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Computer-Aided Analysis of Rigid and Flexible Mechanical Systems NATO ASI Series Advanced Science Institutes Series A Series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an intemational board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical Kluwer Academic Publishers and Physical Sciences Dordrecht, Boston and London D Behavioural and Social Sciences E Applied Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris and Tokyo I Global Environmental Change NATO-PCO-DATA BASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords ancl/or abstracts) to more than 30000 contributions from intemational scientists published in all sections of the NATO ASI Series. Access to the NATO-PCO-DATA BASE is possible in two ways: - via online FILE 128 (NATO-PCO-DATA BASE) hosted by ESRIN, Via Galileo Galilei, 1-00044 Frascati, Italy. - via CD-ROM "NATO-PCO-DATA BASE" with user-friendly retrieval software in English, French and German (©WTV GmbH and DATAWARE Technologies Inc. 1989). The CD-ROM can be ordered through any member of the Board of Publishers or through NATO-PCO, Overijse, Belgium. Series E: Applied Sciences -Vol. 268 Computer-Aided Analysis of Rigid and Flexible Mechanical Systems ediled by Manuel F.O. Seabra Pereira and Jorge A.C. Ambr6sio lnstituto de Engenharia Mecânica, Inslitulo Superior Tecnico, Lisboa, Portugal Springer Science+Business Media, a.v. Proceedings of the NATO Advanced Study Institute on Computer-Aided Analysis of Rigid and Flexible Mechanical Systems Tr6ia, Portugal June 27-July 9, 1993 A C.I.P. Catalogue record for this book is available from the Ubrary of Congress. ISBN 978-94-010-4508-7 ISBN 978-94-011-1166-9 (eBook) DOI 10.1007/978-94-011-1166-9 Printed on acid-free paper AII Rights Reserved © 1994 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1994 Softcover reprint ofthe hardcover lst edition 1994 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photo copying, recording or by any information storage and retrieval system, without written permission from the copyright owner. NA TO·ADV ANCED STUDY INSTITUTE COMPUTER AIDED ANALYSIS OF RIGID AND FLEXIBLE MECHANICAL SYSTEMS TROIA, PORTUGAL 27 JUNE· 9 JULY, 1993 MAIN SPONSORS: NATO: North Atlantic Treaty Organization U.S. Army T ARDEC: United States Army, TARDEC NSF: National Science Foundation OTHER SPONSORS JNICT: Junta Nacional de Investigar;ao Cientffica e Tecnologica FLAD: Fundar;ao Luso Americana para 0 Desenvolvimento IDMEC: Instituto de Engenharia Meciinica CEMUL: Centro de Mecanica e Materiais da Universidade Tecnica de Lisboa DIRECTOR Manuel F.O. Seabra Pereira, IDMEC-Instituto Superior Tecnico, Portugal SCIENTIFIC COMMITTEE: Michel Geradin, Universite de Liege, Belgium Edward J. Haug, University of Iowa, USA Manfred Hiller, University of Duisburg,Gemlany Parviz Nikravesh, University of Arizona, USA CONTENTS List of Participants ix Preface xv PART I -Methods in Rigid Multibody Dynamics 1 Constrained Multibody Dynamics R. A Wehag,?, M.J. Belczynski 3 Construction of the Equations of Motion for Multibody Dynamics Using Point and Joint Coordinates P. A Nikravesh, H. E. Affifi 31 Dynamics of Multibody Systems with Minimal Coordinates M. Hiller, A Kecskemethy 61 Symbolic Computations in Multibody Systems W. Schiehlen 101 On-Line Dynamic Analysis of Mechanical Systems T. R. Kane 137 Topological Description of Articulated Systems