Chapter 6 Dynamic Finite-Element Analysis of Impact and Explosion

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1、6DynamicFinite-ElementAnalysisofImpactandExplosion6.1IntroductionAgreatdealofworkhasbeenpublishedonfinite-elementtechniques.[2.150,3.1–3.168]Thischapterpresentsthedynamicfinite-elementanalysisforimpactandexplosion.Plasticityandcrackingmodelsareincluded.Solidisoparametri

2、celements,panelandlineelementsrepresentvariousmaterials.Solutionproceduresarerecommended.Thischapterendswithsomeload–timefunctionsforselectedcasesusingfinite-elementanalysis.Therearemanypub-licationsonthetopicofimpactandexplosionwhichcanbeusedforin-depthstudies.6.2Fini

3、te-ElementEquationsAthree-dimensionalfinite-elementanalysisisdevelopedinwhichaprovi-sionhasbeenmadefortime-dependentplasticityandrupturinginsteelandcrackinginmaterialssuchasconcrete,etc.Theinfluenceofstuds,lugsandconnectorsisincluded.Concretesteellinersandstudsarerepres

4、entedbysolidisoparametricelements,shellelementsandlineelementswithorwithoutbondlinkages.Tobeginwith,adisplacementfiniteelementisadopted.ThedisplacementfieldwithineachelementisdefinedinFig.6.1asn{x}=[N]{x}e=(N[I]{x}).(6.1)iii=1Thestrainsandstressescanthenbeexpressedasn{}

5、=([Bi]{xi})=[D]{σ}.(6.2)i=1Inordertomaintainequilibriumwiththeelement,asystemofexternalnodalforces{F}cisappliedwhichwillreducethevirtualwork(dW)tozero.In7706DynamicFinite-ElementAnalysisofImpactandExplosionζ=ζc=constantη=ηc876Z'Y'η=+1ξX'56ζζηZηξ43ξYXξ=+112global(i)8-n

6、odedsolidelementco-ordinateswithlineelementξX'1918176320ζ75131416Z'Y'121511ηX'4ηξY'2108ξ97Z865312Z'41Y123panelelementline(ii)element313029X2832ζ20ξ2126global25271222324co-ordinatesη192171618ξY'1039151113812Z'14746lineelement125876359η4Z'Y'ξ(iii)10X'43112121(a)panelele

7、mentFig.6.1.(a)Isoparametricelements.(i)Parentelement,three-dimensionalisoparametric-derivedelement;(ii)solidelement(20-noded);(iii)32-nodedsolidele-ment.(b)Lineelementswithinthebodyofthesolidisoparametricelements(ISS=isoparametricsolidelement)6.2Finite-ElementEquatio

8、ns77187Z5ζ6ηYξ34Xglobalco-ordinates12lineelements191817η=ηc=constantξ=ξc201416Z'Y'1312ζη1511ISSX'ζηξ=ξcξ=constantY'ζ=ζc10X'9