Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling
We present an efficient algorithm to find an optimal fiber orientation in composite materials. Within a two-scale setting fiber orientation is regarded as a function in space on the macrolevel. The optimization problem is formulated within a function space setting which makes the imposition of smoot...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2015
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| In: |
Computational optimization and applications
Year: 2015, Volume: 62, Issue: 1, Pages: 111-129 |
| ISSN: | 1573-2894 |
| DOI: | 10.1007/s10589-013-9630-z |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s10589-013-9630-z Verlag, Volltext: https://link.springer.com/content/pdf/10.1007%2Fs10589-013-9630-z.pdf Verlag, Volltext: https://link.springer.com/article/10.1007/s10589-013-9630-z 
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| Author Notes: | S. Frei, H. Andrä, R. Pinnau, O. Tse |
| Summary: | We present an efficient algorithm to find an optimal fiber orientation in composite materials. Within a two-scale setting fiber orientation is regarded as a function in space on the macrolevel. The optimization problem is formulated within a function space setting which makes the imposition of smoothness requirements straightforward and allows for rather general convex objective functionals. We show the existence of a global optimum in the Sobolev space H1(Ω). The algorithm we use is a one level optimization algorithm which optimizes with respect to the fiber orientation directly. The costly solve of a big number of microlevel problems is avoided using coordinate transformation formulas. We use an adjoint-based gradient type algorithm, but generalizations to higher-order schemes are straightforward. The algorithm is tested for a prototypical numerical example and its behaviour with respect to mesh independence and dependence on the regularization parameter is studied. |
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| Item Description: | First online 28 December 2013 Gesehen am 05.09.2017 |
| Physical Description: | Online Resource |
| ISSN: | 1573-2894 |
| DOI: | 10.1007/s10589-013-9630-z |