CAD CAM robotics and factories of the future volume II automation of design, analysis and manufacturing ( TQL )

The geometric modeling techniques are used for shape description in terms of boundary points fixed as well as design variables and geometric entities like lines, circular arcs and spline

Birendra Prasad (Editor)

CAD/CAM

Robotics and Factories

of the Future

Analysis and Manufacturing

3rd International Conference on CAD/CAM Robotics and Factories of the Future

(CARS and FOF'88) Proceedings

With 97 Figures

Springer Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong

Editorial Board

Chainnan

Birendra Prasad

Senior Engineering Staff

Artificial Intelligence Services

Technical System Development

Electronic Data Systems

D Sriram H.-P.Wang

DOI 10.1007/978-3-642-52323-6

This work is subject to copyright.AII rights are reserved, whetherthe whole orpart ofthe material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks Duplication of this publication or parts thereofis only permitted under the provisions of the German Copyright Law

of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid Violations fall under the prosecution act of the German Copyright Law

© Springer-Verlag Berlin, Heidelberg 1989

Softcover reprint of the hardcover 1st edition 1989

The use of registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use

216113020543210 -Printed on acid-free paper

Conference Objective

Improving cost competitiveness and remaining abreast in high nology are some of the challenges that are faced by a developing enterprise in the modern times In this context, the roles of engi-neering, manufacturing and plant automation are becoming important factors to enhance productivity and profitability, and thereby in-crease market share and product quality The commuter automobile, actively controlled car, the U.S space station, the unmanned plat-form, and commercial space ventures are all real life examples of a few explorations now being undertaken on earth and space - requiring a greater dependence by people on machines Complete shop floor automa-tion - a "lights out" plant may be unrealistic to many but automating and integrating the engineering and manufacturing process, where it makes sense from a cost/benefit stand point, are certainly viable

tech-u~dertakings

Hence, the objective of the Third International Conference on CAD/CAM, Robotics and Factories of the Future (FOF) is to bring to-gether researchers and practitioners from government, industries and academia interested in the multi-disciplinary and inter-organizational productivity aspects of advanced manufacturing systems utilizing CAD/CAM, CAE, ClM, Parametric Technology, AI, Robotics, AGV technolo-

gy, etc It also addresses productivity enhancement issues of other hybrid automated systems that combine machine skills and human intel-ligence in both manufacturing (aerospace, automotive, civil, electri-cal, mechanical, industrial, computer, chemical, etc.) and in non-manufacturing (such as forestry, mining, service and leisure, process industry, medicine and rehabilitation) areas of application such an exchange is expected to significantly contribute to a better under-standing of the available technology, its potential opportunities and challenges, and how it can be exploited to foster the changing needs

of the industries and the marketplace

Conference Scope

The conference included the following areas of active research and application:

CAED: CAD, CAT, FEM, Kinematics, Dynamics, Simulation, Analysis,

Computer Graphics, Off-line Programming

CIM: CAD/CAM, CNC/DNC, FMS, AGV, Integration of CNC, Interactions

between Robotics, Control, Vision, AI, Machine ligence, and other Automation Equipments, and communi-cations Standards

Intel-Design/Build Automation: Parametric Programming, Design, Sensitivity,

optimization, Variational Geometry, Generic Modeling, Identification, Design Automation, Value Engineering" Art

to Part, Quality, cost & Producibility

Knowledge Automation: Artificial Intelligence, Expert Systems

Robotics: Mechanical Design, Control, Trajectory Planning, Mobility,

End Effecters, Maintenance, Sensory Devices, Work Cells, Applications, Testing and Standardization

Factory of the Future: Planning of Automation, Management,

Organiza-tion, Accounting, Plant Design, Informative Systems, tivity Issues, Socioeconomic Issues, Education, Seminars and Training

Produc-Conference Theme

The theme of the 3rd International Conference was:

C4 (CAD/CAM/CAE/CIM) Integration, Robotics, and Factory Automation for improved productivity and cost containment

Association for computing Machinery (ACM), USA

National Science Foundation (NSF), USA

Society of Automotive Engineers (SAE), USA

Automotive Industry Action Group (AIAG), USA

Robotic Industries Association (RIA), USA

Electronic Data Systems (EDS), General

Motors Corporation, USA

The International Association of Vehicle

Design (IAVD), UK

International Society for Computational

Methods in Engineering (ISCME), UK

American Institute of Aeronautics and

Astronautics (MI) (AlAA), USA

American Society of Civil Engineers (MI) (ASCE), USA Center for Robotics and Advanced Automation

(CRAA), Oakland university, USA

American Society of Engineering Education (ASEE), USA Engineering Economics Division (EED-ASEE), USA

Japan Technology Transfer Association (JTTAS)

American society of Engineers from India (ASEI), USA Michigan society of Architects (MSA), USA

CAD/CIM Alert, Massachusetts, USA

Automation and Robotics Research Institute,

university of Texas at Arlington, TX, USA

Committee Chairpersons

Conference General Chairperson: Dr Siren Prasad, Electronic Data Systems, GM, USA

Program chairpersons: Dr Sur en N Dwivedi,

UWV, USA ; William R Tanner,

Cresap Manufacturing Cons., USA

Doug Owen, EDS, USA

Technical Chairpersons: Rakesh Mahajan,

Deneb Robotics, Inc., USA;

Dr Jean M Mallan, EDS, USA

International Chairpersons: Dr Ario·Romiti, Politechnico di Torino, ITALY ;

Dr Marcel Staroswiecki, Universite De Lille, FRANCE ; Dr Jon Trevelyan,

Computational Mechanics Institute, UK

Panel Session Chairpersons: Dr Frank Bliss, EDS, USA ; Dr Subra Ganesan,

Oakland University, USA

Workshops Chairperson: Dr Pradeep K Khosla, carnegie Mellon University, USA

Video/Tech Display Chairperson: Dr Addagatla

J G Babu, University of South Florida, USA Student Session Chairperson: Dr Hamid R Parsaei, University of Louisville, USA

Exhibits Chairpersons: Jon Keith Parmentier, Tektronix Inc., USA; Forrest D

Brummett, GM, USA

Receptions Chairperson: Umesh B Rohatgi, Charles

S Davis Associates Inc., USA;