J. Wittenburg 159 PART n -Dynamics of Flexible Mechanical Systems 197 Flexibility in Multibody Dynamics With Applications to Crash worthiness J.AC. Ambr6sio, M. S. Pereira 199 Finite Element Modelling Concepts in Multibody Dynamics M. Geradin, A Cardona, D.B. Doan, J. Duysens 233 Kinematic and Dynamic Simulation of Rigid and Flexible Systems With Fully Cartesian Coordinates J. Garcia de Jalon, J. Cuadrado, A Avello, J.M. Jimenez 285 Computer Implementation of Flexible Multibody Equations A A Shabana 325 Flexibility Effects in Multibody Systems R. L. Huston, Y. Wang 351 viii PART HI " Kinematic Aspects of Multibody Systems 377 On Twist and Wrench Generators and Annihilators J. Angeles 379 Application of Computer Aided Kinematics to Modelling of Contacts in Robotic Manipulation J. de Schutter, H. Bruyninckx, S. Dutre 413 PART IV "Computational Issues and Numerical Methods 445 Reduction of Multibody Simulation Time by Appropriate Fonnulation of Dynamical System Equations R. Schwertassek 447 Computational Challenges in Mechanical Systems Simulation L. R. Petzold 483 Numerical Integration of Second Order Differential-Algebraic Systems in Flexible Mechanism Dynamics A. Cardona, M. Geradin 501 PART V " ManlMachine Interaction and Virtual Prototyping 531 Dynamic Simulation for Vehicle Virtual Prototyping J. S.,Freeman,E.J. Haug,J. G. Kuhl,F.F. Tsai 533 Man/Machine Interaction Dynamics and Perfonnance Analysis, Biomechanics and NDISCOS Multibody Equations R~~~ ill INDEX 609 LIST OF PARTICIPANTS Lecturers: Jorge AmbrOsio IDMEC -P610 do I.S.T., Av. Rovisco Pais, 1096 Lisboa, Portugal Jorge Angeles McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada Alberto Cardona INTEC, Giiemes 3450, 3000 Santa Fe, Argentina Jeffrey S. Freeman Center for Computer Aided Design, Coli. of Engineering, University of Iowa, Iowa City, Iowa 525242, USA Harold P. Frisch Robotics Branch, Code 714.1, Goddard Space Center, Greenbelt, Maryland 20771, USA Michel Geradin LTAS -Universite de Liege, Rue Ernest Solvay 21, 4000 Liege, Belgium Manfred Hiller Fachgebiet Mechanik, Universitat Duisburg, Lotharstr. 1,4100 Duisburg, Germany Ronald L. Huston Dept. of Mech. and Industrial Eng., Univ. of Cincinatti, Cincinatti, Ohio 45221-0072, USA J. Garcia de Jalon CElT, po Manuel de LardiZlibal 15,20009 San Sebastian, Guipuzcoa, Spain Thomas R. Kane Division of Applied Mechanics, Durand Bldg, Stanford Univ., Stanford, CA 94305, USA Parviz Nikravesh Dept. of Aerospace and Mech. Engng., University of Arizona, Tucson, AZ 85721, USA Manuel S. Pereira IDMEC -P610 do I.S.T., Av. Rovisco Pais, 1096 Lisboa, Portugal Linda Petzold Comp.Scie.Depl.(4-192 EE/CS Big), 200 Union Street SE, Univ.of Minnesota, Minneapolis MN55455, USA W. Schiehlen Institut B fur Mechanik, Pfaffenwaldring 9, Univ. Stuttgart, D-7ooo Stuttgart 80, Germany J. De Schutter K.U.L., Afdel. Mech. Konst. en Prod., Celestijnenlaan 300 B, B-3OO1 Hevcrlee, Belgium Richard Schwertassek Inst. fur Dynamik der Flugsystem, DLR Oberpfaffenhoffen, D-8031 Wessling, Germany ix x Abmed Sbabana University of Illinois at Chicago, Dept. of Mech. Engng.