Analytical and numerical investigations of form-finding methods for tensegrity structures [Elektronische Ressource] / vorgelegt von Giovani Gomez Estrada
152 Pages
English

Analytical and numerical investigations of form-finding methods for tensegrity structures [Elektronische Ressource] / vorgelegt von Giovani Gomez Estrada

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Analytical and numerical investigationsof form-finding methods fortensegrity structuresVon der Fakult¨at Informatik, Elektrotechnik undInformationstechnik der Universit¨at Stuttgartzur Erlangung der Wu¨rde einesDoktors der Naturwissenschaften (Dr. rer. nat.)genehmigte AbhandlungVorgelegt vonGiovani Gomez Estradaaus MexikoHauptberichter: Prof. Dr. Hans-Joachim BungartzMitberichter: Prof. Dr. Manfred BischoffMitberichter: Prof. Dr. Thomas ErtlTag der Einreichung: 19.10.2006Tag der mu¨ndlichen Pru¨fung: 12.07.2007Max-Planck-Institut fu¨r Metallforschungund Universit¨at Stuttgart, 2007Contents1 Introduction 11.1 Statically indeterminate structures . . . . . . . . . . . . . . . . . . . . . . 21.2 Tensegrity structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Applications and challenges of tensegrity structures . . . . . . . . . . . . . 51.4 State of the art of form-finding methods for tensegrity structures . . . . . . 71.5 Overview of the research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6 Outline of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Tensegrity structures 132.1 Attraction and repulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Basic hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Geometry and tension coefficients . . . . . . . . . .

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Published 01 January 2007
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Language English
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Analyticalandnumericalinvestigations
ofform-ndingmethodsfor
tensegritystructures

VonderFakulta¨tInformatik,Elektrotechnikund
InformationstechnikderUniversita¨tStuttgart
zurErlangungderWu¨rdeeines
DoktorsderNaturwissenschaften(Dr.rer.nat.)
genehmigteAbhandlung

Vorgelegtvon
GiovaniGomezEstrada
ausMexiko

Hauptberichter:Prof.Dr.Hans-JoachimBungartz
Mitberichter:Prof.Dr.ManfredBischo
Mitberichter:Prof.Dr.ThomasErtl
TagderEinreichung:19.10.2006
Tagdermu¨ndlichenPru¨fung:12.07.2007

Max-Planck-Institutfu¨rMetallforschung
undUniversita¨tStuttgart,2007

Contents

1Introduction1
1.1Staticallyindeterminatestructures......................2
1.2Tensegritystructures..............................4
1.3Applicationsandchallengesoftensegritystructures.............5
1.4Stateoftheartofform-ndingmethodsfortensegritystructures......7
1.5Overviewoftheresearch............................9
1.6Outlineofthedissertation...........................11

2Tensegritystructures13
2.1Attractionandrepulsion............................13
2.2Basichypotheses................................14
2.3Applications...................................16
2.4Geometryandtensioncoecients.......................18
2.5Rankconditionsandnullity..........................21
2.6Initialstiness..................................23
2.7Form-ndingoftensegritystructures.....................25
2.8Example:thetriplex..............................29

3Analyticalform-ndingoftensegritycylinders33
3.1Tensegritycylinders...............................33
3.2Geometricarrangementoftensegritycylinders................34

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4

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6

3.3Analyticalform-ndingprocedure.......................37
3.4Enumeratingsolutions:regularconvexandstarpolygons..........40
3.5Analysisoftensioncoecients,forcesandlengths..............43
3.6Afullexample:the9-plex...........................46
3.7Implementation.................................49
3.8Conclusionsandnalremarks.........................51

Stabilityandnon-uniquenessofthesolutionfortensegritycylinders52
4.1Introduction...................................52
4.2Stabilityandglobalequilibrium........................53
4.3Non-uniquenessoftheanalyticalsolutionfortensegritycylinders......56
4.4Initialstiness..................................61
4.5Afullexample:the30-plex..........................66
4.6Conclusionsandnalremarks.........................69

Numericalform-ndingoftensegritystructures73
5.1Introduction...................................73
5.2Form-ndingwithprototypes.........................75
5.3Fromtensioncoecientstocoordinates....................76
5.4Fromcoordinatestotensioncoecients....................79

5.5Examplesof2Dand3Dtensegritystructures.................81
5.6Implementation.................................89
5.7Complexityandconvergence..........................92
5.8Numericalexample...............................95
5.9Conclusionsand