解熱彈性問題和正交各向異性彈性問題的多域組合虛邊界元法

1、同濟(jì)大學(xué)土木工程學(xué)院碩士學(xué)位論文解熱彈性問題和正交各向異性彈性問題的多域組合虛邊界元法姓名：米東申請學(xué)位級別：碩士專業(yè)：結(jié)構(gòu)工程指導(dǎo)教師：許強(qiáng)20080301ABSTRACTPhysics，mechanics，aswellasmanyengineeringproblemscanberegardedaSinitialvalueorboundaryvalueinequationsofmathematicalphysicsInwhichsom

2、esimpleproblemsCanbesolvedbyanalyticalmethod，butformostofcomplexissuesitiSsolvedbyapproximationalgorithmusuallyBoundaryelementmethodiSakindofnumericalalgorithmonboundary；itisbasedontheboundaryime掣alequationandemploysthee

3、lementdiscretizationtechniqueDirectboundaryelementmethodhaSrelativelybroadspaceoftheapplicationbuttherearestillsomeshortcomings：calculatingsomephysicalquantitiesnearboundarythereistheboundarylayereffectduetothequasisingu

4、laritytheaccuracyofthesolutionisreduced；andthecoefficientmatrixiSfuUandasymmetricwhichwastetoomuchtimeinsolvingprocess；besides，theadaptabilityofthenonlinearproblemiscomparativelybadInrecentyears，howtodealwithsingularinte

5、gralandavoidtheboundary，layereffectisafocalproblemforresearchersSomescholarsdoanumberofresearchworksontheindirectboundaryelementmethodtoovercometheshortcomingsofdirectboundaryelementmethod，andsomenumericapproximationmeth

6、odswerepresentedaccordinglyoneofwhichisvirtualboundaryelementmethodLeastsquaresmethodandmatchingcollocationmethodaretwofrequentlyusedideaswhichareappliedtovirtualboundaryelementmethodNowadaystheideawhichappliesmultidomai

7、ncompositevirtualboundaryelementmethod(VBEM)tosolvepotential，fluctuant，electromagneticandelasticissuesetciScomparativelymatureInordertodemonstrateitscapacityinengineeringapplication，thispaperpresentstheideastosolve2DTher

8、mo—ElasticproblemandtheelasticproblemoforthotropicbodiesForThermoElasticproblem，thesolvingprocessiSdividedintotwopartsthefirstpartistosolveheatconductionproblemwithVBEMwhichisbasedonassumptiveheatsourcemethodandthesecond

9、partiSusingVBEMtosolvecorrespondingelasticproblemFortheelasticproblemoforthotropicbodiesemployingthefundamentalsolutionthatiSsuitablenotonlytoorthotropicmediabutalSOtoisotropicmediaanewideaforsolvingtheelasticbodiesposse

10、ssedorthotropiccharacterandcomposedofdifferentmaterialsispresentedItiSworthmentioningthatthemethodhasuniversalsignific觚ceitCallsolvethemultidomaincompositeproblemoforthotropicmediaandtheissuecomposedofisotropicandorthotr

11、opicmediaCanbesolvedbythemethodinthisPaperinaddition，thismethodcanevolvetosolvetheproblemofisotropicmediaItisworthemphasizingthattheideaofmultidomaincompositevirtualboundaryelementmethodCanevolvetosolvetheproblemofsingle