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Inductor shape optimization for electromagnetic casting

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Abstract

The design of inductors in electromagnetic shaping of molten metals consists in looking for the position and the shape of a set of electric wires such that the induced electromagnetic field makes a given mass of liquid metal acquire a predefined shape. In this paper we formulate an inverse optimization problem where the position and shape of the inductors are defined by a set of design variables. In a first formulation of the inverse optimization problem we minimize the difference between the target and the equilibrium shapes while in a second approach we minimize the L 2 norm of a fictitious surface pressure that makes the target shape to be in mechanical equilibrium. Geometric constraints that prevent the inductors from penetrating the liquid metal are considered in both formulations. The optimization problems are solved using FAIPA, a line search interior-point algorithm for nonlinear optimization. Some examples are presented to show the effectiveness of the proposed approaches.

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Author notes

  1. Alfredo Canelas

    Present address: Mechanical Engineering Program - COPPE, Federal University of Rio de Janeiro, Cidade Universitária, Ilha do Fundão, P.O. Box 68503, CEP 21945-970, CT, Rio de Janeiro, Brazil

Authors and Affiliations

  1. Instituto de Estructuras y Transporte, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, C.P. 11300, Montevideo, Uruguay

    Alfredo Canelas

  2. IECN, Nancy-Université, CNRS, INRIA, B.P. 70239, 54506, Vandoeuvre lès Nancy, France

    Jean R. Roche

  3. Mechanical Engineering Program - COPPE, Federal University of Rio de Janeiro, Cidade Universitária, Ilha do Fundão, P.O. Box 68503, CEP 21945-970, CT, Rio de Janeiro, Brazil

    José Herskovits

Authors
  1. Alfredo Canelas
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  2. Jean R. Roche
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  3. José Herskovits
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Correspondence to Alfredo Canelas.

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Canelas, A., Roche, J.R. & Herskovits, J. Inductor shape optimization for electromagnetic casting. Struct Multidisc Optim 39, 589 (2009). https://doi.org/10.1007/s00158-009-0386-0

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  • DOI: https://doi.org/10.1007/s00158-009-0386-0

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