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2.Stateoftheartandessentialdefinitions
Aplanesteelsheetfoldedinonedirectionischaracterizedbyorthotropic
properties[90].Thegreatlongitudinalflexuralstiffnessletsthesheetpreserve
straightnessofitsfold’saxes[5,93].Thesmalltransverseflexuralstiffnesslets
thesheetadaptthefold’swidthtosupportingconditionsrelativelyfree[23,24].
Thesmalltorsionalstiffnessofafoldedsheetaroundatwistaxis,paralleltothe
neutralaxesofitsfoldsbeforethetwist,enablesadoptingthemutualinclination
ofthecrosswiseedgesoftheshellsheetingtothedirectionsoftwodirectrices
[24,91,95].
Becausethedirectricesareusuallyskewlines,thenthetransformationof
asheetingleadstoobtainacorrugateddoubly-curvedwarpedshell[23,96].The
othertwolongitudinaledgelinesoftheshellfoldarealsoskew.Similarly,
neutralaxesofshellfoldsarealsoskewstraightlines,sodiversifiedwidths
appearalongfold’slength.Acontractionoftheshellfoldappearsinahalfofits
length,andmaximumextensionoccursatitsbothtransverseedgescalledalso
crosswiseends[23,24].Inaddition,thesupportingconditionsofsubsequent
shellsheetingfoldsareusuallyalsodiversified[89],sotheadjacentfoldsinthe
shellsheetingaffecteachother[6].Thus,thesupportingconditionsofthe
subsequentfoldsinthesheetingchangealongeachshelldirectrix,andvarious
typesandvaluesoftheshapetransformationsofthesubsequentfoldsmayoccur
[6,23].
Topreservebothabalancestateofeachshellfoldwithtakingaccountof
thefold’seffortassmallaspossibleandstability,oneshouldtrytotakecontrol
onthetwistdegreeofthesubsequentfoldsinthesheeting[24,91].Because
eachfoldischaracterizedbyopencross-sectionsandthin-walledplanar
elements,itstwistmaybebig,buttheirwarpingandstrainscanbesmall.One
shouldtakecareofthefollowingrelations:
a)thefold’scontractionshouldbelocatednearthehalfofthefold’slength
ascloseaspossibleandthestretchingatthebothcrosswiseendsofthesame
foldshouldbecomparable,
b)theinfluenceoftheadjacentshellfoldsoneachotherinthewholeshell
shouldbeassmallaspossible,somutualdisplacementofthesefoldsalongtheir
sharedlongitudinaledgewillbepossiblesmall[18,93].
AdamReichhartfirstand,next,JacekAbramczykhaveutilizedthegreat
possibilitiesinshapingdiversifiedoriginalandattractiveroofshellfreeforms
resultingfromthefold’sshapetransformations,Fig.1-2[3,14,98].Adam
Reichharthaselaboratedaninnovativemethodandalgorithmofanumerical
programmakingitpossibletoshapetheroofshellfreeforms.Foldsofroof
shellscreatedinthiswayareregardedasundergoingeffectivetwistshape
