Lecture Notes in Engineering

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C. A Brebbia Wessex Institute of Technology Ashurst Lodge, Ashurst Southampton S04 2AA (UK)

Consulting Editors

Chemical Engineering: J. H. Seinfeld Dept. of Chemical Engg., Spaulding Bldg. Calif. Inst. of Technology Pasadena, CA 91125 (USA)

Dynamics and Vibrations: P. Spanos Department of Mechanical and Civil Engineering, Rice University P. O. Box 1892 Houston, Texas 77251 (USA)

Earthquake Engineering: AS. Cakmak Dept. of Civil Engineering, Princeton University Princeton, NJ 08544 (USA)

Electrical Engineering: P. Silvester Dept. of Electrical Engg., McGill University 3480 University Street Montreal, PO H3A 2A7 (Canada)

Geotechnical Engineering and Geomechanics: C.S. Desai College of Engineering Dept. of Civil Engg. and Engg. Mechanics The University of Arizona Tucson, AZ 85721 (USA)

Hydrology: G. Pinder School of Engineering, Dept. of Civil Engg. Princeton University Princeton, NJ 08544 (USA)

Laser Fusion - Plasma: R. McCrory Lab. for Laser Energetics, University of Rochester Rochester, NY 14627 (USA)

S.AOrszag Applied and Computational Mathematics 218 Fine Hall Princeton, NJ 08544 (USA)

Materials Science and Computer Simulation: S. Yip Dept. of Nuclear Engg., MIT Cambridge, MA 02139 (USA)

Mechanics of Materials: FA Leckie Dept. of Mechanical Engineering Univ. of California Santa Barbara, CA 93106 (USA)

A R. S. Panter Dept. of Engineering, The University Leicester LE1 7RH (UK)

Fluid Mechanics: K.-P' Holz Inst. fUr Stromungsmechanik, Universitat Hannover, Callinstr. 32 D-3000 Hannover 1 (FRG)

Nonlinear Mechanics: K.-J. Bathe Dept. of Mechanical Engg., MIT Cambridge, MA 02139 (USA)

Structural Engineering: J. Connor Dept. of Civil Engineering, MIT Cambridge, MA 02139 (USA)

w. Wunderlich Inst. fUr Konstruktiven Ingenieurbau Ruhr-Universitat Bochum U niversitatsstr. 150, D-4639 Bochum-Ouerenburg (FRG)

Structural Engineering, Fluids and Thermodynamics: J. Argyris Ins!. fur Statik und Dynamik der Luft- und Raumfahrtkonstruktion Pfaffenwaldring 27 D-7000 Stuttgart 80 (FRG)

.".

Lecture Notes in Engineering Edited by C. A. Brebbia and S. A. Orszag

63

H. A. 'Eschenauer, C. Matlheck N. Olhoff (Eds.)

Engineering Optimization in Design Processes Proceedings of the International Conference Karlsruhe Nuclear Research Center, Gennany September 3-4, 1990

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest

Series Editors C. A. Brebbia . S. A. Orszag

Consulting Editors J. Argyris . K.-J. Bathe' A. S. Cakmak . J. Connor· R. McCrory C. S. Desai . K -Po Holz . F. A. Leckie . G. Pinder· A. R. S. Pont J. H. Seinfeld . P. Silvester· P. Spanos' W. Wunderlich· S. Yip

Editors Hans A. Eschenauer Institute of Mechanics and Control Engineering University of Siegen 0-5900 Siegen Germany

Claus Mattheck Karlsruhe Nuclear Research Center Institute of Materials and Solid State Research IV 0-7500 Karlsruhe Germany

Niels Olhoff Institute of Mechanical Engineering Aalborg University DK-9220 Aalborg Denmark

ISBN-13:978-3-540-53589-8 e-ISBN-13:978-3-642-84397-6 001: 10.1007/978-3-642-84397-6

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.

