Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Optimizing fiber orientation in fiberreinforced materials using efficient upscaling
 Computational Optimization and Applications 62 (2015), No.1, pp.111129 ISSN: 09266003 ISSN: 15732894 

 English 
 Journal Article 
 Fraunhofer ITWM () 
Abstract
We present an efficient algorithm to find an optimal fiber orientation in composite materials. Within a twoscale 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(). 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 adjointbased gradient type algorithm, but generalizations to higherorder 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.