(M/C 251), 2039 Engineering Research Facility, 842 West Taylor Street, Chicago, Illinois 6OfIJ7-7022, USA Roger Webage System Simulation & Tech. Division, AMSTA-RY, U.S. Army T ARDEC, Warren MI 48397-5000, USA J. Wittenburg Institut fur Technische Mechanik, Universitat Karlsruhe, D-76139 Karlsruhe, Germany Participants: Joao Abrantes Laborat6rio Biomeciinica, Faculdade de Motricidade Humana, 1499 Lisboa, Portugal Venkatesb Agaram L.O.M., Dept. Mecanique, Swiss Federal Inst. of Techn., CH-1015 Lausanne, Switzerland Sunil Agrawal Ohio University, Dept. Mech. Engng., Athens, OH 45701, USA Claudia Oitaven Alves Instituto Gulbenkian de Ciencia, Centro de Biologia, R. Quinta Grande, Apanado 14,2781 Oeiras , Portugal Martin Anantbaraman Universitat Duisburg, FB 7 FG 16, Lotharstraf3e 1,47057 Duisburg, Germany Kurt S. Anderson Institut fur Mechanik, TH Darmstadt, Hochschulstrasse 1, D-6100 Darmstadt, Germany Daniel Bach Institut fur Mechanik, HG F38.1, ETH Zentrum, CH-8092 Zurich, Switzerland Behnam Bahr Wichita State Univ., Mech. Eng. Dept., 1845 N. Fairmount, Wichita, KS67260-0035, USA J. Infante Barbosa ENIDH -Escola Nautica, Av. Bonneville Franco, Parro d'Arcos 2780 Oeiras, Portugal Eduardo Bayo University of California, Dept. of Mech. Engng., Santa Barbara, CA 93106, USA M. Belczynski System Simulation & Tech. Division, U.S. Army TACOM, (AMSTA-RY), Warren, MI 48397-5000, USA F. Bennis Laboratoire d'Automatique de Nantes, Ecole Centrale Nantes, URA CNRS 823, 1 Rue de la Noe, 44072 Nantes Cedex 03, France Roman Bogacz Inst. of Fundamental Tech. Res., Polish Academy of Sciences, ul. Swietokrzyska 21, 00-049 Warsaw, Poland xi Marco Borri Dipart. di Ingegn. Aerospaziale, Politecnico di Milano, via Golgi 40, 20133 Milano, Italy Hans Brauchli Institut fur Mechanik, HG F38.1, ETH Zentrum, CH-8092 Zurich, Switzerland Pasquale Campanile C. Ricerche FIAT, Ente Veicoli/Calcoli, Strada Torino 50, 10043 Orbassano (TO), Italy Marco Ceccarelli Dept Industrial Engng., Univ. of Cassino, Via Zamosch 43, 03043 Cassino (FR), Italy J.Choi Dept. Mech. Eng (M/C 251)-2039 ERF, Univ. of Illinois at Chicago, Box 4348, Chicago, IL 60680, USA Kenneth Clark Mathematical Sc. Div., U.S. Army Res. Office, Research Triangle Park, NC 27709, USA Jose Sa da Costa I.S.T.-DEM, Av. Rovisco Pais, 1096 Lisboa, Portugal M. A. Crisfield Imperial Coll1ege, Dept. Aero., Prince Consort Road, London SW7 2BY, United Kingdom J. Cuadrado University of Navarra, Manuel de Lardizabal 15,20009 San Sebastian, Spain Joiio P. Dias Instituto Superior Tecnico, Dept. Eng. Meciinica, A v. Rovisco Pais, 1096 Lisboa, Portugal D.B.Doan L.T.A.S., Universite de Liege, Rue Ernest Solvay 21,4000 Liege, Belgium Robert Dombroski U.S.Army Ardec, SMCAR-FSA-F Bldg 61N, Picatinny Arsenal-NJ 07806-5000, USA J. Duysens L.T.A.S., University of Liege, 21, Rue Ernest Solvay 21, B-4000 Liege, Belgium Haluk Erol Istanbul Technical University, Faculty of Mech. Engng., Gumussuyu, Istanbul, Turkey Yanis Erotokritos Inst. of Sound & Vibration Research, Univ. of Southampton, S09 5NH, United Kingdom Christian Goualou Ecole Centrale de Paris, L.R.S.A. -Res. Lab. for Auto. Safety, Grande Voie des Vignes, 92295 Chatenay-Malabry, France Simon Guest Univ Cambridge, Dept.of Eng.,Trumpington Street, Cambridge CB2 IPZ,United Kingdom John Hansen Technical University of Denmark, Dept. of Solid Mechanics, Building 421,2800 Lyngby, Denmark

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This book contains the edited version of the lectures presented at the NATO ADVANCED STUDY INSTITUTE on "COMPUTER AIDED ANALYSIS OF RIGID AND FLEXIBLE MECHANICAL SYSTEMS". held in Troia. Portugal. from the 27 June to 9 July. 1993. and organized by the Instituto de Engenharia Mecanica. Instituto Supe