Dr Bhagwan D Dashairya, Inventors Council of Michigan, Ann Arbor, MI, USA

Administration Chairperson: Dr Prakash C

Shrivastava, GM, USA

Conference Directory: Dr Yogi Anand, Consultant, Rochester Hills, MI, USA

Committees'Roster

PROGRAM COMMITIEE

Dr Sudhlr Aggarwal, Bell

Communications Research, USA

Dr, John S Bara., University 01 Maryland,

USA

Dr Marc Becque~ Unlverslt.' Ubro De

Bruulle., BELGIUM

Thomas H CaiaU, EDS, USA

James P Cal., GM, USA

Micha.1 F Carter, GM, USA

Dr, M Colsaltis, UGRA CEN.FAR FRANCE

J P Crestin, DDREET, FRANCE

Kenneth A Crow, Western Data Systems,

USA

Dr A F D'Sou:a, liT, USA

Catherln Foregon, DDREET, FRANCE

Michael J Frelling, Tektronix Lob., USA

Dr Ramana V Grandhl, Wright Stat

Dr Jack Horgan, Ari •• Technology, USA

Dr Ming C Huang, EDS, USA

Dr Ichlro Inou., NEC Corp., JAPAN

William B Johnson, Rockwell

International, USA

Dr Senlay Joshi, Pennsylvania Stat

University, USA

Richard B Katnlk, GM, USA

Dr Rakesh K Kapanla VPI & Stat

University, USA

Gerald A Kasten, NlA T.ch Corp., USA

Prof F Kimura, University 01 Tokyo,

JAPAN

Dr Andrew Kusiak, University of

Manitoba, CNlADA

Dr Hsin·VI LoI, North Carolina Ag & Toch

State Unlve"lty, USA

Dr Paiya Uu, Siemens Corp., USA

Dr Surosh M Mangrulkar, Ford Motor Co., USA

Dwight Morgan, GMF RoboUcs, USA

Dr Michael Mulder, UniverSity 01 Portland, USA

Yasuo Nagai, institute 01 New Generation Computer Technology, JAPAN

Dr Shlgeo Nakagakl, Toshiba Fuchu Works, JAPAN

Dr Los:lo Nemes, CSIRO, AUSTRAUA

Dr Elstratios Nikolaldls, VPI & Stat

Dr Sudhakar Paldy, Rochester Institut 01 Technology, USA

Prof V M Ponomaryov, Academy 01 Sciences, USSR

M.C Portmann, INRIA-Lorralne, FRANCE J.M Proth, INRIA·Lorraln., FRANCE Prof J G Postalro, Unlveralte' De Ulle, FRANCE

Dr Tim Pryor, Diffracto, Ud., CANADA Prof J Ragot, Unlverslte' De Nancy, FRANCE

Arthur D Rogers, Integrated Automation Corp., USA

Joseph D Romano, A T Koamey, USA

Dr Anll Salgal, Tulia University, USA

Dr Sunil Selgal, Worcester Polylochnlc institute, USA

Harshad Shah, Eagl Technology Inc., USA

Dr Rom P Sharma, Westem Michigan University, USA

Dr, Kang G Shin, University of Michigan, USA

Anthony R Skomra, AutomaUon Technology Products, USA

Dr William M Spurgeon, University 01 Michigan Dearborn, USA

Dr Raj S Sodhi, New Ja y Institute 01 Technology, USA

Rick Stapp, Auto Simulations Inc, USA

Dr Rajan Surl, University 01 WisconSin, USA

Dr Bharat Thacker, Universal Computer Applications, USA

Dr Joe Torok, Rochester Institute 01 TeChnology, USA

Michael J Tracy, Smith Hinchman &

Gryfls Associates Inc, USA

Dr H S T:ou, University 01 Kentucky, USA Don H Turner, Arthur Young & Co., USA Donald A Vincent, RIA USA

Dr Hsu·Pin Ben Wang, University 01 Buffalo, USA

Dr Peter Ward, SDRC Englneerlng Services Ltd., UK

Dr Ronald L Websler, Morton Thlokol Inc., USA

Dr Tony Woo, National Science Foundation, USA

Dr Wei Uang Xu, Beijing Instltule 01

Aeronautics & Astronautics PRC

Dr Y F Zheng, Clemson University, USA

Dr William J Zd.bllck, Molcut Res Associates, USA

Dr John S Zuk, Brooklyn PolytechniC University, USA

x

ADVISORY COMMITTEE

Tony Affuso, EDS, USA

Dr Carloa A er.bbla, W x In.tltut of

Rudi Gem, EDS, USA

W C Hamann, Ford Motor Company, USA

Dr Pierro Har.n, Intelligence Loglcl.lle,

FRANCE

Russ.1I F Henke, Automation T.chnology

Products, USA

Prof K Iwata, Kobe University, Japan

Dr Munlr M Kamal, GM Research

laboratorl.s, USA

Dr Marshall M Uh, National Science

Foundation, USA

Dr M E Merchant, Metcut Research

Associates, Inc., USA

Dr Howard Morall, National ScI.nce

Foundation, USA

Georg E Munson, University of

Califomia Santa Barbara, USA

Dr Jay Nathan, Unlv.rslty of Scranton,

USA

Dr G J OIling, Chrysl.r Motor., USA

Dr A P.t.rs, rNWA FRG

Kar.n L Resmussen, GM, USA

Robert B Schwar1l, Fru.hauf Corp., USA

Oonnls E Wisnosky, Wizdom Systems

Inc., USA

INDUSTRIAL COMMITTEE

W Robert Bu.II, Ford Motor Comparry,

USA

Edward J Carl, m, USA

Dr Robert G Cubensky, Chrysl.r Motors,

USA

Etim Sam Ekong, Unlsys Corp., USA

EdwIn J Fablszak, Jr., MSC/CAD COMP

Inc., USA

Dr Henry H Fong, MARC Analysis Research Corporation, USA

D Galara, EDF/DEFVSEP, FRANCE

Dr Dan G Gam., Davidson Research, USA John E Gotz, Fru.hauf Corporation, USA

Dr Abid Ghuman, Chrysl.r Molors, USA GI.nn R Gramling, Hewl.tt.Packard Company, USA

Jam.s D Hock, GM, USA

Dr ANn Jain, BP Am.rlca Inc., USA

Dr Hiroshi Kawanishl, NEC Corporation,

JAPAN

Dr Kant Kothawala, EMRC, USA

Dr Virendra Kumar, General E1.ctric Company, USA

Dr Peter A Marks, Automation Technology Products, USA

Dr Sanjay Mittal, Xerox USA Wallace M Murray, Morton Thlokollnc., USA

laJos Imre Nagy, Ford Molor Company, USA

Ram G Narula, Bachtel Corporation, USA

Dr Frank Plonka, Chrysler Motors, USA Donald L Smith, Ford Motor Company, USA

Dr Gerald A Thompson, Hughe Aircraft Co., USA

UNIVERSITY COMMITTEE

Dr David Ardayfoo, Wayne Stata University, USA

Dr V.S Chadd&, University of Ootrolt, USA

Dr John B Cheatham, Jr~ Ace University, USA

Dr Rollin C Oix, Ilinolsinstitut of

Dr Paul G Ranky, Unlv.rslty of Surr.y, UK

Dr S S Rao, Purdu University, USA

Dr Eugene I Rivin, Wayne Stat University, USA

Dr Rak.sh Sagar, South Bank Polyt.chnlc, UK

Dr Har.sh C Shah, Stanford University, USA

Dr Nanua Singh, Unlv.rsity of Windsor, CANADA

Dr Ouwuru Sriram, Massachusetts Institut of Technology, USA

Dr K.s Tararnan, lawr.nce Institut of T.chnology, USA

Dr Nar.n R Vir., Howard University, USA

Dr wayne W Walt.r, Rochest.r Institute

Maria Emilia Camargo (Santa Marla)

Edger Pereira (porto Alegre)

CANADA

B Manas Das (Calgary)

Mark B Zaremba (Hull)

DENMARK

Finn Fabricius (lyngby)

FRANCE

BourJault Alain (Besancon)

Phlilipe Pract (Besancon)

Marcel Staroswleckl (Vilienewe-D'Ascq)

Oaude Viebet (Evry)

A Morecld (Warsaw)

REPUBLIC OF CHINA Shul-Shong Lu (T Ipei) ROMmIA Voleu N Chloroanu (Slghetu Marmatiei) Mircea Ivaneseu (Cralova)

SPAIN

R Core (Madrid) THAlLmD

R Sadananda (Bangkok) UNITED KINGDOM John Billingsley (portsmouth) Carlos A Brebbla (Southampton)

M A Dorgham (Milton Keynes) David G Hughes (Plymouth) David Paul Stoten (BrIstol)

