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USACM

Fifth US National Congress on Computational Mechanics

University of Colorado at Boulder, August 4-6, 1999

USNCCM99 is the official Congress of the U.S. Association for ComputationalMechanics, USACM, an affiliate of the International Association for ComputationalMechanics, IACM. The Congress is being held on the Boulder Campus of the Universityof Colorado, Wednesday-Friday, August 4-6, 1999, followed by a Short Course onSaturday, August 7, 1999.

Scientific Program Committee :

The Scientific Program Committee rosters current members of the Executive Committeeof the U.S. Association for Computational Mechanics. It also includes USACM friendsand sponsors who have generously contributed their time and effort to the success of theAssociation.

Satya N.Atluri Wing-KamLiu, Vice PresidentKlaus-JrgenBathe Ahmed K.Noor

TedBelytschko J. TinsleyOdenDavidBenson MichaelOrtiz

Thomas A.Cruse, Treasurer J. N. ReddyJacobFish, Secretary Mark S.Shephard, PresidentJoe E.Flaherty LenSchwer

Tom J. R.Hughes RobertSpilker

Local Organizing Committee:

The Local Organizing Committee is comprised of five faculty members of theUniversity of Colorado at Boulder, three from the Department of Aerospace EngineeringSciences and two from the Department of Civil, Environmental, and ArchitecturalEngineering.

CharbelFarhat, Short Course CoordinatorCarlosFelippa, Web Master

K. C.Park, Social ProgramSteinSture, Co-Chair

KasparWillam, Co-Chair

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PREFACE

After more than thirty years of intense activities, the field of Computational Mechanicsis still a growing area. It spans from computational mathematics and numerical solutionof large-scale mathematical-physical problems, to innovative computer simulations inapplied mechanics and computational engineering. Four national congresses have beendevoted exclusively to this topic: Chicago 1991; Washington 1993; Dallas 1995; SanFrancisco 1997. In contrast to the previous congresses of USACM, the venue of the bi-annual Congress moved from a metropolitan hotel-based location to a universitycampus-based venue. We are privileged to host USNCCM99 at the Boulder Campus ofthe University of Colorado, Wednesday-Friday, August 4 - 6, 1999.

The major theme of the Congress is recent developments in computationalmethodologies and innovative applications. This topic encompasses a wide spectrum ofdisciplines, starting from non-traditional Finite Element Analysis, to Multi-PhysicsProblems in science and engineering, and High Performance Computing aspects. Themain objective is to bring together the diverse computational communities, and topromote the interaction between computational researchers and software developers inuniversities and industries.

The Local Organizing Committee comprised of Charbel Farhat, Carlos Felippa, K.C.Park, Stein Sture and Kaspar Willam made a determined effort to involve engineeringscientists not only from academia and government research laboratories, but also fromkey software houses. One major change from previous Congresses is the reliance onMiniSymposia organized by scientists and practicing engineers. Part of this outreachwas to include colleagues and friends to become actively involved in the congressprogram. We are proud to announce that eighty five individuals volunteered their timeand effort to organize forty MiniSymposia which range from single six paper sessions toa nine session symposium with forty nine papers in one case.

Program Topics

The congress program features 700 Invited and Contributed Papers on computationalmethodologies and applications:

Computational Methods :

Finite Element Formulations, Boundary Element Formulations, Meshfree (ElementFree) Methods, Particle Methods; Adaptive Techniques, Multi-Scale Methods(Macro-Micro and Nano-Mechanics), Coupled Multi-Field Problems; NonlinearSolvers, Coupled Solvers, Parallel Computing, Domain Decomposition Methods,Computational Mathematics, Symbolic Computation, Numerical Optimization,Inverse Methods; Nonlinear Dynamics and Control.

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Application Areas :

Structural Mechanics, Solid Mechanics, Acoustics, Materials Engineering,Deterioration Mechanics, Fluid Mechanics and Thermal Mechanics,Electromagnetics, Stochastic Systems and Probabilistic Mechanics, SystemIdentification and Damage Detection, Coupled Problems in Environmental Sciences,Geophysics, Geomechanics, Biomechanics, Visualization, CAD-CAE and IntegratedSystem Engineering, Commercial Finite Element Software.

Program Format

In view of the strong response the three day congress program was arranged in fifteenparallel tracks and nine sessions of six papers each starting with a Plenary Lecture eachmorning. Altogether the final schedule features 132 sessions and 700 papers folded into40 MiniSymposia which include 36 Keynote Lectures.

PROGRAM SCHEDULE: August 4-6, 1999TIMING Wednesday Thursday Friday

08:00- 09:00am Plenary Lecture Plenary Lecture Plenary Lecture09:00- 09:30am Coffee Break Coffee Break Coffee Break09:30- 11:30am WTS1 TTS1 FTS1

11:30- 01:00pm Lunch Break Lunch Break Lunch Break01:00- 03:00pm WTS2 TTS2 FTS203:00- 03:30pm Tea Break Tea Break Tea Break03:30- 05:30pm WTS3 TTS3 FTS3

07:00- 09:00pm Opening ReceptionCongress BanquetClosing Barbecue

Post-Congress Short Course:

On Saturday, Aug. 7, 1999, a Short Course was organized by Charbel Farhat and JacobFish. This educational outreach program features Michael Ortiz, Thomas Hughes andCharbel Farhat who will present extended lectures on Micro-Mechanics, StabilizedFinite Element Methods and on Domain Decomposition techniques, respectively.

MiniSymposia

A good number of colleagues and friends in the USA and Europe were involved inorganizing the 40 MiniSymposia at USNCCM99. Together with the three PlenaryLectures they form the body of this Book of Abstracts the content of which is listed below:

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TABLE OF CONTENT

Plenary Lectures

Ted Belytschko:Nonlinear Finite Elements: Status and Recent Progress...............................................8

Noboru Kikuchi :Advances in Computational Design and Optimization with Applications to MEMS...8

Rene de Borst :Recent Issues and Future Prospectives in Computational Mechanics of Materials......9

MiniSymposia

Kenneth F. Alvin and K. C. Park :Inverse Problems.........................................................................................................11

Francisco Armero, Paul Steinmann, Howard Schreyer and Kaspar Willam :Computational Failure Mechanics...............................................................................25

Gernot Beer and Gnther Hofstetter :Computational Mechanics of Tunneling.....................................................................49

Pl Bergan, Sanjay Govindjee, Robert L. Taylor and Nils-Erik Wiberg :Computational Dynamics............................................................................................55

Jacob Bielak, T.L. Cruse, Giulio Maier and Ronald Pak :Advances in Boundary Element Methods...................................................................73

Scott A. Cannan, Steve J. Owen and Sunil Saigal :Trends in Unstructured Mesh Generation...................................................................97

Ignacio Carol, Woody Ju and George Voyiadjis :Progress in Damage Mechanics................................................................................127

Paul Dawson, Lallit Anand and Robert Haber :Micromechanical and Multi-Scale Models for Material Processing Applications...139

Charbel Farhat, Carlos Felippa, Thomas L. Geers and Roger Ohayon :Computational Acoustics and Fluid-Structure Interaction........................................151

Carlos Felippa, Ekkehard Ramm and Wolfgang Wall :Advanced Finite Element Methods...........................................................................173

Jacob Fish :Computational Advances in Modeling Heterogeneous Materials.............................185

Joseph E. Flaherty and Mark Shephard :Adaptive and Parallel Finite Element Methods.........................................................219

Leopoldo Franca and Thomas J.R. Hughes :Stabilized Finite Element Methods...........................................................................233

Krishna Garikipati, N. Aluru and R.W Dutton :Computational Mechanics Applied to Semiconductor and MicroelectronicTechnology................................................................................................................251

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Walter Gerstle :Software Issues in Computational Mechanics...........................................................261

Roger Ghanem :Computational Methods for Propagation of Uncertainty in Physical Systems.........269

Gerhard A. Holzapfel :Computational Biomechanics....................................................................................281

Gregory M. Hulbert and Noboru Kikuchi :Applications in the Automotive Industry..................................................................293

Andrew Knyazev :Very Large Eigenvalue Problems..............................................................................299

Tod Laursen :Contact-Impact Problems and Nonlinear Mechanics................................................313

Wing Kam Liu, J.-S Chen, Ted Belytschko and Leonard Schwer :Meshfree Methods.....................................................................................................325

Herbert Mang and Gnther Meschke :Computational Mechanics of Concrete.....................................................................355

Roberta Massabo and Brian Cox :Computational Modeling of Composites..................................................................371

Joop Nagtegaal and David Fox :Advances in Commercial Finite Element Software..................................................385

Raju Namburu and P. Raboin :High-Performance Computing and Computational Structural Mechanics................397

Tinsley Oden :Advances in a Posteriori Error Estimators and Adaptive Error Analysis.................407

Roger Owen, Djorje Peric and Eugenio Oate :Computational Plasticity...........................................................................................419

K.C. Park and Ed Wilson :History of the Finite Element Method.......................................................................433

Glaucio Paulino :Functionally Graded Materials..................................................................................437

Alan Pifko :Applications in Engineering Practice........................................................................455

