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10
Definition2
Boundaryconditionsofashellfoldconsistofzerovalueofthe
displacementperpendiculartothedirectionoftherespectivedirectrix,zero
valueoftherespectivebendingmomentandconstantvalueofitstwist
angleateachfoldendsupportedbythedirectrix.Theso-calledhardsimple
supportingofthebothfold’sendsaffectsonlinearrelationsforsmalltwist
angleandnon-linearrelationsformiddleandbigangleoffold’stwist.The
bordersconditionsresultfromshapesandmutualpositionofthetworoof
directrices,theorientationofeachfoldtowardstherelevantdirectricxand
amethodofassemblingthefoldstotheshelldirectricesensuringthe
freedomoffold’swidthincrements.
Fig.1-2.Propertiesofasheeting
referencesurface
Definition3
Thefoldshapeadaptationisregardedaseffectiveshapetransformation,if
eachshellsheetisloadedonlywiththefold’sownweightorverysmall
forcesappliedperpendicularlytothesheetingreferencesurfaceofthe
foldedsheeting,seeFig.1-2[25].
Asaresultofthesheet’stransformation,opencross-sectionsofthethin-
walledfoldseasilychangetheirwidth,heightandinclinationtothevertical[22,
92].Thereforeitisveryimportanttoensureafreedomofthesechangesduring
thetransformationtopreservethepossiblysmalleffortofthefolds.Inaddition,
decreasingcapacityofthefolds,appearinginstabilityandinitialgeometrical
imperfectionsoffold’swallshavetobeanalyzed[15,24,35,109,110].
Definition4
Anaxisoffoldisasumofthecentresofgravityofallcross-sectionofthe
fold.Fortheeffectivelytransformedsheetingsinvestigated,axesoftheirall
foldsarestraightduetotherespectivesupportingconditionsprovidedby
roofdirectricesandintermediatemembers.
