Truss topology design under harmonic loads: Peak power minimization with semidefinite programming
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912333220020224 |
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| author | Ma, Shenyuan Marecek, Jakub Kungurtsev, Vyacheslav Tyburec, Marek |
| author_facet | Ma, Shenyuan Marecek, Jakub Kungurtsev, Vyacheslav Tyburec, Marek |
| contents | Designing lightweight yet stiff structures that can withstand vibrations is a crucial task in structural optimization. Here, we present a novel framework for truss topology optimization under undamped harmonic oscillations. Our approach minimizes the peak power of the structure under harmonic loads, overcoming the limitations of single-frequency and in-phase assumptions found in previous methods. For this, we leverage the concept of semidefinite representable (SDr) functions, demonstrating that while compliance readily conforms to an SDr representation, peak power requires a derivation based on the non-negativity of trigonometric functions. Finally, we introduce convex relaxations for the minimization problem and provide promising computational results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Truss topology design under harmonic loads: Peak power minimization with semidefinite programming Ma, Shenyuan Marecek, Jakub Kungurtsev, Vyacheslav Tyburec, Marek Optimization and Control Designing lightweight yet stiff structures that can withstand vibrations is a crucial task in structural optimization. Here, we present a novel framework for truss topology optimization under undamped harmonic oscillations. Our approach minimizes the peak power of the structure under harmonic loads, overcoming the limitations of single-frequency and in-phase assumptions found in previous methods. For this, we leverage the concept of semidefinite representable (SDr) functions, demonstrating that while compliance readily conforms to an SDr representation, peak power requires a derivation based on the non-negativity of trigonometric functions. Finally, we introduce convex relaxations for the minimization problem and provide promising computational results. |
| title | Truss topology design under harmonic loads: Peak power minimization with semidefinite programming |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.16175 |