Peter Pinsky and K.J. Cho :Computational Methods for Multiscale Simulation of Materials..............................473

Sharif Rahman and Martin Dunn :Computational and Probabilistic Methods for Fatigue and Fracture........................483

Daniel Rixen and P. Le Tallec :Domain Decomposition Techniques.........................................................................497

Robert Sani :Advances in Computational Fluid Dynamics............................................................513

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Mike Saran, Michal Kleiber and D. A. Tortorelli :Optimization and Sensitivity Analysis......................................................................523

Bernard Schrefler and Hari Rajaram :Coupled Problems in Enviromental Engineering......................................................537

Enrico Spacone :Recent Issues in Nonlinear Frame Analysis..............................................................547

Stein Sture and Boris Jeremic :Geotechnical Applications........................................................................................553

Tayfun Tezduyar :Methods for Flow Simulation and Modeling............................................................577

Franz-Josef Ulm and Yunping Xi :Computational Durability Mechanics.......................................................................591

Acknowledgements

We are pleased to acknowledge the financial support of USNCCM99 by the US AirForce Office of Scientific Research, USAFOSR. In addition we thank the GraduateSchool, the College of Engineering and Applied Sciences, as well as the Department ofAerospace Engineering Sciences and the Department of Civil, Environmental, andArchitectural Engineering of the University of Colorado at Boulder for their financialassistance. We are grateful for their confidence and active support without which theorganization of USNCCM99 would have not been possible.

Kaspar Willam Boulder, July 1999

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Plenary Lectures

Plenary Lecture 1 : Ted Belytschko

Nonlinear Finite Elements: Status and Recent Progress.............8

Plenary Lecture 2 : Noboru Kikuchi

Advances in Computational Design and Optimization withApplications to MEMS................................................................8

Plenary Lecture 3 : Rene de Borst

Recent Issues and Future Prospectives in ComputationalMechanics of Materials................................................................9

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Nonlinear Finite Elements: Status and Recent Progress

Ted Belytschko

Chairman and Walter P. Murphy Professor of Comp. Mech. Dept. of Mechanical Engineering. NorthwesternUniversity. E-mail : t-belytschko@nwu.edu

ABSTRACTThe state of the art of nonlinear finite element analysis is reviewed. To provide a framework for

the review, nonlinear problems are categorized according to levels of difficulty. The categorization isbased on the major factors which contribute to the difficulty of a nonlinear problem: the degree ofsmoothness (or roughness) of the problem, the resolution required and the stability of the response.Roughness can occur both in time and space. The smoothness in time is shown to depend on factors suchas contact-impact, the character of the loading, and the smoothness of the constitutive response.Smoothness in space depends also on the character of the loading, but is impaired dramatically by failurephenomena such as cracking. Stability is also shown to have dramatic effects on the difficulty of aproblem. Instabilities can be classified as geometric instabilities and material instabilities. Materialinstabilities may result in localization of deformation, which dramatically increases the need for resolutionor a discontinuous treatment of the motion. Some methods for improving the smoothness throughregularization are then described.

The second half of the talk will deal with the treatment of discontinuities in space, such as shearbanding and cracking. The development of meshless methods for this class of problems will be described.Recent developments in meshless methods will be reviewed and the salient difficulties in the methodexamined. These include the quadrature of the Galerkin weak form, the treatment of essential boundaryconditions and the speed of computation. The development of new methods for the inclusion of cracks andother discontinuities will then be described. These methods are based on the property that finite elementshape functions are partitions of unity. It is shown how cracks can be modeled by simply introducingdiscontinuous enrichment function with branch functions at the crack tip. The methods are also explainedas an extension of the global-local techniques that have been used in finite elements for some time. Thekey advantage of these new methods is that the enrichment function is multiplied by the finite elementshape function, which serves as a window on the global function and lends sparsity of the discreteequations.

REFERENCES[1] T. Belytschko and T. Black, Elastic Crack Growth with Minimal Remeshing, International Journal for

Numerical Methods in Engineering, Vol 45, 601-620, (1999).[2] T. Belytschko, Y. Krongauz, J. Dolbow and C. Gerlach, "On the Completeness of Meshfree Particle Methods",

International Journal for Numerical Methods in Engineering, Volume 43, 785-819 (1998).[3] T. Belytschko, Y. Krongauz, D. Organ, M. Fleming and P. Krysl, "Meshless methods: An overview and recent

developments", Computer Methods in Applied Mechanics and Engineering, Volume 139, 1-47 (1996).

Advances in Computational Design and Optimization with Applications to MEMS

Noboru Kikuchi

Department of Mechanical Engineering and Applied Mechanics. The University of Michigan Ann Arbor, MI 48109-2125, USA Kikuchi@engin.umich.edu

ABSTRACTIn this talk we shall introduce the homogenization design method for determining the optimal

configuration of various structures and microstructures for smart structures and materials. Especially, weshall apply the topology optimization methodology to design porous piezoceramic components, actuators,

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and other type of compliant mechanisms to increase their performance. To this end, we shall setup multi-objective optimization problem which is solved by applying the sequential linear programming method.After describing the optimization method we have developed so far for smart materials and structures,especially MEMS applications, we shall also review other computational design methods introduced byother research organizations. Because of complexity of the designed microstructures and structuralconfigurations, standard manufacturing methods may not be applicable. To overcome this difficulty, weshall also apply the layered manufacturing method to develop prototype of the designed structures andmicrostructures, and we shall test their performance by using the prototypes whether or not they actuallyperform designed functionality. This research has been carried out by several graduate students in theUniversity of Michigan, among of them are Drs. Emilio Silva, Shinji Nishiwaki, and Marry Frecker, andMr. Bing-Chung Chen.

Recent Issues and Future Prospectives in Computational Mechanics of Materials

Rene de Borst

Koiter Inst Delft / Faculty of Aerospace Eng. Delft Univ. of Technology. E-mail: R.deBorst@lr.TUDelft.nl

ABSTRACTFailure in most engineering materials is preceded by the emergence of narrow zones of intense

straining. During this phase of so-called strain localisation, the deformation pattern in a body rathersuddenly evolves from relatively smooth into one in which thin zones of highly strained materialdominate. In fact, these so-called zones of strain localisation act as a precursor to ultimate fracture andfailure. Thus, in order to accurately and properly describe the failure behaviour of materials it is of pivotalimportance that the strain localisation phase is modelled in a physically and mathematically correctmanner, and that proper numerical tools are utilised to actually solve strain localisation phenomena inboundary value problems. In recent years the study of strain localisation in solids has received anincreasing amount of attention, even though typical localisation phenomena like Lueders bands and rockfaults have been known and studied for many decades. For instance, an important theoretical contributionwas published by Hadamard [1] already in the beginning of this century, and in his monograph `Plasticity',Nadai [2] recognised the wide range of materials in which localisation phenomena occur, and showedmany examples of shear bands in metals, sandstone, marble and paraffin. Later, landmark contributionshave been published by Hill [3], Thomas [4], Mandel [5] and Rice [6], leading to a greater understandingof strain localisation, and in particular of shear banding. While the study of strain localisation was firstprimarily devoted to metals, much attention has recently also been given to localisation phenomena ingeological materials (rocks, soils), see for instance the comprehensive treatise by Vardoulakis and Sulem[7], to (micro)-cracking in concrete [8] and to the propagation of necks in polymers.

Until the mid-1980s analyses of localisation phenomena in materials were commonly carried outfor standard, rate-independent continuum models. This is sufficient when the principal aim is to determinethe behaviour in the pre-localisation regime and some properties at incipient localisation, such as thedirection of shear bands in tension tests, and in biaxial and triaxial devices. However, there is a majordifficulty in the post-localisation regime, since localisation in standard, rate-independent solids isintimately related to a possible change of the character of the governing set of partial differentialequations. In the static case the elliptic character of the set of partial differential equations can be lost,while, on the other hand, in the dynamic case we typically observe a change of a hyperbolic set into anelliptic set. In both cases the rate boundary value problem becomes ill-posed and numerical solutionssuffer from spurious mesh sensitivity.

The inadequacy of the standard, rate-independent continuum to model zone of localised strainingcorrectly can be viewed as a consequence of the fact that force-displacement relations measured in testingdevices are simply mapped onto stress-strain curves by dividing the force and the elongation by theoriginal load-carrying area and the original length of the specimen, respectively, without taking intoaccount the changes in the micro-structure. Therefore, the mathematical description ceases to be ameaningful representation of the physical reality.

To remedy this problem one must either introduce additional terms in the continuum descriptionwhich reflect the changes in the micro-structure [9-11], or one must take into account the inherent

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viscosity of most engineering materials. The effect is that the governing equations do not change typeduring the loading process and that physically meaningful solutions are obtained for the entire loadingrange. A more mathematical way to look at the introduction of additional terms in the continuumdescription is that the Dirac distributions for the strain at failure are replaced by continuous straindistributions, which lend themselves for description by standard numerical schemes. Although the straingradients are now finite, they are very steep and the concentration of strain in a small area can still bereferred to as strain localisation or localisation of deformation.

