ABSTRACT
InChapter10wedevelopedtheconceptofastructuralelementsuffering transientdeflectionundertheinfluenceofanimposedblastloading.Forthe purposesofanalysis,theelementcanberepresentedasasingledegreeof freedomsystemsubjectedtoatransientloadwhichhasthevaluef(t)ata timet.Theinherentstiffnessoftheelementprovidesresistancetodeflection. ThemagnitudeofthisresistanceisdenotedbyR(x)atdeflectionx.Applying Newton'ssecondlawtotheelementgivestheequation
F(t)- R(x)=Mx(11.1) Inordertopredictthetransientresponseofastructuralelementanincre-
mentalsolutionofEquation11.1isdeveloped.Initially,whenx=0,the systemoffersnoresistanceandsotheaccelerationoftheelementcanbe foundfromaknowledgeoftheinitialforceF(O)andthemassoftheelement M.Assumingtheaccelerationtobeconstantduringthefirstsmalltime increment,thedisplacementisfoundandtheresistanceevaluatedatthe endofthefirstincrement.ThesubstitutionofthesevaluesintoEquation 11.1,togetherwiththeupdatedvalueofF,allowsthenewaccelerationto bedeterminedandtheprocessrepeated.Thisincrementalapproachprovidesadeflection-timehistoryforthetransientdisplacementofthestructuralelement.Themaximumdeflectionoftheelementiscomparedwiththat whichcanbetoleratedwithinspecifieddamagecriteriatodetermine whethertheelementwillsurvive.
