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1、InternationalAppliedMechanics,Vol.30,No.11,1994TOWARDATHEORYOFORTHOTROPICSHELLSANDPLATESREINFORCEDBYSTIFFENINGRIBSA.N.Guz',N.A.Shul'ga,andV.F.MeishUDC539.3Inthedynamicloadingofthin-walledelasticsystemswithvariousirregularities(platesandshellswithreinforcingribs,elasticsyst
2、emswithconcentratedmasses,compoundelasticsystems,etc.),themostimportantfeaturesarethewavenatureoftheprocessandthevariabilityofthephysicomechanicalparametersoftheelasticsystemnearindividualinclusions.Indynamicproblemsconcerningelasticsystems,localperturbationsinsmallregions
3、mayresultinsubstantialstressandstrainredistributionsthroughoutthesystemduetothewavenatureoftheprocessesthattakeplace[1,4].Inthevicinityofdiscreteinclusions,anelasticsystemischaracterizedbyapronouncedthree-dimensionalstate[2].Suchasituationrequirestheconstructionofawavetheo
4、ryforplatesandshellsthatwilladequatelyreflectthedistributionofthestressandstrainfieldsthroughthethicknessoftheproduct.Onewayofsatisfyingthisneedistodevelopalineartheoryofplatesandshellsthataccountsfornormalandtransverseshearstrains(amodelwithsixdegreesoffreedominplateandsh
5、elltheory).Inconstructingsuchatheoryforelasticsystems,thestressesandstrainsareapproximatedindependentlythroughthethicknessofthesystem.Thedisplacementsofanarbitrarypointofashellareapproximatedusingamodelbasedonrepresentationofthedisplacementvectorintheformofalinearfunctiono
6、fthedegeneratethicknesscoordinate.PostulatingindependentapproximationsofthedisplacementsandstressesinthethicknessdirectionleadstocontradictionsinthegeneralizedHooke'slaw.Theequationsofmotionofelasticelements(inparticular,theequationsofmotionofreinforcedshellsofrevolution)a
7、rederivedwiththeuseofReissner'svariationalprinciple,whichmakesitpossibletoresolvetheseinconsistencies[3,5].Inthisapproach,theelasticrelationsexpressingtherelationshipbetweenthenormalandshearstressesandthecorrespondingstrainsaresatisfiedintegrallythroughthethicknessoftheela
8、sticelementswithsuitableweightfunctions.Thismakesitpossibletoobtaintheequationsofmotionof
