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CHAPTER1
Introduction
1i1iOVerViewontheissueofthemodellingofconstruction
elementswithVariableproperties
Acommontopicofconsiderationsinthepresentmonographareconstructionelements
withVariablepropertiesȂplatesandbarsiTheVariabilityofpropertiescanbejumpǦwise
orcontinuousanditcanconcernacrosssectionandȀormaterialpropertiesiinparticular
theYoungmodulusandmaterialdensityiTheissueofmodellingofelementswithVariable
propertiesisVeryspaciousihenceinthemonographonlyseVeralselectedproblemsare
relatedtoitȂthusithetitleofthemonographisformulatedas
Selectedproblemsof
modellingofconstructionelementswithVariablematerialandgeometricalproperties
i
ItmustbeemphasizedthattheVariabilityisrelatedonlytospatialchangesofthe
propertiesȂtheyareconstantintimei
ApplicationoftheelementswithVariablepropertiesisdriVenbyaconcernofthebest
possibleadaptationoffeatures(formistiffness)ofanelementtodistributionofinternal
forceseXistinginitiinparticularthedistributionofbendingmomentsiSaVingsincosts
andmaterialiinturnidictatethatiTheconstructioneconomicsrequiresthentofind
apossibilitytocalculatestructuresconsistingoftheelementswithVariablepropertiesi
ThereforeischolarshaVebeenseekingforyearsmethodsofanapproXimatesolVingof
equationsdescribingabehaViorofsuchstructuresiAshistoricalpublicationsregarding
platesionecannameaworkbyHolzer(1918)oncircularplateswithVariablethickness
oraworkbyOlsson(1934)onrectangularplateswithVariablestiffnessiaswellasthe
classicalmonographbyTimoshenkoetali(1959)whichisstillusedasaValuable
handbookiIncaseofproblemsofstaticbendingofbarsandplatebandswithoutactionof
bigaXialforcesiacalculationofdeflectionsanddistributionofinternalforcesconsistsin
arelatiVelysimpleithoughsometimestediousintegrationȂthemoreiftheVariabilityof
features(stiffness)iseXpressedbypowerfunctionofabarlengthcoordinateiItismuch
morecompleXihoweVeritoobtainpracticalandeXactsolutionsfortheproblemsof
dynamicsandstabilityofbarswithVariablepropertiesiaswellasstaticsidynamicsand
stabilityofplatespresentingsuchfeaturesiKrynickiandMazurkiewicz(1966)madesuch
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