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Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling

Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling

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FREI, Stefan, Heiko ANDRÄ, René PINNAU, Oliver TSE, 2015. Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling. In: Computational Optimization and Applications. Springer. 62(1), pp. 111-129. ISSN 0926-6003. eISSN 1573-2894. Available under: doi: 10.1007/s10589-013-9630-z

@article{Frei2015Optim-55773, title={Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling}, year={2015}, doi={10.1007/s10589-013-9630-z}, number={1}, volume={62}, issn={0926-6003}, journal={Computational Optimization and Applications}, pages={111--129}, author={Frei, Stefan and Andrä, Heiko and Pinnau, René and Tse, Oliver} }

2015 Pinnau, René 2021-12-07T10:51:10Z Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling eng Tse, Oliver Frei, Stefan Andrä, Heiko Pinnau, René Frei, Stefan Andrä, Heiko 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 H<sup> 1</sup>(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. 2021-12-07T10:51:10Z Tse, Oliver terms-of-use

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