This paperproposesanoptimumdesignmethodfortwo-dimensionalheatconductionproblemwith heat transferboundaryconditionbasedontheboundaryelementmethod(BEM)andthetopology optimization method.Thelevelsetmethodisusedtorepresentthestructuralboundariesandthe boundary meshisgeneratedbasedoniso-surfaceofthelevelsetfunction.Amajornovelaspectofthis paper isthatthegoverningequationissolvedwithoutersatzmaterialapproachandapproximatedheat convectionboundaryconditionbyusingthemeshgeneration.Additionally,theobjectivefunctionalis defined alsoonthedesignboundaries.First,thetopologyoptimizationmethodandthelevelsetmethod are briefly discussed.Usingthelevelsetbasedboundaryexpression,thetopologyoptimizationproblem for theheattransferproblemwithheattransferboundaryconditionisformulated.Next,thetopological derivativeoftheobjectivefunctionalisderived.Finally,severalnumericalexamplesareprovidedto confirm th idityofthederivedtopologicalderivativeandtheproposedoptimumdesignmethod

1-s2.0-S0955799715001526-main.pdf
1-s2.0-S0957417414004114-main.pdf
1-s2.0-S1047320313000473-main.pdf

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