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Preface

These proceedings contain the texts of 37 contributions presented at the International Conference

on Engineering Optimization in an Industrial Environment, which took place on 3 - 4 September

1990 at the Karlsruhe Nuclear Hesearch Center, I~H Germany.

The presentations consisted of oral and poster contributions arranged in five sessions:

• Shape and layout optimization

• Structural optimization with advanced materials

• Optimal designs with special structural and material beha viour

• Sensitivity analysis - Programme systems

• Optimization with stability constraints - Special problems

The editors wish to express their appreciation to all authors and invited speakers for their in­

teresting contributions.

The proceedings cover a wide range of topics in structural optimization representing the present

state of the art in the fields of research and in the industrial environment as well. The editors hope

that this book will also contribute towards new ideas and concepts in a world of ever decreasing

natural resources and ever increasing demands for lighter and yet stronger and safer technical

components.

I"inally, the editors wish to thank all colleagues who helped in the organisation of the conference,

especially Mrs. E. Schroder anq Dr. K.llethge, as well as Mr. A. von lIagen and Mrs. E. Haufelder,

Springer Publishing Company, Heidelberg for the good cooperation and help in the publication of

these proceedings.

H. Eschenauer

Siegen

C. Mattheck

Karlsruhe

December 1990

N.Olhoff

Aalborg

Sept. 3, 1990

9.00 - 9.10 h

9.10 - 9.30 h

9.30 - 10.10 h

Session 1 Chairpersons:

10.30 - 10.50 h

10.50 - 11.10 h

11.10-11.30h

11.30 - 11.50 h

11.50 - 12.10 h

12.10 - 12.30 h

Session 2 Chairpersons:

14.00 - 14.20 h

14.20 - 14.40 h

14.40 - 15.00 h

Programme of the International Conference on Engineering Optimization in Design Processes

Sept. 3 - 4,1990, Karlsruhe Nuclear Research Center

Welcome Addresses

H. Eschenauer WRO) Structural Optimization - a Need in Design Processes?

C. Mattheck, S. Burkhardt, D. Erb WRO) Shape Optimization of Engineering Components by Adaptive Biological Orowth

Shape and Layout Optimization H. Eschenauer, N. Olhoff

M.P. Bendspe (DK), H.C. Rodrigues (P) Integrated 'I'opology and Boundary Shape Optimization of2D-Solids

H.P. Mlejnek, U. Jehle, R. Schit'rmacher WRO) Some Approaches to Shape l"inding in Optimal Structural Design

O. Krzesinski (PL) Shape Optimization and Identification of2D Elastic Structures by the BEM

O. Rozvany, M. Zhou (I"RO) Applications of the COC - Algorithm in Layout Optimization

M. Week, W. Sprangers WRO) Shape Optimization in Machine '1'001 Design

H. Baier, B. Specht (FRO) Shape Optimization and Design Element Selection for Problems with Constrained Static and Dynamic Response

Structural Optimization with Advanced Materials M. Bends0e, H. Eschenauer

P. Pedersen (OK) Optimal Design with Advanced Material

P.U. Post (FRO) Optimization of the Long-Term Behaviour of Composite Structures under Hygrothermal Loads

J. BuhlmeierWRO) Design of Laminated Composites under Time Dependent Loads and Materiall3ehaviour

15.00 - 15.20 h

15.20 - 15.40 h

Session 3 Chairpersons:

16.00 -16.20 h

16.20 -16.40 h

16.40 - 17.00 h

17.00-17.20h

17.20 -17.40 h

Sept. 4, 1990

Session 4a Chairpersons:

9.00 - 9.20 h

9.20 - 9.40 h

9.40 - 10.00 h

10.30 - 12.30 h

Session 4b

Chairpersons:

14.00 - 14.20 h

14.20 - 14.40 h

14.40-15.00h

v

M. Rovati, A. Taliercio (1) Optimal Orientation ofthe Symmetry Axes of Or tho tropic 3D-Materials

Ch. Secllelberg. G. Helwig, H. Baier WHG) Strategies for Interactive Structural Optimization and (Composites) Material Selection

