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Planar contraction design with specified fibre orientation distribution at the outlet

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Abstract

In the present study, an optimal shape design problem of a papermachine headbox is considered to control the fibre orientation distribution at the outlet of contraction. First, by the aid of a bijective transformation, we transform the optimization problem governed by weak formulation on a fixed domain. Then, by means of a process of embedding, the class of admissible shapes is replaced by a class of non-negative Radon measures. The modified problem consists of the minimization of a linear functional over a set of pairs of positive Radon measures satisfying linear constraints. Each measure of optimal pair is approximated by a finite combination of unitary atomic measures and furthermore the approximate solution of the first problem is found by the optimal solution of a finite-dimensional linear programming problem. The solution of this problem is used to construct an optimal piecewise constant control. Finally, using the approximate control signals, we obtain the approximate optimal shapes.

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Acknowledgments

The author would like to thank to the editor and the anonymous referees for comments which improved this paper.

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Authors and Affiliations

  1. Department of Mathematics, Quchan Institute of Engineering and Technology, Quchan, Iran

    B. Farhadinia

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  1. B. Farhadinia
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Correspondence to B. Farhadinia.

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Farhadinia, B. Planar contraction design with specified fibre orientation distribution at the outlet. Struct Multidisc Optim 46, 503–511 (2012). https://doi.org/10.1007/s00158-012-0775-7

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  • DOI: https://doi.org/10.1007/s00158-012-0775-7

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