XI

Letter from the President, ISPE

Dear Participants and Guests;

1987-1988 was the best and the most fruitful year in the history of ISPE With your continued suppon and co-operation, ISPE has seen considerable growth and popularity You will agree that our focus is very much mainstream and activities are clearly aimed towards bringing all the peninent issues found in technological, business, socio-economic, and organizational horizons for discussion and resolution

After successful sponsorship of three conferences in the USA, ISPE is now sponsoring the Fourth Intemational Conference at 1.1 T Delhi, India during December 19-22, 1989 I hope, with your active participation and suppon, the fourth conference is bound to be a success

We would like you to know that your continued technical input, written to share constructive ideas and innovative development strategies have been our backbone your involvement has been the key to our success but our continued growth requires more efforts The society is constantly in need of creative ideas and experienced hands So far,

we have been carrying out the responsibilities with sustained contributions from a limited number of members Now, we are requesting your cooperation and help

With this letter, I extend a personal invitation to each of you to come up with fresh ideas and new ways of thinking - a pannership that can strengthen ISPE technical and financial foundations so that we could be more aggressive in promoting yours interests and improving the quality of life to which ISPE stands

With good wishes,

Dr Suren N Dwivedi West Virginia University Morgantown, West Virginia USA

ISPE Conference Mission

ISPE was founded in 1984 with the goal to accelerate the tional exchange of ideas and scientific knowledge with absolutely no barriers of disciplines or fields of technological applications The

strategy and 4M resources (manpower, machine, money and management) to enhance productivity - to increase profitability and competitiveness, and thereby improve the quality of life on land, sea, air and space One of the aims of the society is to provide opportunities for contact between members through national and international conferences, semi-nars, training courses and workshops The Society also aims to create

a channel of communication between academic researchers, neurs, industrial users and corporate managers

entrepre-ISPE embraces both the traditional and non-traditional fields of engineering, manufacturing and plant automation, all areas of computer technologies, strategic planning, business and control Equal empha-sis is being placed on the cross-fertilization of emerging technolo-gies and effective utilization of the above 4M resources

Acknowledgements

The Third International Conference on CAD/CAM, Robotics and

society for Productivity Enhancement (ISPE) and was endorsed by more than 18 societies, associations and international organizations The conference was held in southfield, Michigan at Southfield Hilton Hotel during August 14-17, 1988 Over 450 people from 12 foreign countries

forums (panels), 61 specialty sessions, 3 plenary sessions and 4

symposia were concurrently held

I wish to acknowledge with many thanks the contributions of all the authors who presented their work at the conference and submitted the

the role of keynote, banquet, and plenary sessions speakers whose contributions added greatly to the success of the conference My sincere thanks to all sessions chairmen and sessions organizers I believe that the series of the International Conferences on CAD/CAM, Robotics and Factories of the Future which emphasizes on cross-fertilization of technology, strategy and 4M resources (manpower, machine, money and management) will have a major impact on the correct use of productivity means - to increase profitability and competitive-ness, and thereby improve the quality of life on land, sea, air and space

I acknowledge with gratitude the help and the guidance received from the various organizing committees I also wish to extend my gratitude

to the sponsoring organizations Grateful appreciations are due to stUdent volunteers from Oakland University, Wayne State University, University of Detroit and University of Michigan for their enthusias-tic participation and help in organizing this conference Thanks are also due to all my colleagues, friends, and family members who extend-

ed their help in organizing this conference and making it a success

In particular, I acknowledge the help and cooperation extended by Electronic Data Systems (EDS) without which this would not have been possible

I would like to appreciate the excellent work done by Verlag in publishing this proceedings

Springer-B Prasad

Conference Chairman and Chief Editor

Conference Proceedings

The papers included in this volume were presented at the Third International Conference on CAD/CAM, Robotics and Factories of the Future (CARS & FOF '88) held in southfield, Michigan, USA during August 14-17, 1988

CARS & FOF '88 featured 11 panels, 6 symposia and 4 workshops The symposia covered six specific themes of productivity tracks (repre-senting foundations of connectivity) in "The Look of the Future in

Automated Factories" • Under each symposium, several key sessions were planned, focussing both on the opportunities and challenges of new or emerging technologies and the applications Over 250 papers from over

12 countries covering a wide spectrum of topics were presented in the following six symposia:

Symposium I: CAED - Product & Process Design

Symposium II: CIM & Manufacturing Automation

Symposium III: Design/Build Automation

Symposium IV: AI & Knowledge Automation

Symposium V: Robotics & Machine Automation

Symposium VI: Plant Automation & FOF

The conference proceedings are published in three bound volumes by Springer-Verlag The three Volumes are:

Volume I: Integration of Design, Analysis and Manufacturing

Volume II: Automation.of Design, Analysis and Manufacturing

Volume III: Robotics and Plant Automation

Volume I includes papers from Symposia I and II, Volume II includes papers from symposia III and IV, and Volume III includes papers from Symposia V and VI The papers presented in the panel sessions and plenary sessions are distributed to the Volumes based upon the subject matters The complete list of papers for all volumes are included at the end of each Volume

Preface

This volume is about automation - automation in design, automation

in manufacturing, and automation in production Automation is tial for increased productivity of quality products at reduced costs That even partial or piecemeal automation of a production facility can deliver dramatic improvements in productivity has been amply demon-strated in many a real-life situation Hence, currently, great ef-forts are being devoted to research and development of general as well special methodologies of and tools for automation This volume re-ports on some of these methodologies and tools

essen-In general terms, methodologies for automation can be divided into

or closed-loop, is fairly clearly understood In such a situation, it

is possible to create a mathematical model and to prescribe a matical procedure to optimize the output If such mathematical models and procedures are computationally tractable, we call the correspond-ing automation - algorithmic or parametric programming

mathe-There is, however, a second set of situations which include

process-es that are not well understood and the available mathematical models are only approximate and discrete While there are others for which mathematical procedures are so complex and disjoint that they are

heuristics are quite suitable for automation We choose to call such automation, knowledge-based automation or heuristic programming

The papers in this volume range from highly theoretical to ized treatment of very practical problems The techniques borrowed from artificial intelligence have to do with the use of knowledge bases, the art of reasoning, and the application of the concept of expert systems These papers, more or less, divide themselves into the following four chapters:

The works reported in the first two chapters of this volume deal with algorithmic/parametric programming The rest of the volume deals with heuristic programming

Contents

CHAPTER I: Computer-Aided Design

Introduction •.••• •• ••• •••• ••.••••••.•••••.•.• 1 I.l Shape Optimization • • • •••.•••••• • 3

A Geometry-Based 2-Dimensional Shape Optimization

Methodology and a Software System with Applications

V Kumar, M.D German, and S.-J Lee ••• ••.•••.•• • 5 optimum Design of continuum Structures with SHAPE

E Atrek, and R Kodali •• ••• •• •• •• • • 11 The Velocity Field Matrix in Shape optimal Design

A.D Belegundu, and S.D Rajan •.•••• ••••••••• • •• •• 16 Implementation Issues in Variational Geometry and

Constraint Management

J.C.H Chung, J.W Klahs, R.L Cook, and T Sluiter ••••••.• 22 I.2 Probabilistic Design Optimization •.•• •• ••• ••.•••••• 29 Probabilistic Vibration Analysis of Nearly Periodic Structures K.F Studebaker, and E Nikolaidis •• •• •• 31 Experience Gained From First-Order Reliability Methods (FORM)

in Structural Analyses

D Diamantidis .•• •• •••.•.• •• • • 36 Reliability Analysis of Layered Cylindrical Structures

under Combined Mechanical and Thermal Loads

S Thangjitham, and R.A Heller ••• •• • • 41 Design Reliability optimization Using Probabilistic Design