In fact, strain localisation is but one, albeit the most important, of possible material instabilityphenomena in solids. In this contribution we shall first categorise the different material instabilityphenomena using a one-dimensional linear stability analysis. Next, we shall point out a broad frameworkto mathematically regularize the ill-posed set of equations that arises after the onset of localisation.Broadly speaking, this framework involves the introduction of gradients, either in space or in time, ofcoupled plasticity-damage theories. In order to keep the formulation transparent, we shall ignore theinherent anisotropic character of plasticity and damage when real microstructural changes develop, such asis the case during strain localisation. Illustrative examples using finite elements will be given.

The last part of the manuscript is devoted to high resolution numerical techniques to properlycapture thin zones of highly strained material and to the influence of imperfections on failure patterns. Inthis light we will pay attention to meshless methods, which, through their inherent property of a higher-order continuity are ideally suited for inclusion of high-order spatial gradients in constitutive relations, tothe inclusion of discontinuities or zones with steep strain gradients directly in finite elements, and torandomly distributed imperfections in quasi-brittle and (visco)-plastic materials.

REFERENCES[ 1] J. Hadamard. Lecons sur la Propagation des Ondes. Herman et fils, Paris (1903).[ 2] A. Nadai. Plasticity. McGraw-Hill, New York and London (1931).[ 3] R. Hill. A general theory of uniqueness and stability in elastic-plastic solids, J. Mech. Phys. Solids, 6, 236-249

(1958).[ 4] Y. Thomas. Plastic Flow and Fracture of Solids. Academic Press, New York (1961).[ 5] J. Mandel. Conditions de stabilite et postulat de Drucker. In: Proc. IUTAM Symposium on Rheology and Soil

Mechanics. Springer-Verlag, Berlin, 58-68 (1966).[ 6] J.R. Rice. The localization of plastic deformation. In: Theoretical and Applied Mechanics. North-Holland,

Amsterdam, 207-220 (1976).[ 7] I. Vardoulakis, J. Sulem. Bifurcation Analysis in Geomechanics. Blackie, London (1995).[ 8] Z.P. Bazant, J. Planas. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press, Boca

Raton (1998).[ 9] E.C. Aifantis. On the microstructural origin of certain inelastic model. Trans. ASME J. Eng. Mater. Technol.,

106, 326-330 (1984).[10] R. de Borst, H.-B. Muehlhaus. Gradient-dependent plasticity: formulation and algorithmic aspects. Int. J. Num.

Meth. Eng., 35, 521-539 (1992).[11] N.A. Fleck, J.W. Hutchinson. Strain gradient plasticity. Adv. Appl. Mech., 33, 295-361 (1997).

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Inverse ProblemsKenneth F. Alvin and K. C. Park

SESSION 1

Keynote : THE EVOLVING ROLE OF VALIDATION AND INVERSE METHODS IN STRUCTURAL DYNAMICSD.R. Martinez and K.F. Alvin...........................................................................................................................................12

MODAL IDENTIFICATION OF MIR USING INVERSE SYSTEM DYNAMICS AND MIR/SHUTTLE DOCKINGDATA

D.C. Kammer and A.D. Steltzner......................................................................................................................................13

BAYSIAN MODEL UPDATING AND ROBUST RELIABILITYJ.L. Beck, C. Papadimitriou, L.S. Katafygiotis and S.K. Au..............................................................................................13

ON REGULARIZATION IN GEOTECHNICAL INVERSE ANALYSIS BASED ON ENTROPY MINIMIZATIONY. Honjo............................................................................................................................................................................14

AN ITERATIVE SUPERSONIC WING DESIGN USING AN INVERSE PROBLEMK. Matsushima, T. Iwamiya, S. Jeong and S. Obayashi....................................................................................................15

SESSION 2

DATA FUSION FOR THE STEADY INVERSE HEAT CONDUCTION PROBLEML.G. Olson and R.D. Throne.............................................................................................................................................15

INVERSE DETERMINATION OF UNSTEADY THERMAL BOUNDARY CONDITIONS DURING COOLING OFTHREE - DIMENSIONAL OBJECTS WITH SPECIFIED LOCAL COOLING RATES AND MAXIMUM THERMALSTRESS LEVELS

G.S. Dulikravich and B.H. Dennis....................................................................................................................................16

A COMPARISON OF SEVERAL INVERSION ALGORITHMS FOR THERMAL AND MECHANICAL SYSTEMSB. Travis...........................................................................................................................................................................17

ADJOINT METHODS FOR THE INVERSE DESIGN OF COMPLEX NATURAL CONVECTION SYSTEMSR. Sampath and N. Zabaras..............................................................................................................................................17

DESIGN OF EXPERIMENTS TO ESTIMATE TEMPERATURE DEPENDENT THERMAL PROPERTIESK.J. Dowding....................................................................................................................................................................18

SESSION 3

EFFECT OF CORRELATION AMONG MEASURED DEFLECTIONS ON ESTIMATED LAYER MODULIK. Matsui, Q. Dong and I. Kurobayashi...........................................................................................................................19

STRUCTURAL HEALTH MONITORING VIA DYNAMICS LOCALIZATION AND TRANSMISSION ZEROBEHAVIOR

G. Reich and K.C. Park....................................................................................................................................................20

EXTRACTION OF RITZ VECTORS AND THEIR APPLICATION TO STRUCTURAL DAMAGE DIAGNOSISH. Soon and K.H. Law......................................................................................................................................................20

THE DEVELOPMENT AND APPLICATION OF A DAMAGE DETECTION TOOLBOX FOR MATLABJ.P. Lynch, H. Soon and K.H. Law...................................................................................................................................21

INCORPORATION OF ACCURATE SENSITIVITY ANALYSIS INTO A SCALABLE MP STRUCTURALDYNAMICS FEM CODE

K.F. Alvin, G.M. Reese, D.M. Day and M. Bhardwaj.......................................................................................................22

EXPERIMENTAL VALIDATION OF TRANSIENT FINITE ELEMENT MODEL PREDICTIONSS.W. Doebling , F.M. Hemez , W. Rhee and P. Beardsley.................................................................................................23

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Keynote : THE EVOLVING ROLE OF VALIDATION AND INVERSE METHODSIN STRUCTURAL DYNAMICS

D.R. Martinez and K.F. Alvin

(1) - Structural Dynamics and Vibration Control Dept. E-mail : drmarti@sandia.gov(2) - Sandia National Laboratories. E-mail : kfalvin@sandia.gov

ABSTRACTInverse problems have played an important role in structural dynamics analysis of aerospace and

weapon systems during the last few decades. This period has seen increasing use of finite element analysisprocedures, which have been augmented by inverse methods to achieve significant accuracy andefficiency in computational analysis. This synthesis of analysis methods has been so successful that it isnow increasingly common to perform virtual testing of aerospace components using computationalmodeling and simulation for qualification and certification. The most common example of this approach isin the qualification of satellite payloads, which typically do not see a fully-integrated test-based simulationof the dynamic launch loading environment. Instead, a combination of subsystem random vibration tests,system-level acoustics and static proof loads tests are integrated through computational analysis, which isgrounded and validated through modal testing and inverse methods.

Inverse methods for structural dynamics have evolved over time from the ad hoc adjustment ofparameters to sophisticated, staistically-based parameter estimation methods using large quantities ofexperimentally -estimated modal parameters, sensitivity analysis, and optimization techniques. Theincreased use of statistics-based methods have improved the robustness of such procedures, as well assetting the stage for computational analysis-based reliability assessment. As a deeper understanding ofcontinuous parameter estimation procedures has developed, together with powerful algorithmimplementations, research in inverse methods has begun to consider such conceptual modeling issues aserror localization and connectivity determination. These applications have traditionally been consideredissues of model validation. In fact, validation of models was often concluded from successfulidentification of parameters.

In the current environment of rapidly increasing computational capability, inverse methods andvalidation are again evolving. Programs such as DOE's Accelerated Strategic Computing Initiative (ASCI)are leading a revolution in physics-based modeling and simulation capabilities. Emerging from thisrevolution are new finite element codes, such as Sandia's SALINAS structural dynamics application,which can perform implicit solutions of models with over 10 million unknowns. This level of modelingfidelity can reduce the kinds of gross modeling simplifications that motivated many applications of inversemethods, for example the estimation of overall compliance in joints and interfaces. As modeling andsimulation strives towards a higher, physics-based predictive capability based on first principles,validation methodology and inverse methods must increasingly focus on the phenomnenologicalidentification and validation of subgrid physics such as material constitutive and interfacial microslipmodels. While experiment design can help to isolate subgrid models for identification and validationpurposes, new inverse methods must be developed to help isolate, identify, and validate the contributingphysics in a complex application. Furthermore, probabilistic-based uncertainty quantification methods areneeded to develop and refine reliability analysis, as well as to quantify model biases and uncertaintiesobservable from validation exercises.