Optimal Designs with Special Structural and Material Behaviour P. Pedersen, G. Cheng

H. Eschenauer, Th. Vietor WHG) Some Aspects on Structural Optimization of Ceramic Structures

J. Blachut (GB) Shape Optimization of FHP Dome Closures under Buckling Constraints

V.V. Kobelev (USSR) Numerical Method for Shape Optimization using BEM

L. lIarzheim, C. Maltheck 3D-Shape Optimization: Different Ways Leading to an Optimized Design

D. Radai. Sh. Zhang WRG) Multiparameter Design Optimization in Hespect of Stress Concentrations

Sensitivity Analysis - Programme Systems A. Osyczka, G. Hozvany

N.Olhoff(DK) On Elimination of Inaccuracy in Semi-Analytical Sensitivity Analysis

V. Braibant, P. Morelle, C. ["Ieury (B) Recent Advances in the SAMCEI? Optimization System

G. Muller, P. Ticfenthalel' WRG) Design Optimization with the Commercial FEM Program ANSYS

Poster Session and Exhibition

Sensitivity Analysis . Programme Systems

H. Baier, A. Gajewski

G. Cheng, Y. Gu, W. Xicheng (China) Improvement of Semi-Analytical Sensitivity Analysis and MCADS

V.I'. Malkov, V.V. Toropov (USSH) Simulation Approach to Structural Optimization using Design Sensitivity Analysis

S. Kibsgaard (l)K) MODU LEF - A l<'EM Tool for Optimization

15.00 - 15.20 h

15.20 - 15.40 h

Session 5

Chairpersons:

16.00 - 16.20 h

16.20-16.40h

16.40 - 17.00 h

17.00-17.20h

17.20-17.40h

17.40-17.50 h

VI

A. Osyczka (PL) CompuLer Aided MulLicriLerion Optimization SysLem in Use

W. Heylen, S. Lammens, P. Sas (B) Dynamic Structural Optimization by Means of the U .A. Model Updating Technique

Optimization with Stability Constraints­

Special Problems

C. Mattheck, N. Olhoff

B. Bochenek, M. Zyczkowski (ilL) Optimal I-Section of an Elastic Arch under Stability Constraints

H.H. Miiller-Slany (FRG) Application of Optimization Procedures to Substructure Synthesis

A. Gajewski (PL) Multimodal Optimization of U nifOl'mly Compressed Cy lindrical Shells

B.W. Kooi (NL) The "Cut-and-Try" Method in the Design oCthe Bow

H. Huber-Belzer, C. MaLlheck (l<'RG) Computer-Simulated Self-Optimization of Bony Structures

Closure Address

Poster presentations

A. Borkowski, S. Jozwiak, M. Danicka (I'L) Truss Optimization Using Knowledge Base

J. Holnicki-Szulc, J .'1'. Gierlinski (PL) Optimal Redesign Process Simulated by Virtual Distortions

P. Knodel WRG) On Optimal Structures in Engineering

H. Moldenhauer, K. Bethge (l<'RG) Application of the CAO-Method to Axisymmetrical Structures under Non-Axisymmetrical Loading

T.J. Heiter, It'.G. Hammerslorfer, 1-I.J. Bohm (Al Numerical Simulation ofInternal and Surface Bone Remodeling

