Topological Optimization of Buckling

352 Pages·2018·11.42 MB·English

by  Bingchuan Bian

BingchuanBian
TopologicalOptimizationofBuckling
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Bingchuan Bian
Topological
Optimization
of Buckling
Author
Prof.BingchuanBian
TaishanUniversity
Dept.ofMechanicalandarchitecturalEngineering
Taian
271021SHANDONG
China
BingchuanBianisassociateprofessorattheMechanicalandArchitecturalengineeringCollegeofthe
TaishanUniversity.Beforethat,heworkedinLunengTaishanElectricPowerEquipmentCo.,Ltdin
ShandongProvince,China.Hemainlyengagesinteachingandscientificresearchforthe
optimizationdesignofmechanicalstructuresandintheresearchanddevelopmentofelectricpower
equipment.
Hepublishedmorethan30papersinacademicjournalsandinternationalconferences.
ISBN978-3-11-046116-9
e-ISBN(PDF)978-3-11-046227-2
e-ISBN(EPUB)978-3-11-046127-5
LibraryofCongressCataloging-in-PublicationData
Names:Bian,Bingchuan,author.
Title:Topologicaloptimizationofbuckling/BingchuanBian.
Description:Berlin;Boston:deGruyter,[2018]|Includesbibliographical
referencesandindex.
Identifiers:LCCN2018007857|ISBN9783110461169(hardcover)
Subjects:LCSH:Buckling(Mechanics)|Strengthofmaterials.|Engineering
mathematics.
Classification:LCCTA656.2.B532018|DDC624.1/76–dc23LCrecordavailableat
https://lccn.loc.gov/2018007857
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie;detailed
bibliographicdataareavailableontheInternetathttp://dnb.dnb.de.
©2018WalterdeGruyterGmbH,Berlin/Boston/HuazhongUniversityofScience&TechnologyPress
Typesetting:IntegraSoftwareServicesPvt.Ltd.
Printingandbinding:CPIbooksGmbH,Leck
Coverimage:Eskemar/iStock/GettyImages
www.degruyter.com
Acknowledgments
IamindebtedtoProfessorYunkangSuiforhisguidanceduringthepreparationof
this manuscript.Mr.Sui’sprofound wisdom,meticulousapproach,and innovative
methodscontinuetoinfluenceandinspireme.Iwasfortunateenoughtohavespent
fouryearsatBeijingUniversityofTechnology.Inadditiontoacademictraining,Mr.
Suimentoredandimpartedvariouslifeskills.Thesehaveimmenselyhelpedme.
I am also grateful to Associate Professor Baorui Ye who provided help and gui-
danceduringmystudytime.
I also thank my teachers’ selfless help in my doctoral study at Engineering
Numerical Simulation Center of Beijing University of Technology. I also thank all
studentsfortheircooperation.
Iamgratefultoalltheleaders,teachersatTaishanUniversityandmyfamilyfor
theirpatience,careandsupport.
ThisresearchwassupportedbyNationalNaturalScienceFoundation(10472003),
Beijing Natural Science Foundation (3042002), Shandong Province Youth Scientist
FundProject(BS2009ZZ007),theTaishanUniversityResearchFundProject(Y07-2-
08)andtheUnitedStatesMSCcompanysupport.
https://doi.org/10.1515/9783110462272-201

