio 80125 Naples NGUYEN QUOC SON Laboratoire de Mecanique des Solides GRIMALDI, Antonio Ecole Polytechnique Dipartimento di Strutture 91128 Palaiseau Codex Universita degli Studi della Calabria Arcavacata di Rende SUQUET, Pierre-M. Laboratoire de Macanique Thuorique 87030 Cosenza Universite Paris VI Japan Tour 66 - 4, Place Jussieu 75230 Paris Cedex 05 FURUHASHI, Rohzo Meiji University TARTAR, L. C. 1-6-5-302 Kita-Aoyama Dapartement de Mathamatiques Minato-ku Bailment 425 Tokyo Universita de Paris-Sud 91405 Orsay Cadex KAWAI, Tadahiko Institute of Industrial Science TEMAM, Roger University of Tokyo Analyse Numerique 7-22-1 Roppongi Bailment 425 Minato-ku Universita de Paris-Sud Tokyo 106 Centre d Orsay 91405 Orsay Cedex MINAGAWA, Sitiro Department of Mechanical Engineering Germany Federal Republic Denkitsushin University BUFLER, H. Chofu Institut für Mechanik der Tokyo Universität Stuttgart OHTSUBO, Hideomi Pfaffenwaldring 7 Department of Naval Architecture 7000 Stuttgart 80 The Faculty of Engineering University of Tokyo KNOTHE, Klaus Institut für Luft- und Raumfahrt Bunkyo-ku T.U.Berlin Tokyo 113 Sekr. SG9(Geb. 4.1) SUMI, Yoichi Salzufer 17-19 Department of Naval Architecture D-1000 Berlin 10 Yokohama National University 156 Tokiwa-dui, Hodogaya-ku STEIN, Erwin Yokohama 240 Lehrstuhl für Baumechanik Technische Universität Hannover Callinstrasse 32 D-3000 Hannover 1
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