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Computer-Aided Analysis of Rigid and Flexible Mechanical Systems NATO ASI Series Advanced Science Institutes Series A Series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an intemational board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical Kluwer Academic Publishers and Physical Sciences Dordrecht, Boston and London D Behavioural and Social Sciences E Applied Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris and Tokyo I Global Environmental Change NATO-PCO-DATA BASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords ancl/or abstracts) to more than 30000 contributions from intemational scientists published in all sections of the NATO ASI Series. Access to the NATO-PCO-DATA BASE is possible in two ways: - via online FILE 128 (NATO-PCO-DATA BASE) hosted by ESRIN, Via Galileo Galilei, 1-00044 Frascati, Italy. - via CD-ROM "NATO-PCO-DATA BASE" with user-friendly retrieval software in English, French and German (©WTV GmbH and DATAWARE Technologies Inc. 1989). The CD-ROM can be ordered through any member of the Board of Publishers or through NATO-PCO, Overijse, Belgium. Series E: Applied Sciences -Vol. 268 Computer-Aided Analysis of Rigid and Flexible Mechanical Systems ediled by Manuel F.O. Seabra Pereira and Jorge A.C. Ambr6sio lnstituto de Engenharia Mecânica, Inslitulo Superior Tecnico, Lisboa, Portugal Springer Science+Business Media, a.v. Proceedings of the NATO Advanced Study Institute on Computer-Aided Analysis of Rigid and Flexible Mechanical Systems Tr6ia, Portugal June 27-July 9, 1993 A C.I.P. Catalogue record for this book is available from the Ubrary of Congress. ISBN 978-94-010-4508-7 ISBN 978-94-011-1166-9 (eBook) DOI 10.1007/978-94-011-1166-9 Printed on acid-free paper AII Rights Reserved © 1994 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1994 Softcover reprint ofthe hardcover lst edition 1994 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photo copying, recording or by any information storage and retrieval system, without written permission from the copyright owner. NA TO·ADV ANCED STUDY INSTITUTE COMPUTER AIDED ANALYSIS OF RIGID AND FLEXIBLE MECHANICAL SYSTEMS TROIA, PORTUGAL 27 JUNE· 9 JULY, 1993 MAIN SPONSORS: NATO: North Atlantic Treaty Organization U.S. Army T ARDEC: United States Army, TARDEC NSF: National Science Foundation OTHER SPONSORS JNICT: Junta Nacional de Investigar;ao Cientffica e Tecnologica FLAD: Fundar;ao Luso Americana para 0 Desenvolvimento IDMEC: Instituto de Engenharia Meciinica CEMUL: Centro de Mecanica e Materiais da Universidade Tecnica de Lisboa DIRECTOR Manuel F.O. Seabra Pereira, IDMEC-Instituto Superior Tecnico, Portugal SCIENTIFIC COMMITTEE: Michel Geradin, Universite de Liege, Belgium Edward J. Haug, University of Iowa, USA Manfred Hiller, University of Duisburg,Gemlany Parviz Nikravesh, University of Arizona, USA CONTENTS List of Participants ix Preface xv PART I -Methods in Rigid Multibody Dynamics 1 Constrained Multibody Dynamics R. A Wehag,?, M.J. Belczynski 3 Construction of the Equations of Motion for Multibody Dynamics Using Point and Joint Coordinates P. A Nikravesh, H. E. Affifi 31 Dynamics of Multibody Systems with Minimal Coordinates M. Hiller, A Kecskemethy 61 Symbolic Computations in Multibody Systems W. Schiehlen 101 On-Line Dynamic Analysis of Mechanical Systems T. R. Kane 137 Topological Description of Articulated Systems