Approach and Taguchi Methods

optimization of Frame structures with Thin Walled

sections of Generic Shape

S Belsare, M Haririan, and J.K Paeng ••• ••••.•.• 55 Optimal Design of Box Beams with Coupled Bending and Torsion Using Multiple Frequency Constraints

R.V Grandhi, and J.K Moradmand •.••• •••••••••••.•• •••• 60 Experiences on Analysis and Optimal Design of Pyramidal

Truss Panels

M.A Wiseman, J.W HOu, and T.A Houlihan •.•••••••••.•• • 65

A Computational Procedure for Automated Flutter Analysis

D.V Murthy, and K.R.V Kaza •• •.•.• ••••• ••.• • • 71

Boundary Element Structural Analysis Formulation

J.H Kane, and M Stabinsky •••••••••••••••••••••••••••••••• 84 Lagrangian Interpretation of Nonlinear Design sensitivity

Analysis with continuum Formulation

J.B Cardoso, and J.S Arora ••••••••••••••••••••••••••••••• 90

A New Reanalysis Technique Suitable of Being used in Design Automation and Opeimization

M No, and s Lopez-Linares •••••••••••••••••••••••••••••••• 95 Calculating Functionals for Arbitrary Geometries

A Tristan-Lopez ••••••.•••••.••••••.••••••••.•••••••••••••• 100 I.5 CAD/CAM Automation ••••••••••••••.•••••••••.•••••••••••••••••• 105

A Graphics User Interface for Interactive Three Dimensional Free-form Design

P.J stewart, and K.-P Beier •••••••••••••••••••••••••••••• 107 XCAD: A CAD Object-oriented Virtual Solid Modeler for an

Expert System Shell

B Trousse ••••••••••••••••••••••••••••••••••••••••••••••••• 112 Chapter II: Automation in Manufacturing

Introduction ••••••••.•••••••••••••••••••••••••••••••••••••••• 117 II.1 Planning and Control •••.•••••••••••••••••••••••••••••••••••• 119 Decentralization of Planning and Control in CIM

S.K Taneja, S.P Rana, and N Singh •••••••••••••••••••••• 121

An Intelligent Tactical Planning System: The Integration of Manufacturing Planning Islands Using Knowledge Based

Technology

M.D Oliff, J Davis, L Vicens ••••••••••••••••••••••••••• 126 Automated Process Planning for Mechanical Assembly Operations

J Yung, and H - P • Wang ••••••••••••••••••••••••••••••••••• 131

An Unorthodox Approach to Job-Scheduling

H Bera •• ••.•• •.•••.•••••••••••••.••.••••••.•• 136

XIX

II.2 Group Technology ••••••••• •••.••••••••••.•••.• •••••••• 143 Development of a Group Technology Workstation

R.M Mackowiak, P.H Cohen, R.A Wysk, and C Goss ••••.••• 145

A Comparison of Hierarchical Clustering Techniques for

Part/Machine Families Formulation

C.-H Chu, and P Pan ••.• •.•.••••••••••.••• ••••••••• 150

An Application of Fuzzy Mathematics in the Formation of

Group Technology Part Family

H Xu, and H.-P Wang •••••••••• •••••••.• •••••.••• 155 Automatic Generation of Production Drawings and Part

Routings for Valve Spools

s.P Pequignot, and A Soom •.• •• • • ••• 160 Chapter III: Applications of Artificial Intelligence

Introduction ••••••• •.••• •• •.•.•.•.•••• 165 III.l AI Tools • •.•.••••.••.•••• ••• • •••••.••••.• 167

THINK: A C Library for Artificial Intelligence Tasks

M.E Grost .•• •• , ••.• •• • •• 169 Using Artificial Intelligence Paradigms in Solving

Manufacturing Problems Demonstrated in the CPC

Stacking/Des tacking Expert System

An Interactive Refutation Learning Approach for Skill

Acquisition in Knowledge-Based CAD System

P.H Cohen, and B Bidanda ••.•.•.•••••••••••••••.•••.•••• 207

xx

III.3 Decision Support Systems ••••••••••••••••••••••••••••••••••• 213

A Frame-Based User Enquiry Method for Supporting strategic Operations Planning

Construction of a Knowledge Base for the Detection of

Decision Errors

F Mili, D Shi, and P Zajko •••••••••••••••••••••••••••• 220

On Representing Human Heuristic Reasoning

F Mili, and A Noui-Mehidiidi ••••••••••••••••••••••••••• 225 Chapter IV: Expert Systems

Introduction ••••.••••••••••••••••••••••••••••••••••••••••••• 231 IV.1 Expert Systems for Diagnostics ••••••••••••••••••••••••••••• 233

An Expert System to Diagnose Failures in Industrial Robots S.R Vishnubhotla •••••••••••••••••••••••••••••••••••••••• 235

An Operations Analysis Expert System for Fiberglass

Expert System for Specifying of CAD Software Systems

K Ghosh, L Villeneuve, and N.D Tai •••••••••••••••••••• 253

An Expert System for IC Factory Design

P.K Ramaswamy, and T.-L Wong ••••••••••••••••••••••••••• 258 Towards an Expert System Architecture for Routine Design

- Focusing on Constraint Representation and an

Application Mechanism for Mechanical Design

Y Nagai ••••••••••••••••••••••••••••••••••••••••••••••••• 263 Knowledge-Based Design Aid for Axisymmetric casting Parts I.C You, C.N Chu, and R.L Kashyap ••••••••••••••••••••• 268 IV.3 Expert Systems for Scheduling, Assembly, and Planning •••••• 275

Expert System Supervision of Robots During a

Vision-Assisted Assembly Task

J.B Cheatham, C.K wu, Y.C Chen, and T.F Cleghorn ••••• 277 Intelligent Lot-Size Advisor for MRP Systems

C.H Dagli ••••••••••••••••••••••••••••••••••••••••••••••• 282 Intelligent Scheduling Systems for Parallel Machines with Different Capability

G Leininger ••••••••••••••••••••••••••••••••••••••••••••• 287 Expert System-Based Finite Scheduler

K Barber, K Burridge, and D Osterfeld ••••••••••••••••• 291 Contents of Volume I •••••••••••••••••••••••••••••••••••••••••••••• 297 Contents of Volume III •••••••••••••••••••••••••••••••••••••••••••• 302 Author Index (Volume II) ••••••••••••••••••••••••••••••••••••••••• 307

Invited Lectures

Keynote Speech:

Eric Mittelstadt,

President and Chief Executive Officer, GMF Robotics

Auburn Hills, MI, USA

Banquet Speech:

Senator Carl Levin,

Chairman, Senate Small Business Sub Committee on

Innovation, Technology and Productivity,

US Senate, Washington, DC, USA

Plenary Sessions:

A Case for Computer Integrated Manufacturing

President and Chief Executive Officer,

Allen Bradley Co., Rockwell International, pittsburgh, PA, USA Future Trends in AI/Robotics - A Pragmatic view