MODAL IDENTIFICATION OF MIR USING INVERSE SYSTEM DYNAMICS ANDMIR/SHUTTLE DOCKING DATA

D.C. Kammer and A.D. Steltzner

(1) - Engineering Mech. And Astronautics. Univ. of Winsconsin. E-mail : dckammer@facstaff.wisc.edu(2) - Engineering Mech. And Astronautics. Univ. of Winsconsin. E-mail : steltzne@cae.wisc.edu

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ABSTRACTA time-domain technique is presented which uses inverse structural dynamics to identify physical

characteristics of a structure which can subsequently be used for damage detection. The term "inverse"refers to the fact that the roles of input and output are reversed from the usual structural dynamicsproblem. If sensors such as accelerometers are placed at the external input locations, modal parameterscorresponding to structural motion with the sensor locations fixed can be identified. If sensors are notcollocated with the inputs, other important structural characteristics can be determined, such astransmission zeros. One of the main advantages of this method is that it only requires measured responsedata. This characteristic makes the approach, referred to as a Remote Sensing System (RSS), applicable incases where the input forces cannot be measured such as Mir/Shuttle docking events.

The objective of this work was to apply the RSS approach to acceleration data collected at 25locations on the Mir space station during the STS-81, STS-89, and STS-91 docking events in an attempt toidentify structural damage in the Kristall-to-base module interface caused by the Progress collision. Inorder to explore the damage detection capability of RSS combined with ERA modal identification for acase with sufficient data, numerical simulations were performed using the FEM representation of the Mir.Five percent rms noise was added to the response of the FEM to three simulated sets of docking forces.The combined RSS/ERA method accurately identified 5 FEM fixed sensor location modes, but none of themodes possessed a significant amount of strain energy in the Kristall-to-base module interface. Basedupon this simulation, it is believed that the Mir/Shuttle docking events do not sufficiently excite theKristall-to-base module interface to provide accurate damage detection in this area.

A sufficient amount of actual docking data was obtained for the RSS/ERA method by combiningthe measured response from all three docking events. This assumes that the effects of docking moments onmeasured responses are second order compared to the linear docking forces. The RSS/ERA approach wasused to identify three normal modes corresponding to having the reference sensors on Kristall fixed. Twoof the modes correlated very well with the FEM and the identification results were very analogous toresults produced by the numerical simulations. Based upon this work, it is believed that RSS provides avaluable new approach to identifying characteristics of large space structures from measured data withoutthe need for measuring the input excitation.

BAYSIAN MODEL UPDATING AND ROBUST RELIABILITY

J.L. Beck, C. Papadimitriou, L.S. Katafygiotis and S.K. Au

(1) - Div. of Engineering and Applied Science, California Inst. of Technology. E-mail : jimbeck@cco.caltech.edu(2) - Div. of Engineering and Applied Science, California Inst. of Technology

(3) - Dept. of Civil and Structural Engineering. Hong Kong Univ. of Sci. and Tech.

ABSTRACTA Bayesian probabilistic framework [1] for model updating is integrated with probabilistic

structural dynamics tools [2] for the purpose of updating structural response and reliability predictionsusing measured vibrational data.

The probabilistic system identification methodology is used to provide more accuraterepresentations of the uncertainties associated with the structural modeling, based on both measuredvibrational data and prior engineering information. The methodology allows for the explicit treatment ofthe uncertainties arising from both measurement and modeling errors. It provides an updated probabilitydensity function for the system parameters, including those related to the prediction-error uncertainties,which accounts for all models that fit the data well, along with the relative plausibility of each of thesemodels. Using this updated distribution for the system parameters, a methodology is presented forcomputing the robust reliability of structures subjected to uncertain future environmental loads, such asearthquake and wind loads. This reliability is "robust" in the sense that it takes modeling uncertainties intoaccount in addition to the uncertainties in the structural loads. The computational difficulties associatedwith calculating the resulting reliability integrals are also addressed and efficient asymptotic andimportance sampling techniques are proposed for treating both identifiable and non-identifiable cases.

The proposed framework can be used to continually monitor and update the predictions ofstructural response and reliability. This provides important information about the integrity of the structureafter severe loading events such as earthquakes and strong winds, or deterioration from long-term

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corrosion and fatigue. The methodology is illustrated with an example structure subjected to earthquakeloads. It is shown that the structural response and reliabilities computed before and after a severe eventusing the measured dynamic data can differ significantly. It is demonstrated that modeling uncertaintiesare important for making reliable predictions at the unmonitored degrees of freedom of a structure. Issuesrelated to optimal sensor locations for improving the reliability of the model response predictions are alsoaddressed. It is suggested that measured dynamic data, whenever available, can improve considerably theaccuracy in predicting structural response and safety of existing structures.

REFERENCES[1] Beck, J.L. and Katafygiotis, L.S. (1998), "Updating models and their uncertainties - Bayesian statistical

framework", J. Eng. Mech. 124(4), 455-461.[2] Papadimitriou, C., Beck, J.L. and Katafygiotis, L.S. (1997), "Asymptotic expansions for reliability and moments

of uncertain systems", J. Eng. Mech., 123(12), 1219-1229.

ON REGULARIZATION IN GEOTECHNICAL INVERSE ANALYSIS BASED ONENTROPY MINIMIZATION

Y. Honjo

(1) - Department of Civil Engineering, Gifu University. E-mail : honjo@cc.gifu-u.ac.jp

ABSTRACTMost of the inverse problems encountered in geotechnical inverse analysis are illposed, thus

some type of regularization procedure need to be applied. In this paper, several regularization proceduresare compared to a simple problem, a laterally loaded pile (2.4m long) in homogeneous sand in a laboratorypit. The regularization procedures employed are the minimum norm solution based on the singular valuedecomposition, Kitagawa's solution, L curve method and the extended Bayesian method (EBM) withABIC (Akaike Bayesian Information Criterion). The obtained solutions are compared with the maximumlikelihood solution (ML), and characteristic of each type of solution is discussed. Furthermore, theobservation noise of different levels are applied to the original data to see the change of solutions for eachmethod. The EMB showed superiority to other types of regularization procedures in a sense itautomatically accomplished the best matching between the observation data and the prior information.

AN ITERATIVE SUPERSONIC WING DESIGN USING AN INVERSE PROBLEM

K. Matsushima, T. Iwamiya, S. Jeong and S. Obayashi

(1) - Space systems Dept Fujitsu Ltd. E-mail : kisam@nal.go.jp(2) - National Aerospace Laboratory, Japan.

(3) - Tohoku University Miyagi Japan

ABSTRACTSupersonic wing design has been performed considering only the load distribution on the wing,

so far. Most existing methods treat a planform and a warp. They don't care the airfoil shape of wingsections. However, to develop a supersonic wing with a new concept such as a natural laminar flow (NLF)wing, the airfoil shape is of primary importance. In addition, the airfoil shape at every span station has tobe determined three - dimensionally.

We have been developing and verifying a numerical inverse design method which determines theairfoil shape at every span station. We are also trying to apply it to the design of the Japanese SST[1]. Thegoal of the method is to find the airfoil geometry which realizes target pressure distribution at all spanstations with a planform fixed. The design procedure of the method is iterative. Starting with the baselineshape, it iterates a Navier-Stokes (N-S) simulation and an inverse problem solver, in turn. A N-S

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simulation provides the pressure distribution by a current shape, then we check if the current shaperealizes the target pressure distribution. An inverse problem solver provides the geometrical correction forairfoil shapes corresponding to the difference between target and current pressure distributions. Theinverse problem solver has been newly developed for the project. The inverse problem is formulated usingthe equation of flow physics and results in integral equations. It is one of the extentions of the formulationpresented by Takanashi[2] for transonic wing design.

The wing of the Japanese SST has been aerodynamically designed at M $B!g (J=2.0, taking thewing - fuselage interaction into account. We prescribe a target pressure which has elliptic load distributionand whose upper surface distribution keeps the laminar boundary layer significantly longer than traditionalwings. The baseline shape of the wing is the result of planform and warp optimizations by the traditionallinear theory. The performance of the baseline model is not as efficient as expected. Therefore,improvement of the wing shape by the new method is necessary. For the inverse problem solver , the half-span of the wing is divided into 82 (spanwise) X 50 (chordwise) panels. The computational time is about 7minutes on a 1.7GFLOP-machine. After twelve iterations of the N-S simulation and the inverse problemsolver, the converged design result has been obtained. The pressure distribution of the designed wingshows good agreement with the target.

REFERENCES[1] K. Matsushima et al., "A Supersonic Inverse Wing Design Method and its Application to Japanese SST", 16th

ICNMFD, July, 1998.[2] S. Takanashi, "Iterative Three-dimensional Transonic Wing Design Using Integral Equations", J. of Aircraft,

22(8), August, 1985.

DATA FUSION FOR THE STEADY INVERSE HEAT CONDUCTION PROBLEM

L.G. Olson and R.D. Throne

(1) - University of Nebraska. E-mail : lolson2@unl.edu(2) - University of Nebraska

ABSTRACTIn many applications, it is not possible to place sensors directly at the locations where

information about temperatures or heat fluxes are desired. For instance, in machining (turning) of highperformance ceramics, we are interested in the temperatures/fluxes at the tool tip in order to monitor toolwear. However, the extreme operating conditions which arise force us to place the sensors away from thetip. Many of these cases may reasonable be modelled as steady or quasi-steady heat condution.