J. Wittenburg 159 PART n -Dynamics of Flexible Mechanical Systems 197 Flexibility in Multibody Dynamics With Applications to Crash worthiness J.AC. Ambr6sio, M. S. Pereira 199 Finite Element Modelling Concepts in Multibody Dynamics M. Geradin, A Cardona, D.B. Doan, J. Duysens 233 Kinematic and Dynamic Simulation of Rigid and Flexible Systems With Fully Cartesian Coordinates J. Garcia de Jalon, J. Cuadrado, A Avello, J.M. Jimenez 285 Computer Implementation of Flexible Multibody Equations A A Shabana 325 Flexibility Effects in Multibody Systems R. L. Huston, Y. Wang 351 viii PART HI " Kinematic Aspects of Multibody Systems 377 On Twist and Wrench Generators and Annihilators J. Angeles 379 Application of Computer Aided Kinematics to Modelling of Contacts in Robotic Manipulation J. de Schutter, H. Bruyninckx, S. Dutre 413 PART IV "Computational Issues and Numerical Methods 445 Reduction of Multibody Simulation Time by Appropriate Fonnulation of Dynamical System Equations R. Schwertassek 447 Computational Challenges in Mechanical Systems Simulation L. R. Petzold 483 Numerical Integration of Second Order Differential-Algebraic Systems in Flexible Mechanism Dynamics A. Cardona, M. Geradin 501 PART V " ManlMachine Interaction and Virtual Prototyping 531 Dynamic Simulation for Vehicle Virtual Prototyping J. S.,Freeman,E.J. Haug,J. G. Kuhl,F.F. Tsai 533 Man/Machine Interaction Dynamics and Perfonnance Analysis, Biomechanics and NDISCOS Multibody Equations R~~~ ill INDEX 609 LIST OF PARTICIPANTS Lecturers: Jorge AmbrOsio IDMEC -P610 do I.S.T., Av. Rovisco Pais, 1096 Lisboa, Portugal Jorge Angeles McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada Alberto Cardona INTEC, Giiemes 3450, 3000 Santa Fe, Argentina Jeffrey S. Freeman Center for Computer Aided Design, Coli. of Engineering, University of Iowa, Iowa City, Iowa 525242, USA Harold P. Frisch Robotics Branch, Code 714.1, Goddard Space Center, Greenbelt, Maryland 20771, USA Michel Geradin LTAS -Universite de Liege, Rue Ernest Solvay 21, 4000 Liege, Belgium Manfred Hiller Fachgebiet Mechanik, Universitat Duisburg, Lotharstr. 1,4100 Duisburg, Germany Ronald L. Huston Dept. of Mech. and Industrial Eng., Univ. of Cincinatti, Cincinatti, Ohio 45221-0072, USA J. Garcia de Jalon CElT, po Manuel de LardiZlibal 15,20009 San Sebastian, Guipuzcoa, Spain Thomas R. Kane Division of Applied Mechanics, Durand Bldg, Stanford Univ., Stanford, CA 94305, USA Parviz Nikravesh Dept. of Aerospace and Mech. Engng., University of Arizona, Tucson, AZ 85721, USA Manuel S. Pereira IDMEC -P610 do I.S.T., Av. Rovisco Pais, 1096 Lisboa, Portugal Linda Petzold Comp.Scie.Depl.(4-192 EE/CS Big), 200 Union Street SE, Univ.of Minnesota, Minneapolis MN55455, USA W. Schiehlen Institut B fur Mechanik, Pfaffenwaldring 9, Univ. Stuttgart, D-7ooo Stuttgart 80, Germany J. De Schutter K.U.L., Afdel. Mech. Konst. en Prod., Celestijnenlaan 300 B, B-3OO1 Hevcrlee, Belgium Richard Schwertassek Inst. fur Dynamik der Flugsystem, DLR Oberpfaffenhoffen, D-8031 Wessling, Germany ix x Abmed Sbabana University of Illinois at Chicago, Dept. of Mech. Engng.