Director, Design Productivity Center,

University of Missouri, Columbia, MO, USA

A New Departure in Programmable Robotic Design

G.N Sandor,

Research Professor and Director, M.E Design and

Rotordynamics Labs, University of Florida,

Gainesville, FL, USA

Cost Management as the criterion for Integrated Design and Manufacturing

Ali Seireg,

Mechanical Engineering Department, university of wisconsin,

Madison, WI, USA

Earth observing Satellite System

University Professor of Computer Science and Director

Robotics Institute, Carnegie Mellon University,

pittsburgh, PA, USA

Engineering Research Centers - A Vision for the 90's

Howard Moraff,

Program Director, Cross-Disciplinary Research,

National Science Foundation,

washington, DC, USA

Robots Beyond the Factory

W.L Whittaker,

Robotic Institute, Carnegie Mellon University,

pittsburgh, PA, USA

Parametric programming is a concept of automating the product design-development cycle by capturing its knowledge in terms of parameters It maintains the real-world relationships between model elements, their physical characteristics and the environments The generic modeling, analysis, and optimization are used as integral parts of the design In this way the parametric system "knows" the identity and behavior of the individual part as well as the environ-ment in which it fits or is subjected to, with all information resid-ing symbolically in a unified data base

This goes beyond the conventional CAD method of capturing geometry

in terms of points, lines and surfaces in a typical CAD/CAM system The algorithmic or parametric programming is based upon the exploita-tion of basic characteristics of the products' life cycle, which are

"generic" in nature The idea is similar to that of creating an

"expert system" except that the knowledge is derived largely from algorithmic sources Heuristic plays a smaller role

The first section of this chapter reports on the advances that have been made in developing techniques for shape optimization The parametric methodologies which are employed for probabilistic reliability analysis, and optimization are the subject of the second section The third section provides some practical examples of optimum design application The fourth section deals with the elements of design methodologies, which are relevant to algorithmic or parametric programming, while the final section reports on the ad-vances in CAD/CAM automation areas

The papers of this chapter are divided into the following sections: I.1 Shape optimization

I.2 Probabilistic Design optimization

I.3 optimum Design Applications

I.4 Design Methodologies

I.S CAD/CAM Automation

Shape Optimization

A Geometry-Based 2-Dimensional Shape

Optimization Methodology and a Software System

with Applications

V Kumar, M D German and S -J Lee

Corporate Research and Development

General Electric Company

Schenectady, New York 12301

Summary

A geometry-based shape optimization methodology and a software system is presented for design optimization of 2-D solids Geometric modeling techniques are used for shape description and for formulation of the optimization problem An automatic mesh generation method is employed for creating the finite element model initially and during the optimization iterations The design optimization of a turbine disc is discussed as an illustrative example

Introduction

There has been a tremendous interest in recent years in using the numerical optimization ogy for structural and mechanical design for a variety of reasons From a technical viewpoint, it provides a quantitative, systematic and computer-automatable interface between engineering and design From a business point of view, on the other hand, it offers a procedure for achieving an optimal or the best possible design with several potential payoffs: weight (and therefore cost) reduction, improved performance and increased engineering productivity Shape optimization is one of the most important topics in structural optimization, and it refers to design of two- and three-dimensional structural components in which the geometry or topology varies during optimi-zation iterations and, therefore, constitutes design parameters The pioneering work of Bennett and Botkin [1-3] on this subject has created interest in both academia and industries, and as a result several papers and reports have been published during the past few years [4-6]

technol-This paper presents a two-dimensional (2-D) shape optimization methodology and an associated software package, SHAPE-OPT, with applications to practical design problems The overall technical approach is based on the integration of concepts of geometric modeling, automatic mesh generation, numerical optimization, finite element methods and pre- and post-processing The geometric modeling techniques are used for shape description in terms of boundary points (fixed

as well as design variables) and geometric entities like lines, circular arcs and splines The tural optimization formulation is also carried out at the geometry level in that the stress and other design constraints are specified in terms of boundary points, geometric entities and domains rather than individual finite elements or mesh points Automatic mesh generation is employed for creating the initial finite element model and also for automatic remeshing as the shape changes during optimization The issues of mesh updating between two successive remeshing and for design sensitivity calculations are also addressed together with a shape control procedure The commercial fInite element code ADINA [7] is employed for structural analysis, and a public-domain software package COPES/ADS [8] is used for numerical optimization The post-processing software packages MOVIE.BYU, SUPERTAB and PLOTlO are utilized for

Integration of Finite Element Analysis and Numerical Optimization

Essential elements of integrating a finite element software with a numerical optimization code are the design sensitivity analysis and an interface program between analysis and optimization pro-grams In the present work, both the finite difference and the semi-analytical (or implicit differentiation) approaches were implemented in the ADINA code for design sensitivity computa-tions The finite difference method was implemented external to ADINA, whereas the semi-analytical approach required substantial internal finite element enhancements Both size and shape optimization problems were considered, for static as well as dynamic cases and encompass-ing a wide range of element types (truss, beam, plate and 2-D continuum) Centrifugal and ther-mal loadings were also included for 2-D solid elements The technical issues involved and their ADINA implementation, a comparison of the two approaches in terms of computational efficiency, solution accuracy and the ease of software implementation, and other related topics will be discussed at length in a forthcoming article [9]

Subsequent to the development of the ADINA design sensitivity analysis procedures as described above, a number of interface programs were developed between ADINA and the optimization software ADS First, an optimizer to analyzer processor OPT-AN was developed which automati-cally updates an ADINA input file to incorporate shape and/or size design changes that occur during various optimization iterations Similarly, an analyzer to optimizer processor AN-OPT was also developed which, through an intermediate binary output file BOF, takes the ADINA output file as the input, computes objective functions and design constraints as specified by the user and transmits this data to the optimizer The AN-OPT processor and the BOF file were also interfaced with a number of post-processing software packages like MOVIE.BYU and SUPERTAB so that the user can display the structural shape, stress contours, iteration histories

of objective functions and constraints and other analysis/design quantities of interest These developments will be described in detail in reference [9]

Geometry-Based Shape Description, Attribute Specification and Problem Formulation

An approach was developed for shape description and contro~ attributes or boundary conditions specification, and optimization problem formulation at the geometry level rather than the finite element level by using the geometric modeling techniques Specifically, an in-house geometric modeler BZGEOM [10] was used, but the concepts developed are generic and can be readily applied with most of the commercially available geometric modeling software packages In this

approach, the shape is described in terms of boundary points and boundary curves (lines, circular arcs and cubic splines) to form simple- or multiple-connected regions Boundary points and curves which are permitted to vary during optimization are termed design points and curves, respectively Design variables are specified in terms of Cartesian coordinates of design points A concept of shape design variable linking was evolved that allows the user to specify different design models (i.e., number and distribution of design variables, and number and types of design curves, etc.) at different optimization stages during the input file preparation stage without having

to restart new batch jobs Similarly, shape control procedures were introduced to eliminate shape

7

irregularities during optimization iterations, for example, by including constraints on slopes and curvatures at certain boundary points These developments are not elaborated upon here any further because of text limitations, but the relevant details can be found in reference [11]

