Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling

S. Frei, H. Andrä, R. Pinnau, O. Tse

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)


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 1(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.
Original languageEnglish
Pages (from-to)111-129
Number of pages19
JournalComputational Optimization and Applications
Issue number1
Publication statusPublished - 2015
Externally publishedYes


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