In this study, we examined techniques for solving such inverse boundary value problems insteady multidimensional heat conduction. In our model problems the conditions were overspecified (heatflux and temperature) on some boundaries of the domain in order to infer heat flux and/or temperature atother domain boundaries. We also assumed that the material properties and geometry were known. Wecompared our new Generalized Eigensystem techniques (GES and GESL) to standard techniques such asSingular Value Decomposition (SVD) and Tikhonov Regularization of various orders. All methodsincluded some form of data fusion - the systematic combination of data from multiple types and locationsof sensors. We studied two test geometries, a circular annulus and a square with rectangular holes, whichhave been examined by other researchers as well. Several temperature distributions were employed, andcases with and without simulated noise were included.

Our results indicate that GESL provides inverse results for these test cases which are far superiorto the other methods studied. The advantage of GESL is larger when moderate noise is present, and oftenGESL gives errors which are five to ten times smaller than SVD or Tikhonov. However, on test caseswhere the temperature distribution contains small regions of high temperature (hot spots) on the sourceboundary all methods give inadequate results. We are currently investigating the use of wavelets toimprove the resolution of these small regions.

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INVERSE DETERMINATION OF UNSTEADY THERMAL BOUNDARYCONDITIONS DURING COOLING OF THREE - DIMENSIONAL OBJECTS WITH

SPECIFIED LOCAL COOLING RATES AND MAXIMUM THERMAL STRESSLEVELS

G.S. Dulikravich and B.H. Dennis

(1) - Dept. of Aerospace Engineering. The Pennsylvania State University. E-mail : ft7@psu.edu(2) - Dept. of Aerospace Engineering. The Pennsylvania State University.

ABSTRACTOne of the technical difficulties encountered by surgeons during organ transplantation is caused

by the shortage of available organs. A possible solution would be to establish an organ bank that couldstore organs with different immunological properties in a frozen state for lengthy periods of time. Whenpreserving living human tissues (kidney, heart, liver, embryo, bone, spleen, semen, etc.) for the purpose ofperforming transplant surgery, the organ is cooled in a special liquid cryo-protective agent (CPA) to aprescribed low temperature and kept at this temperature until used. During the cooling process there is anoptimal cooling rate for each particular type of tissue of an organ in order to maximize the survivability ofthe living cells and reduce the problem of future rejection by the organ recipient's body. One method thatoffers a practical solution is to determine the proper surface thermal conditions of the container in whichthe CPA and the organ are located so that the optimal local cooling rates and the tolerable thermal stressesare achieved at each instant of time at every point in the organ.

The objective of this work is to create a fully automatic procedure for determining andmaintaining locally optimal cooling/heating rates throughout the living tissue while simultaneouslykeeping the local thermal stresses below a specified level, thus maximizing living tissue survivability.Maintaining optimal distributed values of the cooling rates throughout the organ is achieved byappropriately varying temperature distribution on the walls of the container.

A complete three-dimensional mathematical model for predicting convection/conduction coolingof heterogeneous transplant tissues and whole organs submerged in and perfused with a CPA includesconcentration dependent latent heat release during phase change. It also accounts for the temperaturedependent thermal properties of the local tissue and of the CPA. A finite element computer program isused for the prediction of flow-field of the CPA during perfusion of the organ. It has the ability to predictconvective heat transfer on the inner surfaces of the organ. A time-accurate finite element computerprogram is used for the prediction of unsteady heat conduction and thermal stresses within realisticallyshaped three -dimensional heterogeneous organs. In addition, a reliable computer program is used toachieve efficient nonlinear constrained optimization of time-varying container wall temperaturedistribution.

(NOTE: ALL OF THESE CODES HAVE ALREADY BEEN DEVELOPED BY OUR TEAM.WE ARE PRESENTLY TESTING THE ENTIRE SOFTWARE SYSTEM).

A COMPARISON OF SEVERAL INVERSION ALGORITHMS FOR THERMALAND MECHANICAL SYSTEMS

B. Travis

(1) - Earth & Environmental Sciences Division. Los Alamos National Laboratory. E-mail : bjt@vega.lanl.gov

ABSTRACTDetermining an unknown, spatially variable parameter in the governing equation, or an unknown

initial condition or forcing function in thermal or mechanical systems is frequently required, but usuallyconstitutes an ill-posed inverse problem. Further, coupled thermal and mechanical systems are a greaterchallenge for inversion algorithms. While more difficult to solve, they offer the possibility of greaterresolution of unknown parameters. There are a variety of methods for estimating solutions; here, severalare illustrated and compared for canonical thermal and mechanical systems considered separately and incoupled mode:

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1) Courant's method (which creates and uses an approximation of the delta functional);2) Tikhonov regularization (equivalent to RKHS), both with classical derivative regularizers, and

with fractional derivative regularizers, and coupled with an interval method;3) BNN's (biological neural nets, as constrasted with artificial neural networks, ANN's), which

can be thought of as roughly equivalent to regularization with non-simple regularizers;4) Representers, which involve finding coefficients in a basis function expansion for the

unknown parameter function.Each has its strengths and weaknesses, and seems to be more successful for certain kinds of

inverse problems.

ADJOINT METHODS FOR THE INVERSE DESIGN OF COMPLEX NATURALCONVECTION SYSTEMS

R. Sampath and N. Zabaras

(1) - Sibley School of Mechanical and Aerospace Engineering(2) - Sibley School of Mechanical and Aerospace Engineering. E-mail : zabaras@cornell.edu

ABSTRACTInverse and design problems have been under extensive investigation over the past decade. Many

engineering applications of heat transfer and fluid flow can often be posed as inverse design problemswhere one calculates the heat flux conditions in part of the boundary from over-specified boundaryconditions (i.e. temperature and flux) on another part of the boundary [1, 2]. Though there has beenextensive application of inverse problem theory to conduction based problems, there is very little work inthe application of these methods to the design of convection driven systems [3].

In this paper, we present an inverse design formulation for the design of complex naturalconvection systems through the use of thermal boundary flux control. The design problem is stated as afunctional optimization problem in the L2 space. The exact gradient of the cost functional is obtained viathe solution of an adjoint continuum problem. A sensitivity problem is also defined and is used in theimplementation of the conjugate gradient method (CGM).

An object-oriented [4] environment has been developed for the implementation of such systemsthat accounts for the common mathematical structure and implementation techniques for the various sub -problems within the direct, adjoint and sensitivity problems. The simulations are based on a stream-lineupwind/Petrov-Galerkin finite element method solution of the heat and flow equations in each of thedirect, adjoint and sensitivity sub-problems. The direct, adjoint and sensitivity problems are solved insequence in the framework of the CGM to obtain the desired design solution. A numerical example is usedto demonstrate the potential applications of this method.

Applications of this work to systems with various coupled convection/diffusion mechanisms (asfor example is the case in solidification systems) will be discussed. Prospects in using additional means ofcontrol such as electromagnetic stirring [5] will also be considered.

REFERENCES[1] G. Z. Yang and N. Zabaras , "An adjoint method for the inverse design of solidification processes with natural

convection", Int. J. Numer. Methods Engr., 42, 1121 (1998).[2] G. Z. Yang and N. Zabaras , "The adjoint method for an inverse design problem in the directional solidification of

binary alloys", J. Comput. Phys., 140, 432 (1998).[3] N. Zabaras and G. Yang, "A functional optimization formulation and implementation of an inverse natural

convection problem", Comp. Methods Appl. Mech. Engr., 144 (3-4), 245 (1997).[4] R. Sampath and N. Zabaras , "An object-oriented implementation of adjoint techniques for the design of complex

continuum systems", Int. J. Numer. Methods Engr., submitted for publication.[5] R. Sampath and N. Zabaras , "Inverse thermal design and control of solidification processes in the presence of a

strong external magnetic field", J. Comput. Phys., submitted for publication.

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DESIGN OF EXPERIMENTS TO ESTIMATE TEMPERATURE DEPENDENTTHERMAL PROPERTIES

K.J. Dowding

(1) - Sandia National Laboratories. E-mail : kjdowdi@sandia.gov

ABSTRACTTemperature dependence of thermal properties, such as thermal conductivity and volumetric heat

capacity, may not be accurately known for many materials. In such cases parameter estimation techniquescan be combined with experimental investigations to estimate parameters describing the temperaturedependent thermal properties. While optimal experimental conditions to estimate constant thermalproperties have been investigated, conditions when properties vary with temperature have not. Conditionsrefer to the test specimen geometry, duration of the experiment, duration of dynamic boundary conditionssuch as heat flux, and magnitude of boundary conditions.

Experimental conditions are studied to estimate temperature dependent thermal properties forpolyurethane foam. An experimental design that imposes a measurable heat flux on one surface of a testspecimen with an electric heater is proposed. This design usually permits thermal conductivity andvolumetric heat capacity to be simultaneously estimated. Since the foam has relatively low thermalconductivity, the boundary of the specimen opposite the heater can be accommodated in one of two ways.In the first configuration the specimen thickness is made large enough such that the specimen is(thermally) semi infinite. In this case the boundary requires no attention. The second configuration puts ahigh conductivity heat sink in contact with the boundary. This results in nearly an isothermal response atthis surface. To distinguish from the previous configuration, this configuration is referred to as finite.These two configurations are necessitated by experimental as well as analysis concerns.