The attribute specification for traction/displacement boundary conditions and the optimization problem formulation, i.e., objective function and constraints, is also carried out at the geometry level in terms of boundary points, boundary curves and zones rather than at the level of finite ele-ments and associated node points This procedure provides an effective treatment of deaJing with different number of nodes and elements that arise when an automatic mesh generator, to be dis-cussed in a subsequent section, is used to create new finite element models for updated shapes at various optimization iterations If the design constraints were tied to elements and nodes, the number of constraints will change when the shape is remeshed using automatic mesh generator, and this in turn will cause several fundamentally technical as well as software development related problems For similar reasons, many difficulties would also arise if the traction and displacement boundary conditions were specified in terms of elements and nodes In the present work, an in-house software MAP_LOADS [10] was utilized for specifying attributes at the geometry level in

an interactive manner via the use of the geometric modeler BZGEOM It allows linear and splined distributions of pressure and displacement along a line, arc, or spline, and some enhance-ments were also made for specifying fixed displacement, concentrated forces and prescribed tem-perature distributions A number of interface programs were developed for integrating BZGEOM, MAP_LOADS and an automatic mesh generator which is described next

Integration With Automatic Mesh Generation

Shape changes resulting from optimization iterations require updating of the mesh used in the finite element analysis When these changes are small, the mesh can be updated by relocating the nodes, i.e., by utilizing the r-method of mesh refinement For moderate or large shape variations, however, it becomes necessary to modify the mesh topology itself, requiring thereby an altogether new fInite element model The present study employs an in-house geometry-based, fully automatic, 2-D continuum, finite element mesh generator, QUADTREE [12,13], for creating the initial finite element model and also for automatic remeshing as the shape changes during optimi-zation iterations Using the shape description file from the geometric modeler BZGEOM as the input, the QUADTREE software develops through a number of file format translators, the finite element connectivity and nodal data as required by the ADINA input file in a fully automatic manner without the user's intervention Complete remeshing is not required at each optimization iteration; it is performed only when shape changes are significant to warrant an entirely new mesh according to a user supplied criterion The mesh is otherwise updated by simply relocating the boundary nodes followed by the Laplacian method of interior smoothing

The shape design sensitivity analysis involves perturbing a shape design variable by an infInitesimal amount, performing the finite element analysis of the perturbed geometry, and then using the finite difference method (or the semi-analytical approach) to calculate the required gra-dients Automatic remeshing or the use of QUADTREE is not necessary for creating the finite element mesh of the perturbed geometry It is obtained from the mesh associated with the unper-turbed shape by moving the boundary nodes to the perturbed boundary and employing a geometric modeling utility software Since the shape perturbations for design sensitivity calcula-tions are rather small and only one design variable is changed at one time, the interior smoothing

is generally not required It is important to remark that the application of QUADTREE or some

8

other automatic mesh generator is not recommended in the present context since it often leads to inaccurate sensitivity results and several other numerical problems The reason for this is that even for small shape perturbations the QUADTREE software usually results in a different number of elements with a different mesh topology, invalidating the design sensitivity defInition

An Illustrative Problem

The methodology and the software system described above was successfully applied to a variety of 2-D shape optimization problems including the design of a turbine disc as illustrated in Figure 2 The optimization problem in this case consists of fmding the axisymmetric shape which would

minimize the weight of the disc while satisfying constraints on radial, tangential and Von Mises stresses, burst margin and geometric dimensions The shape is described by 16 boundary points connected by 8 boundary curves as shown by numbers enclosed in circles There are 5 design points, designated by ® , with the design variables in the thickness direction as shown by the arrows The disc is subjected to centrifugal and thermal loading, and the loading due to blades is also applied in the form of a uniform pressure at the rim The geometry-based specification of some of the constraints is also shown in Figure 1, clearly denoting that the optimization problem

is formulated in terms of the geometry rather than elements and nodes Two different initial designs, shown in Figure 2a together with the automatically generated QUADTREE meshes, were tried The corresponding final or optimal designs obtained upon convergence of optimiza-tion iterations are illustrated in Figure 2b It is found that both starting designs result in almost the same optimal designs in terms of the disc shape and weight, stress distributions, and the burst margin constraint We observe from Figures 2a and 2b that the fmite element models for initial and optimal designs are quite different from each other, and in fact the QUADTREE meshes changed continuously as the shape was updated by the ADS code during the optimization process This observation clearly demonstrates the necessity of integrating an automatic mesh generation software into an effective and practically usable shape optimization methodology For both the cases considered here, it took less than 10 optimization iterations to converge to the optimal design Similar results were obtained for several other turbine disc design problems [11]

Discussions

Although the SHAPE-OPT software system involves commercial, public-domain and in-house software packages, the methodology presented herein is generic and can be readily adapted to any other choice of software packages When applying SHAPE-OPT to shape design problems with intricate geometries, it became evident that considerable further research is required for shape description and shape control procedures For example, the final (or optimal) shapes in some cases showed unacceptable kinks at some boundary points, slight bumps with an opposite sign curvature and similar other geometric irregularities One approach to address such shape control related issues would involve specifying additional geometric constraints in the optimization prob-lem formulation, for example, the continuity of slopes and curvature signs at certain boundary points Another viable approach of smoothing slight irregularities in the optimal shape would be

to employ the optimal design sensitivity methods In regard to further work on the methodology developed, 3-D shape design problems and integration with adaptive structural problems offer many potentials Similarly multidisciplinary shape optimization, for example design problem requiring simultaneous thermal, structural and fluid, etc., analyses, using a geometry-based approach is a topic of great interest from both research and applications viewpoints

9

Acknowledgments

This work was supported jointly by the GE Research and Development Center in Schenectady, New York, and the GE Aircraft Engine Division in Lynn, Massachusetts Discussions with Mr Jan Aase at GE, Lynn, are gratefully acknowledged

7 "ADINA User's Manual," ADINA R&D, Inc., Watertown, Massachusetts, December 1984

8 G N Vanderplaats and H Sugimoto, "A General Purpose Optimization Program for Engineering Design," Int J Comp Struct., Vol 24, No.1, 1986

9 V Kumar, S J Lee and M D German, "Finite Element Design Sensitivity Analysis and Its Integration with Numerical Optimization for Engineering Design," to appear as GE TIS Report, Schenectady, New York, 1988

10 B W Shaffer, "BZANS User's Manual," GE Aircraft Engine, Lynn, Massachusetts, 1988

11 V Kumar, M D German and S -J Lee, "A Geometry-Based 2-Dimensional Shape

Optimi-zation Methodology and a Software System with Applications," to appear as GE TIS Report, Schenectady, New York, 1988

12 M S Shephard and M A Yerry, "Approaching the Automatic Generation of Finite ment Meshes: ASME J of Comp in Mech Eng., 1983, pp 49-56

Ele-13 C M Graichen and A F Hathaway, "QUADTREE-A 2-D Fully Automatic Mesh erator," GE Report, Schenectady, New York, 1988

specification for an illustrative turbine disc optimization

Optimum Design of Continuum

Structures with SHAPE

E ATREK and R KODALI

Engineering Mechanics Research Corporation

1707 West Big Beaver Road

Troy, Michigan 48084 U.S.A

Summary

SHAPE is a finite element program designed for industrial applications in the shape optimum design of continuum structures No boundary parameterization is required, the structure being represented simply by the finite element model Solids, shells, plates, and plane-stress systems can be optimized under the action of multiple load cases and with multiple constraints on the stresses and on the displacements Prescribed regions of the initial design may be frozen as a means of imposing certain manufacturing constraints The program outputs complete information for each design improvement

Introduction

Structural shape optimization may be viewed as the transformation of the initial domain that the structural shape occupies into a different domain in order to minimize the material volume or cost while satisfying quantifiable constraints mainly related to response and manufacturing Most work up to date has interpreted the domain transformation as the smooth transformation of the initial boundaries into the final boundaries As such, the shape change is basically due to the relocation of points describing the initial boundaries Practically, this approach is implemented by modeling the boundaries of the shape by parametric curves (2-D) or surfaces (3-D), the control nodes of which will relocate to describe the change in shape during the optimization process [e.g see 1,2] The difficulty of properly parameterizing the boundaries for optimization purposes, especially for solids of some complexity, and the need to re-mesh the related finite element model as the elements get distorted due to the boundary variation have been two major obstacles in the widespread acceptance and industrial implementation of this approach