(M/C 251), 2039 Engineering Research Facility, 842 West Taylor Street, Chicago, Illinois 6OfIJ7-7022, USA Roger Webage System Simulation & Tech. Division, AMSTA-RY, U.S. Army T ARDEC, Warren MI 48397-5000, USA J. Wittenburg Institut fur Technische Mechanik, Universitat Karlsruhe, D-76139 Karlsruhe, Germany Participants: Joao Abrantes Laborat6rio Biomeciinica, Faculdade de Motricidade Humana, 1499 Lisboa, Portugal Venkatesb Agaram L.O.M., Dept. Mecanique, Swiss Federal Inst. of Techn., CH-1015 Lausanne, Switzerland Sunil Agrawal Ohio University, Dept. Mech. Engng., Athens, OH 45701, USA Claudia Oitaven Alves Instituto Gulbenkian de Ciencia, Centro de Biologia, R. Quinta Grande, Apanado 14,2781 Oeiras , Portugal Martin Anantbaraman Universitat Duisburg, FB 7 FG 16, Lotharstraf3e 1,47057 Duisburg, Germany Kurt S. Anderson Institut fur Mechanik, TH Darmstadt, Hochschulstrasse 1, D-6100 Darmstadt, Germany Daniel Bach Institut fur Mechanik, HG F38.1, ETH Zentrum, CH-8092 Zurich, Switzerland Behnam Bahr Wichita State Univ., Mech. Eng. Dept., 1845 N. Fairmount, Wichita, KS67260-0035, USA J. Infante Barbosa ENIDH -Escola Nautica, Av. Bonneville Franco, Parro d'Arcos 2780 Oeiras, Portugal Eduardo Bayo University of California, Dept. of Mech. Engng., Santa Barbara, CA 93106, USA M. Belczynski System Simulation & Tech. Division, U.S. Army TACOM, (AMSTA-RY), Warren, MI 48397-5000, USA F. Bennis Laboratoire d'Automatique de Nantes, Ecole Centrale Nantes, URA CNRS 823, 1 Rue de la Noe, 44072 Nantes Cedex 03, France Roman Bogacz Inst. of Fundamental Tech. Res., Polish Academy of Sciences, ul. Swietokrzyska 21, 00-049 Warsaw, Poland xi Marco Borri Dipart. di Ingegn. Aerospaziale, Politecnico di Milano, via Golgi 40, 20133 Milano, Italy Hans Brauchli Institut fur Mechanik, HG F38.1, ETH Zentrum, CH-8092 Zurich, Switzerland Pasquale Campanile C. Ricerche FIAT, Ente Veicoli/Calcoli, Strada Torino 50, 10043 Orbassano (TO), Italy Marco Ceccarelli Dept Industrial Engng., Univ. of Cassino, Via Zamosch 43, 03043 Cassino (FR), Italy J.Choi Dept. Mech. Eng (M/C 251)-2039 ERF, Univ. of Illinois at Chicago, Box 4348, Chicago, IL 60680, USA Kenneth Clark Mathematical Sc. Div., U.S. Army Res. Office, Research Triangle Park, NC 27709, USA Jose Sa da Costa I.S.T.-DEM, Av. Rovisco Pais, 1096 Lisboa, Portugal M. A. Crisfield Imperial Coll1ege, Dept. Aero., Prince Consort Road, London SW7 2BY, United Kingdom J. Cuadrado University of Navarra, Manuel de Lardizabal 15,20009 San Sebastian, Spain Joiio P. Dias Instituto Superior Tecnico, Dept. Eng. Meciinica, A v. Rovisco Pais, 1096 Lisboa, Portugal D.B.Doan L.T.A.S., Universite de Liege, Rue Ernest Solvay 21,4000 Liege, Belgium Robert Dombroski U.S.Army Ardec, SMCAR-FSA-F Bldg 61N, Picatinny Arsenal-NJ 07806-5000, USA J. Duysens L.T.A.S., University of Liege, 21, Rue Ernest Solvay 21, B-4000 Liege, Belgium Haluk Erol Istanbul Technical University, Faculty of Mech. Engng., Gumussuyu, Istanbul, Turkey Yanis Erotokritos Inst. of Sound & Vibration Research, Univ. of Southampton, S09 5NH, United Kingdom Christian Goualou Ecole Centrale de Paris, L.R.S.A. -Res. Lab. for Auto. Safety, Grande Voie des Vignes, 92295 Chatenay-Malabry, France Simon Guest Univ Cambridge, Dept.of Eng.,Trumpington Street, Cambridge CB2 IPZ,United Kingdom John Hansen Technical University of Denmark, Dept. of Solid Mechanics, Building 421,2800 Lyngby, Denmark

Description:
This book contains the edited version of the lectures presented at the NATO ADVANCED STUDY INSTITUTE on "COMPUTER AIDED ANALYSIS OF RIGID AND FLEXIBLE MECHANICAL SYSTEMS". held in Troia. Portugal. from the 27 June to 9 July. 1993. and organized by the Instituto de Engenharia Mecanica. Instituto Supe
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