Experimental conditions for the two configurations are studied to quantify the optimalexperiment to estimate temperature dependent thermal properties. The criteria D-optimality is used toidentify the optimal experiment. Properties are assumed to vary linearly with temperature; a total of fourparameters describe linearly varying thermal conductivity and volumetric heat capacity. Results indicatethat finite configuration is better than the semi infinite, assuming a single experiment is conducted toestimate the linearly varying properties. An alternative to estimate temperature dependent properties is tocombine several experiments, each with a different temperature range. This approach appears to be farbetter than a single experiments. Details of this approach are discussed.

EFFECT OF CORRELATION AMONG MEASURED DEFLECTIONS ONESTIMATED LAYER MODULI

K. Matsui, Q. Dong and I. Kurobayashi

(1) - Tokyo Denki University College of Science and Engineering. E-mail : matsui@g.dendai.ac.jp(2) - Tokyo Denki University College of Science and Engineering(3) - Tokyo Denki University College of Science and Engineering

ABSTRACTA falling weight deflectometer has been widely used to measure surface deflection at several

locations near a loading plate, from which layer moduli are estimated assuming pavement as an elasticmulti-layered system. However, estimated results are affected by various types of errors such as 1)measurement error, 2) model parameter error, 3) modeling error and 4) computational error.

Computational error refers to a round off error during iterative process. This error has to beminimized by careful coding of inverse analysis algorithm because of its unstable nature. Modeling errorarises from assumption of a linear elastic behavior of pavement when it is not. After modeling is selected,model parameters such as layer thickness and Poison ratio which are used to describe a model mayinvolve some error and affect the results. Measured surface deflection always contains some random error.Measurement accuracy can be improved by carefully repeating measurement.

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Some papers in the past examined the effect of measurement error on estimated results. Howeverno paper has focused on the correlation between measured deflections and its effect on estimated results.Authors found that the correlation of measured deflections improves accuracy of estimated moduli when avariation of deflection is same between two sets of data.

General inverse matrix approach is used for the inverse analysis with scaling of unknownparameters coupled with truncated singular value decomposition. This method results in a smallercondition number which contributes to improvement of numerical stability.

After estimating parameter values, their confidence region is also presented.

STRUCTURAL HEALTH MONITORING VIA DYNAMICS LOCALIZATION ANDTRANSMISSION ZERO BEHAVIOR

G. Reich and K.C. Park

(1) - E-mail :reich@titan.Colorado.EDU(2) - University of Colorado. E-mail : kcpark@titan.colorado.edu

ABSTRACTThis work examines the application of a structural flexibility partitioning scheme to localized

damage detection techniques. A novel method of determining the location of damage is developed basedon the invariance of a set of localized transmission zeros. The purpose of this work is to apply thetheoretical conclusions which are developed into a viable and practical damage detection technique forapplication on existing and future damage detection problems.

The structural partitioning scheme is based on the Lagrange multiplier method of applying inter-element dynamic constraints to a partitioned structural system. The natural conclusion of this work is thatthe dynamics of the total structure can be written in terms of the dynamics of each substructure, plus thecoupling dynamics of the interactions between substructures.

The transmission zeros of a transfer function are the frequencies at which no response is seen atthe sensor locations given a harmonic input at the actuator locations. The mathematical description andproperties of transmission zeros are well known from linear system theory. The transmission zeros of aglobal system experiencing damage are shown to vary except for elements at a natural boundary condition.

We propose to combine the flexibility partitioning scheme with the monitoring of transmissionzeros to create a unique damage location identification scheme. The system requires only a few sensors atselected locations to determine the specific localized transfer functions corresponding to a singlesubstructure. The transmission zeros of that transfer function are shown to be invariant to damage in thecorresponding substructure. The technique is demonstrated on several example structures.

EXTRACTION OF RITZ VECTORS AND THEIR APPLICATION TOSTRUCTURAL DAMAGE DIAGNOSIS

H. Soon and K.H. Law

(1) - Department of Civil and Environmental Engineering. Stanford University. E-mail :sohnhoon@leland.stanford.edu

(2) - Department of Civil and Environmental Engineering. Stanford University.

ABSTRACTThere have been increased economic and societal demands to continuously monitor the

conditions and long -term degradation of structures to ensure their safety and adequate performancethroughout their life spans. The need for a systematic approach for global monitoring that can be appliedto large-scale structures has led to recent advances in vibration-based damage identification techniques. Ithas been shown that changes in the modal parameters might not be apparent at an early stage of damage.

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In addition, the uncertainties caused by measurement noise, modeling error involved in an analyticalmodel, and environmental factors such as variations in temperature, humidity and load conditions canimpede reliable identification of damage. Therefore, for reliable damage detection, damage would need tocause significant changes in the modal parameters that are beyond the natural variability caused by theeffects other than damage. To overcome the insufficient sensitivity of modal vectors to damage, wepropose Ritz vectors as a potential alternative to modal vectors. First, we present a new extractionprocedure of Ritz vectors based on a measured flexibility matrix obtained from vibration test data. Themain advantage of the flexibility-based method is that this method allows generating Ritz vectors fromarbitrary load patterns as well as from the actual load patterns employed in the vibration test. The Ritzvector extraction procedure is demonstrated using a grid-type bridge model constructed and tested at theHyundai Institute of Construction Technology (HICT), Korea. Next, we incorporate Ritz vectors into thepreviously proposed Bayesian probabilistic framework [1] and investigate its applicability to damagediagnosis problems. The Ritz vectors generated from the measured flexibility are applied to conduct thedamage diagnosis of the test structure. The diagnosis performances using Ritz and modal vectors are alsocompared.

Ritz vectors are successfully extracted from the vibration tests of the grid-type bridge model andthe experimental Ritz vectors provide a good agreement with analytical ones. Damage diagnoses resultsindicate that the employment of Ritz vectors provides better indication of the actual damage locations thanmodal vectors. The superior performance of Ritz vectors attributes to (1) the better sensitivity of Ritzvectors over modal vectors and (2) the increased amount of information obtained by employing multipleload patterns.

REFERENCES[1] Sohn, H. and Law, K. H., "Bayesian Probabilistic Approach for Structure Damage Detection", Earthquake

Engineering and Structural Dynamics, Vol. 26, pages 1259-1281

THE DEVELOPMENT AND APPLICATION OF A DAMAGE DETECTIONTOOLBOX FOR MATLAB

J.P. Lynch, H. Soon and K.H. Law

(1) - Department of Civil and Environmental Engineering. Stanford University. E-mail :jplynch@leland.Stanford.EDU

(2) - Department of Civil and Environmental Engineering. Stanford University. E-mail :sohnhoon@leland.stanford.edu

(3) - Department of Civil and Environmental Engineering. Stanford University.

ABSTRACTAn important challenge to the engineering research community is to develop methods of

monitoring the health as well as detecting damage in large-scale structures. To date, numerous methodshave been developed employing the vibration characteristics of a structure to predict the locations anddegrees of damage. While numerous MATLAB based toolboxes are available to calculate the modalparameters of a vibrating structure, none to date include the capability to look at these parameters andpredict damage locations and severity. In response to this, the authors have developed a damage detectiontoolbox for MATLAB that can be used in conjunction with available modal analysis software like LosAlamos National Labs DIAMOND. The toolbox employs a user friendly graphical user interface thatprovides the user with displays to view input parameters and to view calculated damage detection results.The objective of the toolbox is to provide a user friendly platform to help researchers to experiment andincorporate additional algorithms for damage detection applications.

Modal analysis software is required to examine the frequency response of a structure and extractthe dominant modes of the structures vibration behavior. This information is then passed on to thedamage detection toolbox, which will detect damage in the structure. The toolbox has been designed tooffer a large degree of flexibility by allowing the user to select from a number of damage detectionalgorithms. These algorithms can be classified in two categories; probabilistic based and deterministicbased.

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The damage detection toolbox uses one probabilistic damage detection algorithm that employsthe use of a Bayesian approach to search for the most probable damage event by comparing relativeprobabilities for different damage hypotheses. The first variation of the Bayesian search algorithm is basedupon the comparison of modal parameters of an analytical model and the modal parameters from themodal analysis software to predict damage locations.[1] The second variation uses the Ritz vectorsextracted from the modal parameters and the Ritz vectors from an analytical model in its comparison topostulate damage locations. These methods are suitable if an inaccurate model of the structure is assumedor if a high degree of noise is inherent in the vibration test data. The toolbox also provides the user withtwo deterministic based damage detection algorithms that use traditional model updating methods toaccurately diagnose damage within a structure.[2] These methods are best suited for instances where thestructure can be accurately modeled and little noise is contained in the vibration test data.

The damage detection toolbox has been successfully used at Stanford University to predictdamage in structures recently tested. The toolbox has been used in the diagnoses of damage for an eightbay truss structure, a simple beam, and in a grid-type bridge model.