SHAPE, on the other hand, will allow the general domain transformation, currently insofar

as the optimum design is contained within the initial domain In this case, the problem simplifies to that of deciding what "points" in the initial design will remain in the final design These points are approximated by small and simple finite elements, the deletion and recovery of which describe the changes in shape If desired, the process can be limited only

12

to the instantaneous boundary layer of elements, and is then equivalent to the special case of boundary transformation as aimed at with the parametric boundary approach Thus, SHAPE eliminates the need for boundary parameterization and large design changes can be accomplished without the need for mesh refinement

Program Description

Input and Output: SHAPE consists of structural senSitIvIty, optimization, and geometry

database management modules completely integrated with the NISA II finite element analysis program [3] by means of interwoven logic As such, it accepts the NISA II finite element model input along with the required optimization input

Whereas the NISA II type input contains the information necessary for analysis of the initial design submitted to SHAPE, the optimization input provides mainly the information regarding design constraints, such as the limiting (allowable) values for response quantities and the description of those regions of the design that are frozen The response quantities on which limits may be specified consist of stresses and displacements at various locations in the structure, and the limiting values may be different for each location as well as for each load case the structure is to be optimized against The frozen regions may include loaded and supported zones in addition to those regions where the design is well defined Other input consists of the allowable number of iterations and information regarding symmetry and/or anti-symmetry boundary conditions used in the initial model

For each improvement in design during execution, a new NISA II type input file is generated along with an updated optimization input file A boundary smoothed NISA II type input file

is also output where the boundaries have been filtered to eliminate the effects of element size A file with a summary of the design procedure and a table of design history is separately output at the completion of execution

The files generated for each improved design may be used with SHAPE or NISA II for a single analysis to create post-processing files that can be read by DISPLAY [4] for viewing the shape or for plotting response contours They may also be used to restart SHAPE, or for editing to produce a more refmed design or are-meshed fmite element model

TheoreticalOverview: For solution of the stiffness equations, SHAPE utilizes the wavefront

solution routines of NISA II The sensitivity analysis which relates the constrained response quantities to the internal design variables is based on a virtual load approach involving only the solution of multiple right hand sides Sensitivity analysis is done only for a set of

"active" or "critical" constraints

13

Major design changes are accomplished through the Lagrange multiplier formulation and the subsequent generation of optimality criteria expressions At a given design, these expressions can be posed as an optimization sub-problem and solved for an automatically selected set of "active" constraints This solution is then used to arrive at the new design Based on the quality of this new design, SHAPE decides on whether to update the active set and re-solve the optimality criteria problem, or to accept the design and to continue into the next stage of optimization In general, several steps of active set updating and re-design may

be necessary at this stage

The next stage involves a series of intermediate designs aimed at increasing the efficiency of the design to try and insure that the optimum design will remain a subset of the most efficient design obtained in this stage "Virtual volume" defined as the ratio of the material volume to the most criticai factor (limiting value of response/actual value of response) is used as a measure of efficiency both in the optimality criteria solution and in the

intermediate design stages It has been found that this is a very effective method of avoiding

most local optima

During the design changes, SHAPE keeps track of the current boundaries, recognizes any holes or breaks that may form, and fills in any internal hinges that may arise

Examples

Fillet: The fillet of Fig 1 or its variations have been investigated extensively by other researchers [e.g see 5-8] The objective is to minimize the stress concentration factor by varying the shape of the fillet The "most efficient design" concept used in SHAPE is directly applicable to this type of problem as the resulting shape of Fig 2 will indicate The maximum smoothed von Mises equivalent stress is reduced from that for the initial design

by a factor of 1.24 For this example, design changes were limited only to the instantaneous boundary of the fillet The contour lines shown in Figs 1 and 2 are for the von Mises equivalent stress For this and the other examples, the final shapes are directly from the boundary smoothed output files

Fig 1 Fillet initial shape Fig 2 Fillet final shape

14

Piston (Fig 3): This is an example of a solid continuum problem where design changes are allowed anywhere except for regions frozen at the outset (outer surface of crown and the skin to a given distance from top of crown, as well as around the pin hole) Under the action of pressure on the crown and body forces due to acceleration, and with a limit on the von Mises equivalent stress, optimization yielded an almost 50% lighter shape (Fig 4)

Fig 3 Piston initial shape Fig 4 Piston final shape

Upper Control Ann (Fig 5): The design of this automotive component required satisfaction

of different limits on the von Mises equivalent stress under the action of nine load cases The design variation was limited only to the instantaneous boundary with material being frozen around the holes The obtained shape shown in Fig 6 satisfies all constraints and is over 35% lighter than the starting shape

Fig 5 Upper control arm initial shape Fig 6 Upper control arm final shape

15

Plate in bending: The simply supported plate of Fig 7 is loaded nonnal to its plane at the

middle, at which point there is a constraint on the displacement in the direction of the load The final shape is given in Fig 8 The contour lines shown are for the out-of-plane translation Some material was frozen at the comers to guarantee minimum support

Conclusion

SHAPE is the first widely available practical finite element program for shape optimum design of structures It can be used to create new designs from generic shapes as well as to refine existing designs

References

1 Botkin, M.E et al, "Shape Optimization of Three-Dimensional Stamped and Solid Automotive Components", The Optimum Shape (lA Bennett, M.A Botkin, eds.), Plenum Press, N.Y (1986) 235-257

2 Fleury, c., "Shape Optimal Design by the Convex Linearization Method", ibidem, 297-320

3 NISA II User's Manual, E.M.R.C., Troy, Michigan 1988

4 DISPLAY II User's Manual, E.M.R.C., Troy, Michigan 1988

5 Schnack, E., "An Optimization Procedure for Stress Concentration by the Finite Element Technique", UNME, 14 (1979) 115-124

6 Haug, E.l et aI, "A Variational Method for Shape Optimal Design of Elastic Structures", New Directions in Optimum Structural Design (E Atrek et al, eds.), Wiley, Chichester (1984) 105-137

7 Kikuchi, N et aI, "Adaptive Finite Element Methods for Shape Optimization of Linearly Elastic Structures", The Optimum Shape (J.A Bennett M.A Botkin, eds.), Plenum Press, N.Y (1986) 139-166

8 Soarez, C.A.M., Choi, K.K., "Boundary Elements in Shape Optimal Design of Structures", ibidem, 199-228

The Velocity Field Matrix in Shape Optimal Design

A.D Selegundu and *S.D Rajan

Mechanical Engineering Department

The Pennsylvania State University

University Park, PA 16802

*Civil Engineering Department

Arizona State University

Tempe, AZ 85287

Introduction The [Q] Matrix

The problem of finding the optimum shape of an elastic body which minimizes an objective function subject to performance

constraints is considered here Shape optimal design of structural and mechanical components has infused interest and excitement into the general area of computer-aided design One of the earliest work involving finite elements and numerical optimization is by Zienkiewicz and Campbell Since then, several researchers have solved a variety

of problems such as the shape optimal design of connecting rods, automobile components, dams, turbine blades, and bicycle chain links Comprehensive surveys on shape optimal design have been published recently [1,2]