Y. Gu, G. Cheng (China) Engineering Oriented Approaches of Structural Shape OpLimizalion

Austria A.K. Maschinek, Th. Reiter

Belgium C. Fleury, S. Lammens

China G. Cheng

Denmark

List of Participants

M.P. Bendsflle, S. Kibsgaard, N. Olhoff, P. Pedersen

"'inland J. Koski, H.. Silvennoien

Fit Germany U. Adriany, J. Aktaa, It. Allrutz, I". Ansorge, II. Baier, C.U. Bauer, M. Beller, K. Bethgc, J. BUhlmeier, S. Burkhardt, H. Bolz, M. Dcligeorges, K. Dcpta, W. Eggert, D. Erb, T. Ertl, H. I~schenauer, M. Fanni, D. l<'reitag, H. I"riedmann, E. Gaber, F. Geyer, D. Glotzel, B. Harter, L.llarzheim, H.llempel, K. Ilornberger, H. Iluber-Betzer, O.lancu, U. Jehle, H. Kahn, K. Kasper, II. Kim, D. Klein, P. Knodel, D. Koch, H. Kussmaul, M. Lawo, C. Mattheck, M. Miller, II.P. Mlejnek, II. Moldenhauer, J. MUller, 11.11. Muller-Slany, H. Pfeifer, A. Pompetzki, U. Post, M. Prinz, D. Radaj, N. Hashwan, A. Hebetzky, G. Hozvany, J. Sauter, J. Schafer, R. Schirrmacher, U. Schneider, G. Schuhmacher, Ch. Seellelsberg, B. Specht, W. Sprangers, M. Teschner, 'I'h. 'I'hiemeier, P. 'I'ierenthaler, Th. Victor, U. Vorberg, I". Walther, II.Ch. Wille, B. Yuan, S. Zhang, M. Zhou, J.E. Zimmermann

Great Britain J. Blachut

Italy C. Cinquini, M. H.ovati, A. 'I'aliercio

The Nethedands H.W. Kooi

Poland B. Bochenek, A. Horkowski, A. Gajewski, J. Holnicki-Szulc, G. Krzesinski, A. Osyczka

Switzerland P. Kim, II. Meier

USA A.H. Diaz

USSIt V.V. Kobelev, V.V. 'roropov

CONTENTS

II. Eschenauer (FRO) Structural Optimization - a Need in Design Processes? .................................... 1

C. Mattheck, S. Burkhardt, D. Erb WRO) Shape Optimization of Engineering Components by Adaptive Biological Crowth .................................................................... 15

Shape and Layout Optimization

M.P. Bendslle (DK), H.C. Rodrigues (1'), J. Rasmussen (OK) 'l'opology and Boundary Shape Optimization as an Integrated '1'001 for Computer-Aided Design ....................................................... 27

11.1'. Mlejnek, U. Jehle, R Schirrmacher WIWj Some Approaches to Shape (?inding in Optimal Structural Design ......................... 35

C. Krzesinski (Pl.) Shape Optimization and Identification of2D-Elastic Structures by the BEM .......................................................................... 51

O. Rozvany, M. Zhou WHC) Applications ofthe COC - Algorithm in Layout Optimization .............................. 59

M. Week, W. Sprangers (It'RO) Shape Optimization in Machine '1'001 Design ............................................. 71

B. Specht, II. Baier, WRO) Shape Optimization and Design Element Selection for Problems with Constrained Static and Dynamic Response ................................ 79

Structural Optimization with Advanced Materials

P. Pedersen (OK) Optimal Design with Advanced Material ................................................ 91

P.U. Post WHO) Optimization of the Long-Term Behaviour of Cumposite Slruclul'es under IIygrothermal Loads .................................................. 99

J. Buhlmeier WRO) Design of Laminated Composites under 'I'ime-Dependent Luads and Materiaillehaviour ....................................................... 107

M. Rovati, A. 'I'aliercio (I) Optimal Orientation of the Symmetry Axes of Or tho tropic 3D-Materials 127

Ch. SeeBelberg, C. lIelwig, H. Baier WHO) Strategies for Interactive Structural Optimization and Composites Material Selection .................................................................. 135

IX

Optimal Designs with Special Structural and Material Behaviour

H. Eschenauer, Th. Vietor WRG) Some A~pect~ on Structural Optimization of Ceramic Structul'es 145

J.llIachut (GB) Shape Optimization ofFRP Dome Closures under Buckling Constraints 155