REFERENCES[1] H. Sohn and K. H. Law. "Bayesian Probabilistic Approach for Structure Damage Detection", Earthquake

Engineering and Structural Dynamics, 26:1259-1281, 1997.[2] F.M. Hemez , "Theoretical and Experimental Correlation between Finite Element Models and Modal Tests in the

Context of Large Flexible Space Structures". PhD Thesis, Aerospace Engineering Sciences, University ofColorado, Boulder, CO, 1993.

[3] D.C. Zimmerman and T. Simmermacher, "Model Correlation using Multiple Static Load and Vibration Tests".American Institute of Aeronautics and Astronautics, 33:2182-2188, 1995.

INCORPORATION OF ACCURATE SENSITIVITY ANALYSIS INTO ASCALABLE MP STRUCTURAL DYNAMICS FEM CODE

K.F. Alvin, G.M. Reese, D.M. Day and M. Bhardwaj

(1) - Sandia National Laboratories. E-mail : kfalvin@sandia.gov(2) - Sandia National Laboratories. E-mail : gmreese@sandia.gov(3) - Sandia National Laboratories. E-mail : dday@cs.sandia.gov

ABSTRACTThe computation of sensitivity coefficients for output quantities of a FEM-based computer

simulation is a necessary component of design optimization, inverse problems, uncertainty analysis andvalidation of structural dynamics models. These sensitivity coefficients are typically analytical or semi-analytical derivatives of output quantities such as displacement, acceleration, frequencies and mode shapeswith respect to particular design parameters of interest. While standard industry analysis codes such asMSC/NASTRAN have sensitivity analysis capabilities, there has been relatively little work in the FEMresearch code environment, where emphasis has been on developing scalable parallel solver technology,as well as nonlinear analysis.

Recently, Sandia National Laboratories has been developing Salinas, a general purpose finiteelement code for structural dynamics, which is targeted for scalable performance on ASCI-class massivelyparallel (MP) computers. To achieve these aims, Salinas incorporates the FETI solver technologydeveloped at CU-Boulder. FETI is a domain decomposition-based multi-level linear solver forunstructured grids, and is particularly suited to the solution of structural mechanics problems. Salinas withFETI has demonstrated scalability for thousands of processors on the distributed memory DOE ASCI Redplatform.

In order for Salinas to meet its mission of supporting DOE stockpile stewardship by providingvalidated high fidelity simulation capabilities together with quantified uncertainties, sensitivity analysishas become an integral piece of the code development effort. Sensitivity analysis has been integrated intothe static analysis, eigenvalue analysis, and transient analysis modules. In all cases, output sensitivities arecomputed by analytical differentiation of the matrix equations of motion, using stiffness and mass matrixsensitivities computed via finite differences. Solution of the resultant sensitivity equations areaccomplished using the FETI solver, or, in the case of eigenvector derivatives, using an iterative conjugate

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gradient algorithm which uses the FETI solver in its preconditioning phase. In all case, the modulesexploit the memory feature of the FETI solver, where search directions are stored between calls to thesolver for cases of multiple force vectors.

The integration of Salinas, FETI, and the sensitivity analysis methods have enabled thecomputation of highly accurate eigenvector sensitivities for systems of over 1 million equations onthousands of processors. In this talk, implementation and performance issues will be addressed, andapplication to structural dynamics problems from the defense industry will be discussed.

EXPERIMENTAL VALIDATION OF TRANSIENT FINITE ELEMENT MODELPREDICTIONS

S.W. Doebling , F.M. Hemez , W. Rhee and P. Beardsley

(1) - Los Alamos National Laboratory. E-mail : doebling@lanl.gov(2) - Los Alamos National Laboratory. E-mail : hemez@lanl.gov

(3) - Los Alamos National Laboratory

ABSTRACTIn many engineering applications, it is advantageous or necessary to have reliable means of

predicting the dynamic behavior of a structural system. However, even as increasingly advancedmathematical tools are developed, the only way to assess the predictive quality of a particular modeling isby correlating the numerical simulation to measurements obtained on the system or its components. Healthmonitoring techniques, for example, identify potential damage in a structure by understanding the sourceof discrepancy between measured and computed modal responses.

Since the overwhelming majority of test-analysis correlation techniques have been developed tohandle finite element analysis in the frequency domain, their application is generally restricted to linearsystems. The objective of this work is to extend the concept of test-analysis correlation to nonlinearsystems, therefore, requiring the analysis to take place in the time domain [1]. Nonlinearities of any typeand nature are considered. The computational procedure consists of assessing the degree of correlationbetween test measurements and simulation results obtained from a time-domain, explicit finite elementmodel. The PCD (Principal Component Decomposition) technique [2] is the metric adopted for comparingthe data sets and the inverse problem is formulated as a 2-point boundary value problem resulting from anoptimal control approach [3].

This presentation discusses experimental results obtained by impacting a population of similarcylinders against a rigid floor. Similar tests are repeated for all unit members of the population, whichprovides us with a statistical characterization of the test response. In addition, finite element simulationsare carried out using an explicit formulation and measured responses are compared to computations in anattempt to determine the important design parameters and assumptions. The modeling difficultiesencountered are discussed. These include how the material behavior is represented; how contact surfacesare handled; and what the most effective modeling (3D?, axi-symmetric?, coarse or refined mesh?) turnsout to be when the objective focuses on improving our modeling rules via test-analysis correlation andinverse problem solving.

REFERENCES[1] Hemez, F.M., and Doebling, S.W., "Test-Analysis Correlation and Finite Element Model Updating for Nonlinear,

Transient Dynamics", 17th International Modal Analysis Conference, Kissimmee, Florida, Feb. 8 -11, 1999, pp.1501-1510.

[2] Hasselman, T.K., Anderson, M.C., and Wenshui, G., "Principal Components Analysis For Nonlinear ModelCorrelation, Updating and Uncertainty Evaluation", 16th International Modal Analysis Conference, SantaBarbara, California, Feb. 2-5, 1998, pp. 664-651.

[3] Dippery, K.D., and Smith, S.W., "An Optimal Control Approach to Nonlinear System Identification", 16thInternational Modal Analysis Conference, Santa Barbara, California, Feb. 2-5, 1998, pp. 637-643.

Minisymposium

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Computational Failure MechanicsFrancisco Armero, Paul Steinmann, Howard Schreyer and Kaspar Willam

SESSION 1: THEORETICAL AND NUMERICAL ASPECTS OF STRAIN LOCALIZATION

LOCALIZATION IN SOFTENING PLASTICITY BY GLOBAL ENERGY MINIMIZATIONG. Chen and G. Baker......................................................................................................................................................27

SOME REMARKS ON ILL-POSEDNESS IN CONTINUUM PROBLEMSA. Benallal........................................................................................................................................................................28

A NEW REGULARIZATION METHOD FOR LOCALIZED FAILURE IN STRAIN-SOFTENING SOLIDS BASED ONASSUMED LOCAL FLUCTUATION MODES ON A MICRO-STRUCTURE

C. Miehe and M. Lambrecht.............................................................................................................................................28

ON LOCALIZATION IN HYDRO-MECHANICALLY COUPLED PROBLEMSR. Larsson and J. Larsson................................................................................................................................................29

NUMERICAL ANALYSIS OF LOCALIZATION CONSIDERING STOCHASTIC MATERIAL DEFECTSM.A. Gutierrez and R. de Borst.........................................................................................................................................30

NUMERICAL SIMULATIONS OF STRAIN LOCALIZATION IN INELASTIC SOLIDS BY USING MESHLESSMETHODS

S. Li and W.K. Liu............................................................................................................................................................31

SESSION 2: NUMERICAL SIMULATION OF FRACTURE

FINITE ELEMENT ANALYSIS OF FRACTURE AND FRAGMENTATIONM. Ortiz............................................................................................................................................................................31

COMPUTATION OF GEOMETRICALLY NON-LINEAR FRACTURE MECHANICS PROBLEMSD. Ackermann and P. Steinmann......................................................................................................................................32

EXPERIMENTAL COMPARISON AND MODEL ASSESSMENT FOR A NOVEL APPROACH TO INELASTICFRACTURE

M.M. Rashid and R. Roy...................................................................................................................................................33

DYNAMIC CRACK GROWTH IN A COMPRESSIVE SHEAR STRENGTH TEST ALONG A POLYMER-GLASSINTERFACE

P. Rahulkumar, A. Jagota, S. Bennison and S. Saigal.......................................................................................................34

SIMULATION OF MODE I CRACK GROWTH IN POLYMERS BY CRAZINGM.G. Tijssens, E. van der Giessen and L.J. Sluys.............................................................................................................34

CRACK GROWTH WITH ENRICHED FINITE ELEMENTS FOR MINDLIN-REISSNER PLATEST. Belytschko, J. Dolbow and N. Mos.............................................................................................................................35

SESSION 3: DAMAGE AND FAILURE

MODEL FOR LARGE STRAIN FAILURE ANALYSIS OF CONCRETE AND ITS APPLICATIONS TO IMPACT ANDBLAST

Z.P. Bazant, F. Caner, M. Adley and S. Akers..................................................................................................................35

SOME COMPUTATIONAL ASPECTS IN NON-LOCAL DAMAGE MODELSA. Rodriguez-Ferran and A. Huerta.................................................................................................................................36