As opposed to the sizing problem in optimal design, the shape problem requires finding a function defining the shape even if this function is parametrized in terms of a finite number of design

parameters Consequently, the smoothness of the boundary is an

important aspect of the problem In addition, the shape should

satisfy designer's needs such as a portion of the boundary remain unchanged, straight lines remain straight, symmetry, and so on It is shown below that these issues indeed relate to the definition of design variables and the scheme used for internal node movement Consider a finite element model of a structure Since the number

of grid points in the model may be large, one has to choose a

relatively small set of design variables that characterize the shape

of the structure, and then relate changes in these design variables to changes in the grid point locations This relation can be expressed

by introducing a 'velocity field matrix,' [Q], as follows Let G be

an (n x 1) vector consisting of the X-, Y- and Z- coordinates of-each grid point Then, we have

where b - (k x 1) design variable vector, and [Q] - dG/db From Eq (I), we note that the columns of [Q] are used to update the geometry Consequently, restrictions on smoothness and other designer's needs mentioned above depend on [Q] Further, [Q] also affects the

distortion of the finite elements as the shape is updated As

discussed below, [Q] can be generated using either natural approach or geometric approach

where gi is the ith column of [Q] and 1i represents a unit load acting

at the ith "control" node The design variables are the magnitudes of the fictitious loads In (2), [Ka] is the stiffness matrix of the auxiliary structure The auxiliary structure has the same shape as the primary (or original) structure but has different boundary

conditions, material properties, and can also have stiffner elements The idea is to model the auxiliary structure in such a manner as to satisfy design requirements

The problem of maintaining a smooth boundary is well exemplified

by the 3-0 cantilever beam problem first examined by Imam [5J Unless special care is given to boundary smoothness, the optimum shape is very irregular and unacceptable Here, beam stiffners are used to generate a smooth shape Consider the 3" x 3" x 18" beam in Fig 1 drawn in perspective view, fixed at one end and loaded at the other The total load at the free end - 2,000 lbs The beam is modeled using

8~node solid (SL08) elements E - 29.5 x 106 psi, v - 0.29, oa

-15,000 psi, NE - 64, NN - 135 The initial design is feasible

The auxiliary structure is also modeled using SL08 elements, and fictitious pressure loads are applied at the free end of the beam

(Fig 2) with a total of 2 design variables In addition, the

auxiliary structure is modeled using longitudinal beam elements (Fig 3) along the boundary Since beam deflections are Hermite cubics, the optimized shape can be expected to be smooth This is in fact the case, as shown in Fig 4, corresponding to a 32% reduction in weight

in 4 iterations The beam stiffners have a dramatic influence in

ensuring that the velocity field is acceptably smooth

Geometric Approach

In the geometric approach, several types of geometric quantities have been used as design variables The earliest approach used the nodal coordinates of the boundary nodes as design variables Not only

is the number of design variables large but final shapes are

unacceptable from a manufacturing viewpoint An improvement on the idea is to locate the boundary nodes via piecewise polynomials that describe the shape of the boundary or linear combination of known

functions [6] There have been other choices less general in nature, such as radial distances or distances from reference lines or

locations To enforce continuity requirements between adjacent

boundary segments, a better strategy is to use splines, Bezier curves

or B-splines [7] The additional advantage is the use of lower-order polynomials

17

18

One of the drawbacks of such approaches is the weak link between the model definition via the design variables and the mesh generator operating on the model definition Either the mesh generation scheme

is situation dependent or a mesh generator has not been used in the optimization loop A more general scheme first introduced by Imam is the use of a design element concept The locations of the internal nodes in the design element are computed using a suitable form of isoparametric mapping A variation of this technique is presented by Braibant and Fleury Reference points or key nodes are used to define subregions (design elements) Movement directions are defined as the permissible directions along which the key nodes can move Using transfinite interpolation techniques, the locations of the non-key nodes are computed Botkin uses a relatively straightforward

isoparametric mapping to compute the internal nodes of design elements defined by eight key nodes However, the design variables are either geometric quantities such as radius and the location of the center of the holes or amplitudes of predetermined shape functions defining the boundary of the design elements

The illustrate the geometric approach, consider the Hermite cubic,_ which can be described in parametric form as

F2(u) - -2u3 + 3u2

As an example, consider the culvert problem (plane strain) shown

in Fig 5 Due to symmetry, only one-half of the structure is

considered The optimum shape of the opening is desired while keeping the outer boundary fixed Fig 6 shows the optimum shape using the Hermite cubic with four design variables The tangents at the

end-points are fixed to avoid sharp corners

Design Sensitivity Analysis

As shown in Ref [3], the design sensitivity expressions can be coded for a general velocity field matrix [0] This is true for either discrete or material derivative (continuum) approaches The importance of this lies in keeping the mesh generation phase

independent of the rest of the program

for the natural approach, and Hermite cubics for the geometric

approach, are given Since the sensitivity can be programmed for any [Q], the program organization can be made very modular The SADDLE system [8,9] has been developed to include shape optimization

capability Future work is underway to integrate adaptive modeling into the iterative process, and to combine geometric boundary

definitions with natural internal node movement

2 Y.L Ding, "Shape Optimization of Structures: A Literature

Survey," Computer and Structures, 24, 985-1004 (1986)

3 A.D Belegundu and S.D Rajan, "A Shape Optimization Approach Based on Natural Design Variables and Shape Functions," Computer Methods in Applied Mechanics and Engineering, 66, 87-106 (1988)

4 K.K Choi and T.M Yao, "3-D Modeling and Automatic Regridding in Shape Design Sensitivity Analysis," Presented at the Symposium on Sensitivity Analysis in Engineering, NASA LaRC, Hampton, VA,

7 V Braibant and C Fleury, "Shape Optimal Design Using

B-Splines," Computer Methods in Applied Mechanics and

Engineering, 44, 247-267 (1984)

8 S.D Rajan and J Budiman, "A Study of Two-Dimensional Plane

Elasticity Finite Elements for Optimal Design," Mechanics of Structures and Machines, 15, 185-207 (1987)

9 S.D Rajan and M.A Bhatti, "SADDLE: A Computer-Aided Structural Analysis and Dynamic Design Language - Part I Design System," Computers and Structures, 22, 185-204 (1986)

19

Implementation Issues in Variational Geometry

and Constraint Management

to solve the constraint equations This paper discusses some of the fundamental issues that have to be resolved in constraint management and non-linear equation solving, such as identifying under and over-constrained systems, allowing partially constrained states, equation solving robustness and convergence, representing geometric entities, and dealing with singularities

Variational geometry and constraint management allow the designer to express design intent by specifying geometric and engineering constraints

in a unified framework [1-41 The designer can then explore different design alternatives by modifying geometric and engineering parameters This design approach provides a foundation for feature-based modeling, shape optimization, and geometric reasoning [5, 61

A considerable amount of knowledge exists for equation solving However, research in variational geometry and constraint management is more recent, especially in addressing efficiency Light and Gossard [71 implemented a 2-D variation geometry system with dimensional constraints utilizing characteristic points Lin [11 was able to improve solving efficiency in 3-D variational geometry by isolating a subset of the affected constraints

In this paper, some new issues in constraint management are discussed, including allowing partially constrained states and accommodating existing geometry Additional issues in non-linear equation solving, including robustness and convergence, representing geometric entities, enforcing unique solutions, handling of singularities, solving partial networks, and resolving conflicts, will be discussed An overview of variational geometry

is also presented