V.V. Kobelev (USSI{) Shape Optimization U~ing Boundary E1ement~ 165

L. Harzheim, C. MaLtheck (FRG) 3D-Shape Optimization: Different Ways Leading to an Optimized Design 173

D. Radaj, Sh. Zhang (FRG) Multiparameter Design Optimization in Respect ofStre~s Concentrations 181

Sensitivity Analysis' Programm Systems

N. Olhoff, J. Rasmussen (DK) Method of Error Elimination for a Class of Semi-Analytical Sen~ilivity Analysi~ Problems ....................................................... 193

G. Muller, 1'. Ticfenthaler WRG) Design Optimization with a Commercial Finite Element Program 201

G. Cheng, Y. Gu, W. Xicheng (China) Improvement of Semi-Analytical Sensitivity Analy~is and MCADS 211

V.I'. Malkov, V.V. Toropov (USSIO Simulation Approach to Structural Optimization ll~ing Design Sensitivity Analy~is ................................................................ 225

S. Kibsgaard (DK) MODU LEI<' - An FEM Tool for Optimization 233

A. Osyczka (PL) Computer-Aided Mlliticriterion Optimization System in Use 241

W. Heylen, S. Lammelll;, P. Sas (B) Dynamic Structural Optimization by Means of the U .A. Model Updating Technique ................................................................ 249

Optimization with Stability Constraints· Special PI'olllems

I3. Bochenek, M. Zyczkowski (PL) OpLimall-SecLion of an Elastic Arch under Stability Constraints 259

11.11. Muller-Slany (FRG) Application of Optimization Procedures to Substructure Synthesi:; 267

A. Gajewski (PL) Multimodal Optimization of Uniformly Compressed Cylindrical Shells 275

B.W. K()oi (NL) The "Cut-and-Try" Method in the Design of the Bow 283

x

H. Huber-Betzer, C. Mattheck (l<'RG) Computer-Simulated Self-Optimization of Bony Structures

A. Borkowski, S. Jozwiak, M. Danicka (PL) Truss Optimization Using Knowledge Base

J. Holnicki-Szulc, J .T. Gierlinski (PL) Optimal Redesign Process Simulated by Virtual Distortions

P. KnOdel (l?RG) On Optimal Structures in Engineering

H. Moldenhauer, K. Bethge WRG) Application ofthe CAO-Method to Axisymmctrical Structures under

293

301

309

317

Non-Axisymmetrical Loading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 325

T.J. Reiter,l<'.G. Rammerstorfer, H.J. Biihm (A) Numerical Simulation ofinternal and Surface Bone Remodeling 333

Y. Gu, O. Cheng (China) Engineering-Oriented Approaches of Structural Shape Optimization 341

Author Index ..................................................................... 355

Baier, H. Dornier GmbH

List of Contributors

Postfach 1420,7990 Friedrichshafen, }t'R Germany

Bendsoe, M.P. The Technical University of Denmark, Mathematical Institute, Bldg. 303 2S00 Lyngby, Denmark

Bethge,K. Kernforschungszentrum Karlsruhe, IMF IV Postfach 3640, 7500 Karlsruhe, FR Germany

Blachut,J. Liverpool U ni versity, Department of Mechanical Engineering P.O. Box 147. Liverpool. L69 3BX. Great Britain

Bochenek, B. Technical University of Cracow, Institute of Mechanics and Machine Design Warszawska 24, 31-155 Cracow, Poland

Bohm,H.J. TU Wien, Institut fiir Leicht- und Flugzeugbau Gullhaulistr. 25 - 29/317.1040 Wien. Austria

Borkowski, A. Polish Academy of Sciences. Institute of l~undamental Technological Hesearch Swiewkrzyska 21. 00-049 Warsaw. Poland

Braibant, V. Samtech S.A. Bd. Frere Orban 25. 4000 Liege, Belgium

Biihlmeier, J. Institute for Computer Applications, Universitiit Stuttgart Pfaffenwaldring 27, 7000 Stuttgart SO, I<'R Germany

Burkhardt, S. Kernforschungszentrum Karlsruhe,lMF IV Postfach 3640.7500 Karlsruhe, Fit Germany

