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Definition8
Aneutralsurfaceofasheetingisasheetingreferencesurfaceifeachits
foldistransformedeffectively.Theneutralsurfaceofaplanarsheetingis
flat.
Definition9
Aneutralaxisofafoldisafold’saxisifthefoldistransformed
effectively.Intheiscase,thebothaxesoffoldandtwistarethesameline.
Itisstraightforeachfoldbeforeandaftereffectivetransformationof
asheeting.
Thereforeespeciallytheadoptionofthemutualpositionofthedirectrices
hasimportantinfluenceontherequiredshapeoftheshell[88].Itisasectorof
awarpedsurfacewithacontractionpassingthroughthehalvesofthefold’s
lengths[1,2,11].Shapesofthecontractionanddirectricesaffectthe
attractivenessoftheroofshellanditsintegrationwiththeentirebuilding
includingelevations[12,18].
Definition10
Awarpedsurfaceofisadouble-curvedundevelopableruledsurface.
Therearetwowaysofdeterminingthewarpedsurfaces.Thefirstone,is
basedonthreedirectrices[58,80].Thesecondoneusestwolines,thatisa
lineofstrictionandasphericalindicatrix[2]beingpresentedinChapters5
and7indetails.
Thestraightedgesbetweenfold’sflangesandwebsstiffeneachfoldand
causethefactthatthemaximumdegreeoftheshapetransformationhastobe
limitedtoavoidlocalelasticinstabilityofthefold’swallsanddistortionofthe
fold’scross-sections[20,24,71,74].Thediversifiedtypesofthefold’sshape
transformationsneedtocarryoutcomplexexperimentalandnumerical
researchesintermsofgeometry,strengthandstability[16,24,36],Fig.1-4.
Theeffectivelytransformedshellsheetingisaone-layershell[24,97].
However,tostiffentheshellroofattheservicestateofabuilding,twofolded
sheetingscanindependentlybetransformedand,next,assembledtodirectrices
andintermediatememberstoobtainmulti-layerroofshell.Thus,twosheetings
canlimitthesamerooffromtheoutsideandinsideofthebuilding.Thefreedom
ofthesheetingtransformationallowstoshapetheshelldirectricesandplane-
walledelevationsofthefreeformbuildingrelativelyfree[10,85],Fig.1-5.