A GENERAL FRAMEWORK FOR DAMAGE THEORIES AND ITS APPLICATIONF. Armero and S. Oller.....................................................................................................................................................37

A RATE-DEPENDENT DUCTILE FAILURE MODEL AND ITS NUMERICAL IMPLEMENTATIONQ.H. Zuo, F.L. Addessio, P.J. Maudlin and J.N. Johnson.................................................................................................37

COMPUTATIONAL MEASURES OF STRUCTURAL DAMAGE FOR GLOBAL FAILURE ANALYSISY. Petryna, W.B. Kraetzig and F. Stangenberg.................................................................................................................38

COMPUTATIONAL FAILURE ANALYSIS OF REINFORCED CONCRETE SHELLSW.B. Kraetzig and S.Y. Noh..............................................................................................................................................39

SESSION 4: GRADIENT AND MICROPOLAR PLASTICITY

ADAPTIVE STRATEGY FOR GRADIENT-REGULARIZED PLASTICITYT. Svedberg and K. Runesson...........................................................................................................................................39

MECHANISM-BASED STRAIN GRADIENT PLASTICITYH. Gao, Y. Huang, W.D. Nix and J.W. Hutchinson...........................................................................................................40

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GRADIENT-VISCOPLASTIC MODELING OF 3D SHEAR BANDINGL.J. Sluys and W.M. Wang................................................................................................................................................41

STRAIN LOCALIZATION IN 3D PRESSURE-SENSITIVE ELASTOPLASTIC COSSERAT CONTINUAM.M. Iordache and K.J. Willam.......................................................................................................................................41

ON THE CONSISTENCY OF VISCOPLASTIC FORMULATIONSA. Carosio and G. Etse.....................................................................................................................................................42

THE VARIATIONAL FORMULATION OF STRESS-UPDATE ALGORITHMS IN THE CASE OF NON-STANDARDBEHAVIOURS

M. Hjiaj, G. de Saxce and G. Guerlement.........................................................................................................................42

SESSION 5: DISCONTINUOUS / DECOHESIVE APPROACHES

ON CONTINUUM AND DISCRETE MODELS INDUCED BY STRONG DISCONTINUITY KINEMATICSJ. Oliver, M. Cervera and O. Manzoli..............................................................................................................................43

MODELING FAILURE AS A STRONG DISCONTINUITY WITH THE MATERIAL POINT METHODH.L. Schreyer and D.L. Sulsky..........................................................................................................................................44

FINITE ELEMENT ANALYSIS OF SLIP SURFACES IN ROCKR.A. Regueiro, C.M. Stone, J.G. Arguello, A.F. Fossum and R.I. Borja...........................................................................45

A NUMERICAL PROCEDURE TO SIMULATE THE EVOLUTION

OF LOCALIZATION WITHOUT USING HIGHER ORDER MODELSZ. Chen.............................................................................................................................................................................45

FAILURE ANALYSIS OF ELASTO-PLASTIC MATERIAL MODELS AT DIFFERENT LEVELS OF OBSERVATIONE. Kuhl, E. Ramm and K. Willam.....................................................................................................................................46

DISCRETE AND SMEARED MODELING OF SNAP-THROUGH FRACTURE IN BUILDINGSJ.G. Rots and P.H. Feenstra.............................................................................................................................................47

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LOCALIZATION IN SOFTENING PLASTICITY BY GLOBAL ENERGYMINIMIZATION

G. Chen and G. Baker

(1) - Department of Civil Engineering. The University of Queensland(2) - School of Engineering The University of Warwick, UK. E-mail : g.baker@mailbox.uq.edu.au

ABSTRACTSmeared crack representations are notorious for predicting a very diffuse crack pattern and

failing to generate effective strain localization. Coupled with this issue is that significant stress is lockedalong side a propagating crack (Rots & Blaauwendraad, 1989). The difficulty is that the 'true' load path isnot captured, and so doubt must be raised over the validity of the corresponding solution; there are manyinstances of course where even peak loads are not predicted accurately with a smeared crack model of,say, concrete.

Localization can of course be viewed as a bifurcation of the displacement field, a generalsymptom of which is that material within the localizing band exhibits strain softening whereas thatimmediately adjacent unloads elastically. The general difficulty with standard smeared algorithms is thatthe uncracked material cannot unload fast enough, and the tangent equilibrium equations necessarily forcea distributed solution (Hunt & Baker, 1995). Our contention is that the tangent elasticity is insufficient tocapture localization and that unloading needs to be induced by some additional principle.

The authors have argued previously (Chen & Baker, 1998) that the correct bifurcation load, andconsequent post - bifucration path, can be predicted by minimizing the increment of "global" second orderwork of the whole structure. That is, a discontinuous bifurcation analysis, while valuable in detectingbreakdown of a constitutive model, corresponds to a local bifurcation. However, softening and quasi-brittle fracture arise with reference to the state of the whole structure, as noted in many experiments,where cracks begin and then close "elastically" while others grow unbounded.

In this article, we formulate the problem based on direct energy minimization. We note that forplastic flow problems, as distinct from holonomic loading, we must minimize increments of work, butshow that only second order work needs to be tested. We implement these ideas with a softening plasticitymodel, having tried Drucker-Prager and Rankine models of mode I fracture in concrete (Feenstra & deBorst, 1995). The solution strategy we use is a local optimization algorithm based on the direct searchscheme of Powell. Gradient techniques, while faster, often break down when the constitutive law has asharp peak, as is often chosen for tension softening of concrete.

We demonstrate the algorithm on mode I problems of a simple panel in tension and pure bendingof a beam. The results capture localization and unloading exactly as required. That is, we provide nocomputational trigger to form strain localization bands in a particular location, such as perturbations ofgeometry or material properties. Yet, cracks form without interference at appropriate spacings. In thesimple mode I problems, in fact we obtain one localized crack across the panel, and one central crack inthe beam. Naturally, standard plasticity does not accurately capture localization in shear problems,because of the high strain gradients across a shear band. Hence, we suggest an extension to gradientplasticity for the constitutive model in mode II problems. However, this does not change our overallenergy minimization process for solution control.

REFERENCES[1]Chen, G. and Baker, G. (1998), "Strain localization in softening solids: extremum principles and path dependence",

Under review.[2]Hunt, G.W. and Baker, G. (1995), "Principles of localization in the fracture of quasi-brittle structures", Jnl. Mechs

Phys. Solids, 43(7), 1127-1150.[3]Feenstra, P. and de Borst, R. (1995), "A plasticity model and algorithm for mode I cracking in concrete", Int. Jnl.

Numer. Meths. Engrg., 38, 2509-2529.[4]Rots, J. and Blaauwendraad, J. (1989), "Crack models for concrete: Discrete or smeared ? fixed, multi-directional

or rotating?", Heron, 34(1), 59pp

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SOME REMARKS ON ILL-POSEDNESS IN CONTINUUM PROBLEMS

A. Benallal

(1) - Laboratoire de Mecanique et Technologie. E-mail : benallal@lmt.ens-cachan.fr

ABSTRACTThe concept of ill-posedness is very common in mechanics and particularly in failure mechanics.

Many contributions have been devoted to the analysis of this concept mainly because of the numericaldifficulties encountered in the description of rupture and its accompagning phenomena such as instabilitiesand localisation. When defined rigorously and extending the classical definition of Hadamard, necessaryand sufficient conditions for ill-posedness to occur have been obtained. In the context of solid mechanicsand in the framework of rate-independent continua, these conditions can be explicitely determined. For ageneral rate-independent solid, these conditions can be resumed to three local conditions. The first one isthe loss of ellipticity of the continuing equilibrium equations, the second is the boundary complementingcondition and the third one is the interfacial complementing condition present only when the solid isheteregeneous. Te first one is related only to the constitutive behaviour whereas the second and the thirdare linked to the constitutive behaviour but also to the type of boundary conditions and interfacialconditions. Although the mechanical interpretation of all these conditions are understood in the case of aninfinite or a semi-infinite solid, this interpretation is not clear in the case of a finite solid. The mainobjective of this talk is to bring some light to this question. Moreover, for a finite solid and in manypractical situations, these conditions are first met in one point of the solid. The ill-posedness and itsconsequences ( numerical for instance) need to be clarified. The talk will also discuss this topic.

A NEW REGULARIZATION METHOD FOR LOCALIZED FAILURE IN STRAIN-SOFTENING SOLIDS BASED ON ASSUMED LOCAL FLUCTUATION MODES

ON A MICRO-STRUCTURE

C. Miehe and M. Lambrecht

(1) - Institute fur Mechanik (Bauwesen), Lehrstuhl I. E-mail : cm@mechbau.uni-stuttgart.de(2) - Institute fur Mechanik (Bauwesen) Lehrstuhl I

ABSTRACTThe simulation of localized failure in strain - softening solids, for example in the form of shear

bands, yields the typical mesh - dependent postcritical results within standard finite element formulations.We here propose a new regularization technique based on a micromechanically motivated approach whichovercomes this problem. The key idea is the introduction of a micro - structure at a typical Gauss - pointof the finite element mesh which bifurcates in the form of an assumed fluctuation field when macroscopic