Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling

• Verfasst von: Frei, Stefan [VerfasserIn]
• Verfasst von: Andrä, Heiko [VerfasserIn]
• Verfasst von: Pinnau, René [VerfasserIn]
• Titel: Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling
• Verf.angabe: S. Frei, H. Andrä, R. Pinnau, O. Tse
• Umfang: 19 S.
• Fussnoten: First online 28 December 2013 ; Gesehen am 05.09.2017
• Titel Quelle: Enthalten in: Computational optimization and applications
• Jahr Quelle: 2015
• Band/Heft Quelle: 62(2015), 1, S. 111-129
• ISSN Quelle: 1573-2894
• DOI: doi:10.1007/s10589-013-9630-z
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1563196344

Abstract

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.