Isogeometric Topology Optimization Based on Topological Derivatives
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915969051394048 |
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| author | Teixeira, Guilherme Henrique Krenn, Nepomuk Gangl, Peter Marussig, Benjamin |
| author_facet | Teixeira, Guilherme Henrique Krenn, Nepomuk Gangl, Peter Marussig, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isogeometric Topology Optimization Based on Topological Derivatives Teixeira, Guilherme Henrique Krenn, Nepomuk Gangl, Peter Marussig, Benjamin Numerical Analysis Computational Engineering, Finance, and Science Optimization and Control 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. |
| title | Isogeometric Topology Optimization Based on Topological Derivatives |
| topic | Numerical Analysis Computational Engineering, Finance, and Science Optimization and Control |
| url | https://arxiv.org/abs/2509.09236 |