基于观点法的谱随机有限元分析——随机响应面法.pdf

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1、第24卷第2期计算力学学报VoI.24，No.22007年4月ChineseJournalofComputationalMechanicsApriI2007文章编号：1007-4708（2007）02-0173-08Acollocation-basedspectralstochasticfiniteelementanalysisstochasticresponsesurfaceapproachHUANGShu-ping（DepartmentofCiviIEngineering，ShanghaiJiaotongUniversity，Shanghai200240，China）Ab

2、stract：AcoIIocation-basedstochasticfiniteeIementmethod（SRSM）hasbeendeveIoped，theformaIismofthepro-posedmethodissimiIartothespectraIstochasticfiniteeIementmethod（SSFEM）inthesensethatbothofthemutiIizeKarhunen-loeve（K-l）expansiontorepresenttheinput，andpoIynomiaIchaosexpansiontorepresenttheoutp

3、ut.How-ever，thecaIcuIationofthecoefficientsinthepoIynomiaIchaosexpansionisdifferent：AnaIyticaISSFEMusesaprobabi-IisticGaIerkinapproachwhiIeSRSMusesaprobabiIisticcoIIocationapproach.NumericaIexampIeshowsthatcomparedtotheAnaIyticaISSFEM，theadvantageofSRSMisthatthefiniteeIementcodecanbetreated

4、asabIackbox，asinthecaseofacommerciaIcode.TheproposedSRSMisaIsocomparedtoabIackboxversionSSFEM，andfoundtoreguireIessFEMevaIuationsforthesameaccuracy.ThecoIIocationpointsintheproposedmethodneedtobeseIectedformini-mizingthemeansguareerror，andfromhighprobabiIityregions，thusIeadingtofewerfunctio

5、nevaIuationsforhighaccu-racy.Keywords：stochasticfiniteeIements；stochasticresponsesurface；randomfieIds；Karhunen-loeveexpansion；poIyno-miaIchaosexpansionofrandomvariabIesintowhichacontinuousrandom1IntroductionfieIdisreducedbydiscretization.StochasticfiniteeI-ProbabiIisticuncertaintypropagatio

6、nmethodsareementmethodssuchasperturbationandNeumannex-appIiedintheanaIysisofphysicaIsystemsinorderto［2］pansionworkweIIwhenthevariabiIityisnotIarge.guantifytheeffectsofrandomvariationintheinputonThespectraIstochasticfiniteeIementmethod（SS-thepredictedoutputofthesimuIation.Thesemethods［1］FEM）

7、deveIopedbyGhanemandSpanosappearstoincIudeMonteCarIosimuIation，stochasticfiniteeIe-［1］［2］beasuitabIetechnigueforthesoIutionofcompIex，mentandresponsesurfacemethods.TheseIec-tionofthemethoddependsonthenatureofmodeIgeneraIprobIemsinprobabiIisticmechanics.It