Implementation of Automated Multilevel Substructuring for Frequency Response Analysis of Structures

201 Pages·2001·5.616 MB·English

by  Matthew Frederick Kaplan

Copyright
by
Matthew Frederick Kaplan
2001
The Dissertation Committee for Matthew Frederick Kaplan certifies that this
is the approved version of the following dissertation:
Implementation of Automated Multilevel
Substructuring for Frequency Response Analysis of
Structures
Committee:
Implementation of Automated Multilevel
Substructuring for Frequency Response Analysis of
Structures
by
Matthew Frederick Kaplan, B.S.A.S.E.
Dissertation
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
The University of Texas at Austin
December 2001
UMI Number: 3037508
Copyright 2002 by
Kaplan, Matthew Frederick
All rights reserved.
________________________________________________________
UMI Microform 3037508
Copyright 2002 ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
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To my wife and family, who knew I could do it and made it possible to try.
Acknowledgments
Thisresearchprojecttookmuchlongerthananyonethoughtandhasreachedheights
noonereallyexpectedatthebeginning. Therearemanypeoplewhohavecontributedalong
the way. I would like to thank Osni Marques, Inderjit Dhillon, and Rich Lehoucq for their
assistance with various eigensolver issues over the years. Thanks also go to Scott Messec
andReubenReyesfortheirhelpwithnetworking,computers,visualization,andmanyother
practical matters. I am grateful to Mintae Kim, Chang-Wan Kim, and Ruijie Liu for being
such good students that they were able to take over my work. I am indebted to Dr. Robert
van de Geijn for his advice, insight, and perspective from the other side of the street. I am
likewiseindebtedtoDr.SuzanneWeaverSmithforheradvice,insight,andperspectivefrom
the other side of the country. It has been my privilege to have worked with Dr. Roy Craig.
I would like to thank Dr. Craig for setting such a high standard and for innumerable acts
of kindness. Two people who have supported this research both morally and substantively
are Chris Tutt and Mladen Chargin. I am very grateful to both of them. I most especially
appreciatemypartnerincrime,MarkMuller,withoutwhomthisresearchwouldneverhave
gone so far. Of the many other people who have helped me along in this process, I would
like to thank Paul Conti, Jeanie Duvall, Nita Pollard, and Donna Soward.
Duringmytenure,thisresearchhasreceivedfinancialsupportfromtheTexasHigher
Education Coordinating Board, ONR, Ford Motor Company, IBM, Cray, Hewlett-Packard,
Sun Microsystems, SGI, Sandia National Laboratories, and NASA. In addition, several
hardware vendors provided extensive access to their technical support personnel. I would
like to thank Doug Petesch, Martin Feyereisen, David Whitaker, Dave Strenski, Dawson
Deuermeyer, and Mark Kelly. I also received funding from AFOSR through the National
Defense Science and Engineering Fellowship Program.
v
Finally,IwouldliketothankDr.JeffBennighofforputtingupwithmeandhelping
me grow academically and professionally. I must also thank Dr. Bennighof for having a
great idea and letting me share the ride. It was a great ride while it lasted. Thank you!
Matthew Frederick Kaplan
The University of Texas at Austin
December 2001
vi
Implementation of Automated Multilevel
Substructuring for Frequency Response Analysis of
Structures
Publication No.
Matthew Frederick Kaplan, Ph.D.
The University of Texas at Austin, 2001
Supervisor: Jeffrey K. Bennighof
In the design of vehicles, such as automobiles, aircraft, spacecraft, or submarines, it
is important to be able to accurately predict dynamic behavior of the structure. With the
extremely high cost of building physical prototypes of these vehicles, there is a growing em-
phasisonanalysisofcomputermodels. Inthisdissertation, amethodknownasAutomated
Multilevel Substructuring (AMLS) is presented for accurately solving frequency response
problems involving large, complex models with millions of degrees of freedom. Conven-
tional methods for addressing these problems, such as mode superposition using a Lanczos
eigensolver or model reduction using component mode synthesis, are reviewed.
The Automated Multilevel Substructuring (AMLS) method partitions finite ele-
ment models into substructures, similar to component mode synthesis methods, but uses
an automated partitioning procedure that reduces the burden on the analyst. The finite
element matrices are projected onto a reduced subspace, on which the frequency response
is computed. Two frequency response algorithms are presented. Both methods require the
solution of a global eigenvalue problem on the reduced subspace. The first method uses
straightforward mode superposition. The second method employs a new iterative approach
vii
in which the modal frequency response leads to a residual problem that is solved using an
iterative splitting method. The global eigensolution and frequency response algorithms are
specificallydesignedtotakeadvantageofthepropertiesofthereducedsubspace. Numerical
examplesarepresentedformodelswithmillionsofdegreesoffreedom. Theperformanceand
accuracy of the AMLS method are compared to the standard commercial software package
forlarge-scalelineardynamicanalysis. TheseexamplesestablishthatAMLScanbeusedto
accuratelyobtaintheresponseofverylargemodelswithsignificantlylesscomputationalre-
sources than competing methods. In comparison to the modal frequency response obtained
with the standard commercial software package using a shifted block Lanczos algorithm,
AMLSranupto6.4timesfaster,usedlessmemory,andrequiredanorderofmagnitudeless
data transfer. Thus, the AMLS method makes it possible to do frequency response analysis
of large, complex structures at higher frequencies than was previously practical.
viii
Contents
Acknowledgments v
Abstract vii
List of Tables xiii
List of Figures xv
Chapter 1 Introduction 1
1.1 Brief History of AMLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 An Overview of the AMLS Method . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Review of Competing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Author’s Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Outline of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 2 Survey of Numerical Methods 10
2.1 Solution Methods for Large Linear Systems of Equations . . . . . . . . . . . . 11
2.1.1 Direct Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Iterative Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Multigrid Methods and Domain Decomposition . . . . . . . . . . . . . 16
2.2 Eigensolution Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 Power Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Similarity Transformation Methods . . . . . . . . . . . . . . . . . . . . 26
2.2.3 Krylov and Lanczos Algorithms . . . . . . . . . . . . . . . . . . . . . . 27
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