Efficient Structural Update for Three-Dimensional Topology Optimization Problems Using Level Set Functions

  • We present a new efficient and robust algorithm for topology optimization of 3D cast parts. Special constraints are fulfilled to make possible the incorporation of a simulation of the casting process into the optimization: In order to keep track of the exact position of the boundary and to provide a full finite element model of the structure in each iteration, we use a twofold approach for the structural update. A level set function technique for boundary representation is combined with a new tetrahedral mesh generator for geometries specified by implicit boundary descriptions. Boundary conditions are mapped automatically onto the updated mesh. For sensitivity analysis, we employ the concept of the topological gradient. Modification of the level set function is reduced to efficient summation of several level set functions, and the finite element mesh is adapted to the modified structure in each iteration of the optimization process. We show that the resulting meshes are of high quality. A domain decomposition technique is used to keep the computational costs of remeshing low. The capabilities of our algorithm are demonstrated by industrial-scale optimization examples.

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Verfasserangaben:Emanuel Teichmann
URN (Permalink):urn:nbn:de:hbz:386-kluedo-23002
Betreuer:Oleg Iliev
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2008
Jahr der Veröffentlichung:2008
Veröffentlichende Institution:Technische Universität Kaiserslautern
Titel verleihende Institution:Technische Universität Kaiserslautern
Datum der Annahme der Abschlussarbeit:07.11.2008
Datum der Publikation (Server):19.01.2009
Freies Schlagwort / Tag:Topologieoptimierung
Topology optimization; domain decomposition; level set method; mesh generation
GND-Schlagwort:Gebietszerlegungsmethode; Gittererzeugung; Level-Set-Methode
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011