Contents
1 Introduction 1
1.1 Background 1
1.2 CurrentDevelopment 3
1.3 SoftwarePlatform 13
1.4 KeyTopicsinBucklingTopologicalOptimizationResearch 14
2 TopologicalOptimizationforContinuousStructurewithBulking
Constrain 17
2.1 Introduction 17
2.2 ICMMethod 18
2.3 DeterminationofFilterFunction 21
2.4 ModelEstablishmentandRealization 28
2.5 SolutiontoOptimization 32
2.6 OptimizationStrategy 34
2.7 ConstrainSelection 36
2.8 OptimizationAlgorithms 48
2.9 NumericalSimulationandCaseStudy 49
2.10 Summary 108
3 TopologicalOptimizationforContinuousStructurewithBulking
andDisplacementConstraint 109
3.1 Introduction 109
3.2 ModelEstablishmentandSolution 110
3.3 OptimizationStrategy 116
3.4 ConstrainSelection 117
3.5 OptimizationAlgorithms 123
3.6 NumericalSimulationandCaseStudy 125
3.7 Summary 172
4 TopologicalOptimizationforContinuousStructurewithBuckling
andStressConstraints 174
4.1 Introduction 174
4.2 DeformationEnergy 175
4.3 TheTheoreticalBackgroundofDeformationEnergy 176
4.4 MethodofGlobalizationofStressConstraintsandStrainRevision
Coefficient 176
4.5 ModelEstablishmentandSolution 178
4.6 OptimizationStrategy 184
4.7 ConstraintSelection 185
4.8 OptimizationAlgorithms 190
VIII Contents
4.9 NumericalSimulationandCaseStudy 191
4.10 Summary 238
5 TopologicalOptimizationforContinuousStructurewithStatic
Constraint 240
5.1 Introduction 240
5.2 ModelEstablishmentandSolution 240
5.3 UpperLimitforConstraint 246
5.4 OptimizationAlgorithms 246
5.5 NumericalSimulationandCaseStudy 248
5.6 Summary 269
6 SoftwareandUserInstructions 274
6.1 Introduction 274
6.2 CompilingandLinkingofaUserProgram 275
6.3 SetupforAnalysisandOutput 275
6.4 TopologicalOptimizationMenuandInputs 276
6.5 OutputandResultsMenu 282
6.6 Summary 292
7 EngineeringApplications 293
7.1 Introduction 293
7.2 SystemOptimizationinIndustryviaMixedProgramming 293
7.3 TopologicalOptimizationintheDesignofaPowerTransformer
LiftingLug 297
7.4 FiniteElementMethodandTopologicalOptimizationina
Small-sizedTransformerFuelTank 306
7.5 TopologicalOptimizationintheDesignofVacuumTank 322
7.6 Summary 331
8 Prospect 333
References 336
Disclaimerforthesoftware 340
Index 341
1 Introduction
1.1 Background
Withthedevelopmentofmodernindustrialtechnology,alargenumberofnewlight
andthinstructuresofhighstrengtharewidelyusedinnationaldefenseandcivilian
industries.Especiallywiththerapiddevelopmentofaviation,aerospaceandatomic
energyindustries,complexstructuresofthebasicrod,plateandshellareappliedtoa
largenumberofindustries.Thus,stabilityofthesebasiccomponentsundervarious
loadshasattractedattentionofmanyscholarstoalargeextent[1].
A majority of engineering accidents in the past have been due to buckling
instability of the structure. For example, the three-span cantilever Quebec
Bridge was built in Canada in 1907. Owing to insufficient flexural strength and
buckling instability of the batten, the entire deck instantly fell into the river,
thereby killing 75 workers. Designers of Hartford state’s stadium in Connecticut
constructed a roof, the grid structure of which considered only the bending
buckling strut; however, torsional buckling, strut support and eccentric tor-
sional buckling were not considered, and the stadium was made available for
public use. On January 18, 1978 – a heavy snowy night – the space grid
structure crashed down due to buckling instability of the pressure bar, causing
a huge loss. The facts stated here completely explain the importance of buckling
in structural design [2].
Engineeringstructuraldesignworkscanbedividedintotraditionaldesignand
optimal design. Design engineers can choose the type of structure and form,
includingthenecessarymaterials,inaccordancewiththeirowntheoreticalknowl-
edge and practical experience in traditional design. The structures are analyzed
afterpreparingtheinitialdesignscheme.Thestrength,stiffness,stability(includ-
ing regional stability and global stability) and the vibration frequency of the
structures are checked in accordance with the results of the analysis. When the
design does not meet the economic and security requirements, then the initial
designismodified,reanalyzedandrecheckeduntilthestructuremeetstheneces-
saryrequirements.Findingareasonabledistributionofmaterialisthemainshort-
comingof traditionaldesign, andthusit isdifficult tocompare the idealsofboth
economic and safe design. Optimal design is all about providing the optimal
mathematical model, solvingthe optimalmodel based on structural optimization
and design theories and methods in accordance with the established structure of
the type, form, condition, material and norms under various constraints. The
optimaldesignisinconvergenceafterseveraliterations.Throughoptimaldesign,
the structure achieves economic unity and security. Optimaldesign encompasses
the structure’s new development and achievements, and it has great significance
andbroadprospects[3–5].
https://doi.org/10.1515/9783110462272-001