Cheng,G. Dalian University of Technology, Research Institute of Engineering Mechanics 116024 Dalian, China

Danicka. M. Polish Academy of Sciences, Adaptive Systems Laborawl'y, Institute of}t'undamental Technological Research ut. Swiewkrzyska 21, 00-049 Warsaw, Poland

Erh,n. Kernforschungszentrum Karlsruhe, IMF IV Postfach 3640, 7500 Karlsruhe, FR Germany

Eschenauer, H. Universitiit-GH Siegen, }t'achbereich 11, lnst. fiir Mechanik und Regelungstechnik Paul-Bonalz-Str. 9 - 11,5900 Siegen, FR Germany

Gajewski, A. Technical University of Cracow, Institute of Physics ul. Podchorazych 1, 30-0S4 Cracow, Poland

Gierlinski, J.T. WS Atkins Engineering Sciences Epsom, Great13rilain

Gu, Y.

XII

Dalian U niversily of Technology, Research Institute of Engineering Mechanics 116024 Dalian, China

Harzheim, L. Kernforschungszentrum Karlsruhe,iMI<' iV Postfach 3640,7500 Karlsruhe,i"R Germany

Heiwig,G. Dornier Gmbll Postfach 1420,7990 i"riedrichshafen, i·'1{ Germany

Heylen, W. Kalil. Universiteit Leuven, Mechanische KonstrukLie en ProdukLie Celestijnenlaan 300 B, 3030 Beverlee, Belgium

Holnicki-Szulc, J. Polish i\cademy of Sciences, institute of Fundamental Technologicalltesearch Swietokrzyska 21, 00-049 Warsaw,Poland

Huber-Betzer, H. Kernforschungszentrum Karlsruhe,iMI>' IV Postfach 3640, 7500 Karlsruhe, FIt Germany

Jehle, U. institute for Computer i\pplications, U niversiliit Stultgart Pfaffenwaldring 27,7000 Slullgart80, I"it Germany

Jozwiak,S. Polish i\cademy of Sciences, Adaptive Syslems Laboratory,Institute of Fundamental Technological Research Swictokrzyska 21, 00-049 Warsaw,Poland

Kibsgaard, S. 'l'he University of Aalborg,lnstilute of Mechanical Engineering i'ontoppidanstraede 101,9220 i\alborg East, Denmark

Knodei, P. Universilat Karlsruhe, Versuchsanstalt fur Slahl,lIolz und Steine Kaiserstr. 12,7500 Karlsruhe I, FR Germany

Kobelev, V.V. USSR i\cademy of Sciences, Institute for Problcms in Mechanics Vcrnadskogo,10l, Moscow,1l7526, USSlt

Kooi, B.W. Free Univcrsity, Department of Biology P.O. Box 7161, 1007 MC i\msterdam, The Netherlands

Krzesinski, G. Technical University of Warsaw, institute of i\ircl'aft Technology and Applied Mechanics ul. Nowowiejska 22124, 00-665 Warsaw, Poland

Lammens, S. Kath. Universiteit Leuvcn, Mechanische Konstruktie en Produktie CclesLijncnlaan 300 13, 3030 lleverlec, Belgium

Malkov, V.I'. Gorky University, Department of Solid Mechanics Gorky, 603600, USSR

Mattheck, C. Kernforschungszentrum Karlsruhe,IMI" IV Postfach 3640,7500 Karlsruhe, FIt Germany

Mlejnek. H.P.

