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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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Hauptverfasser: Frei, Stefan (VerfasserIn) , Andrä, Heiko (VerfasserIn) , Pinnau, René (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 2015
In: Computational optimization and applications
Year: 2015, Jahrgang: 62, Heft: 1, Pages: 111-129
ISSN:1573-2894
DOI:10.1007/s10589-013-9630-z
Online-Zugang: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
Volltext
Verfasserangaben:S. Frei, H. Andrä, R. Pinnau, O. Tse

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520 |a 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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