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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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Metadaten
Author:Emanuel Teichmann
URN (permanent link):urn:nbn:de:hbz:386-kluedo-23002
Advisor:Oleg Iliev
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2008
Year of Publication:2008
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2008/11/07
Date of the Publication (Server):2009/01/19
Tag:Topologieoptimierung
Topology optimization; domain decomposition; level set method; mesh generation
GND-Keyword:Gebietszerlegungsmethode; Gittererzeugung; Level-Set-Methode
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011