XIII

Institute for Computer Applications, Universitiil Stuttgart Pfaffcnwaldring 27,7000 Stuttgarl80, FH Germany

Moldenhauer. H. 1m Bruckengarlen 9a, 6074 Hodermark, FH Germany

Morelle, P. Sam tech S.A. Bd. Frere-Orban, 25, 4000 Liege, Belgium

Muller. G. CAD-FEM GmbH 8017 EbersberglM unchen, FR Germany

Mullel'-Slany, H.H. Univcrsiliil-Gll Sicgen Fachbereich ll,lnsl. fUr Mcchanik und ltegelungstechnik l'aul-Bonatz-Str. 9 - II, 5900 Siegen, FR Germany

Olhofl', N. Aalborg U ni versity, Institute of Mechanical Engineering 9220 Aalborg, Denmark

Osyczka,A. Technical University of Cracow , Institute of Machine Technology Warszawska 24, 31-155 Cracow, Poland

Pedersen, P. 'rhe Technical University of Denmark, Department of Solid Mechanics, Bldg. 404 2800 Lyngby, Denmark

Post,P.U. Festo KG l'ostfach, 7300 Esslingen, FH Germany

Kadaj, D. Daimler Benz AG, Forschung Grundlagcn Postfach 60 02 02, 7000 Stuttgart 60, I>'R Germany

Ram merstorfer, I>'.G. TU Wien,lnstitut fur Leicht- und Flugzeugbau Gullhausstr. 25-29/317, 1040 Wien, Austria

Rasmussen, J. Aalborg University. institute of Mechanical Engineering Pontoppidanstraede 101,9220 Aalborg, Denmark

Reiter, Th. 'ru Wien, institut fUr Leicht- und Flugzeugbau Gullhausstr. 25 - 29/317,1040 Wien, Austria

i(odrigues, H.C. Technical University of Lisbon, Mechanical Engineering Department, institut.o Superior Tecnico 1096 Lisbon Codex, Portugal

XIV

ltovat.i.M. University of'l'rento. Department ofSLructural Mechanics and AutomaLion in Design Via Mesiano 77.38050 Trento, Italy

ltozvany. G. UniversiUiL-GlI Essen,1<'achbereich 10, Bauwesen Postfach 103764,4300 Essen 1. FR Germany

Sas .... Kath. UnivcrsiLeit Leuvcn, Mechanische KonsLrukLie en ProdukLie CelesLijnenlaan 300 B. 3030 Hcverlec, Belgium

Schirrmacber. H. InsLiLute for CompuLer ApplicaLions, UniversiUiL StuLLgarL PfafTenwaldring 27,7000 Stuttgart 80, I~U Germany

Seefielberg. Ch. Dornicr GmbH Postfach 1420,7990 I"riedrichshafcn, FU Germany

Specht, B. Dornier GmbH Postfach 1420,7990 Friedrichshafen, I"U Germany

Sprangers, W. RWTII Aachen,lnsLitutfiir Werkzeugmaschinen und Betriebslehre SLeinbachsLr. 53/54,5100 Aachen, I~R Germany

Taliercio. A. Politecnico di Milano, Dept. of Structural Engineering Piazza Leonardo da Vinci, 32, 20 133 Milano,ltaly

Tiefenthaler. P. CAD-I~I~M GmbH 8017 Ebersberg/Miinchen, 1<'U Germany

Toropov, V. V. Gorky University, DeparLment of Solid Mechanics Gorky, 603600, USSI~

Vietor, Th. Univen;iLiiL-Gll Siegen,l"achbereich ll,lnst. £iiI' Mechanik und l{egelungsLechnik Paul-Bonatz-SLr. 9 - 11,5900 Siegen,l"U Germany

Weck.M. ItW'J'11 Aachen, LehrsLuhl fiir Werkzeugmaschinen Stcinbachstr. 53/54, 5100 Aachen, FR Germany

Xicheng. W. Dalian University of Technology, Research Institute of Engineering Mechanics 116024 Dalian, China

Zhang.Sh. Daimler Benz AG, I~orschung Grundlagen Postfach 60 02 02, 7000 StutLgart 60, FU Germany

Zhou.M. UniversiLat-GH Essen,l;'achbereich 10, Bauwesen PosLfach 103764,4300 Essen 1,1"R Germany

Zyczkowski. M. Technical UniversiLy ofCracow,lnstituLe of Mechanics and Machine Design Warszawska 24, 31-155 Cracow, Poland