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Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling

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Listed:
  • S. Frei
  • H. Andrä
  • R. Pinnau
  • O. Tse

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 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. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • S. Frei & H. Andrä & R. Pinnau & O. Tse, 2015. "Optimizing fiber orientation in fiber-reinforced materials using efficient upscaling," Computational Optimization and Applications, Springer, vol. 62(1), pages 111-129, September.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:1:p:111-129
    DOI: 10.1007/s10589-013-9630-z
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    References listed on IDEAS

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    1. Olaf Benedix & Boris Vexler, 2009. "A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints," Computational Optimization and Applications, Springer, vol. 44(1), pages 3-25, October.
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