Authors
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Guilherme Henrique Teixeira
Graz University of Technology, Graz,
Austria
0000-0003-3857-5291
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Nepomuk Krenn
Johann Radon Institute for Computational and Applied Mathematics, Linz,
Austria
0009-0008-2110-6433
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Peter Gangl
Johann Radon Institute for Computational and Applied Mathematics, Linz,
Austria
0000-0001-8906-821X
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Benjamin Marussig
Graz University of Technology, Graz,
Austria
0000-0001-6076-4326
Abstract
Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric approach to topology optimization driven by topological derivatives. The combination of a level-set method together with an immersed isogeometric framework allows seamless geometry updates without the necessity of remeshing. At the same time, topological derivatives provide topological modifications without the need to define initial holes [7]. We investigate the influence of higher-degree basis functions in both the level-set representation and the approximation of the solution. Two numerical examples demonstrate the proposed approach, showing that employing higher-degree basis functions for approximating the solution improves accuracy, while linear basis functions remain sufficient for the level-set function representation.
Keywords:
topology optimization, isogeometric analysis, topological derivative, level-set method, immersed methods, higher-degree basis functionReferences
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