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Canelas, Alfredo; Novotny, Antonio A.; Roche, Jean R.;

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In this paper we describe a new method for the topology design of the inductors used in the electromagnetic casting technique of the metallurgical industry. The method is based on a recently proposed topology optimization formulation of the inverse electromagnetic casting problem, and uses level-sets together with first and second order topological derivatives of the objective functional, which are herein given, to efficiently find the optimal solution. Results for two numerical examples show that the technique described can be efficiently used in the design of suitable inductors.

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Palavras-chave: Inverse problem, Topological derivatives, Shape optimization, Electromagnetic casting.,


DOI: 10.5151/meceng-wccm2012-18780

Referências bibliográficas
  • [1] H. K.Moffatt. Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part Fundamentals. Journal of Fluid Mechanics, 159:359–378, 1985.
  • [2] J. A. Shercliff. Magnetic shaping of molten metal columns. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 375(1763):455–473, 1981.
  • [3] A. Henrot, J.-P. Brancher, and M. Pierre. Existence of equilibria in electromagnetic casting. In Proceedings of the Fifth International Symposium on Numerical Methods in Engineering, Vol. 1, 2 (Lausanne, 1989), pages 221–228, Southampton, 1989. Comput. Mech.
  • [4] A. Canelas, J. R. Roche, and J. Herskovits. The inverse electromagnetic shaping problem. Structural and Multidisciplinary Optimization, 38(4):389–403, 2009.
  • [5] A. Canelas, J. R. Roche, and J. Herskovits. Inductor shape optimization for electromagnetic casting. Structural and Multidisciplinary Optimization, 39(6):589–606, 2009.
  • [6] A. Canelas, A. A. Novotny, and J. R. Roche. A new method for inverse electromagnetic casting problems based on the topological derivative. Journal of Computational Physics, 230(9):3570–3588, 2011.
  • [7] S. Amstutz and H. Andrä. A new algorithm for topology optimization using a level-set method. Journal of Computational Physics, 216(2):573–588, 2006.
  • [8] A. Gagnoud, J. Etay, and M. Garnier. Le problème de frontière libre en l´evitation ´electromagn´etique. Journal de M´ecanique Th´eorique et Appliqu´ee, 5(6):911–934, 1986.
  • [9] A. Henrot and M. Pierre. Un problème inverse en formage des m´etaux liquides. RAIRO Mod´elisation Math´ematique et Analyse Num´erique, 23(1):155–177, 198
  • [10] A. Novruzi and J. R. Roche. Second order derivatives, Newton method, application to shape optimization. Technical Report RR-2555, INRIA, 1995.
  • [11] M. Pierre and J. R. Roche. Computation of free surfaces in the electromagnetic shaping of liquid metals by optimization algorithms. European Journal of Mechanics. B Fluids, 10(5):489–500, 1991.
  • [12] J.-C. N´ed´elec. Acoustic and Electromagnetic Equations. Integral Representations for Harmonic Problems, volume 144 of Applied Mathematical Sciences. Springer-Verlag, New York, 2001. ISBN 0-387-95155-5.
  • [13] K. E. Atkinson. The numerical solution of integral equations of the second kind, volume 4 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge, 1997. ISBN 0-521-58391-8.
  • [14] M. Pierre and J. R. Roche. Numerical simulation of tridimensional electromagnetic shaping of liquid metals. Numerische Mathematik, 65(1):203–217, 1993.
  • [15] J. R. Roche. Gradient of the discretized energy method and discretized continuous gradient in electromagnetic shaping simulation. Applied Mathematics and Computer Science, 7(3):545–565, 1997.
  • [16] J. R. Roche. Adaptive Newton-like method for shape optimization. Control and Cybernetics, 34(1):363–377, 2005.
  • [17] A. Novruzi and J. R. Roche. Newton’s method in shape optimisation: A threedimensional case. BIT. Numerical Mathematics, 40(1):102–120, 2000.
  • [18] T. P. Felici and J.-P. Brancher. The inverse shaping problem. European Journal of Mechanics. B Fluids, 10(5):501–512, 1991.
  • [19] H.A. Eschenauer, V.V. Kobelev, and A. Schumacher. Bubble method for topology and shape optmization of structures. Structural Optimization, 8(1):42–51, 1994.
  • [20] J. Sokolowski and A. ?Zochowski. On the topological derivative in shape optimization. SIAM Journal on Control and Optimization, 37(4):1251–1272, 1999.
  • [21] J. C´ea, S. Garreau, Ph. Guillaume, and M. Masmoudi. The shape and topological optimizations connection. Computer Methods in Applied Mechanics and Engineering, 188 (4):713–726, 2000.
  • [22] G. Allaire, F. de Gournay, F. Jouve, and A.-M. Toader. Structural optimization using topological and shape sensitivity via a level set method. Control and Cybernetics, 34(1): 59–80, 2005.
  • [23] S. Amstutz, S. M. Giusti, A. A. Novotny, and E. A. de Souza Neto. Topological derivative in multi-scale linear elasticity models applied to the synthesis of microstructures. International Journal for Numerical Methods in Engineering, 84(6):733–756, 2010.
  • [24] S. Amstutz and A. A. Novotny. Topological optimization of structures subject to von Mises stress constraints. Structural and Multidisciplinary Optimization, 41(3):407–420, 2010.
  • [25] M. Burger, B. Hackl, and W. Ring. Incorporating topological derivatives into level set methods. Journal of Computational Physics, 194(1):344–362, 2004.
  • [26] A. A. Novotny, R. A. Feijóo, E. Taroco, and C. Padra. Topological sensitivity analysis for three-dimensional linear elasticity problem. Computer Methods in Applied Mechanics and Engineering, 196(41-44):4354–4364, 2007.
  • [27] S. Amstutz, I. Horchani, and M. Masmoudi. Crack detection by the topological gradient method. Control and Cybernetics, 34(1):81–101, 2005.
  • [28] G. R. Feijóo. A new method in inverse scattering based on the topological derivative. Inverse Problems, 20(6):1819–1840, 2004.
  • [29] B. B. Guzina andM. Bonnet. Small-inclusion asymptotic ofmisfit functionals for inverse problems in acoustics. Inverse Problems, 22(5):1761–1785, 2006.
  • [30] M. Hintermüller and A. Laurain. Electrical impedance tomography: from topology to shape. Control and Cybernetics, 37(4):913–933, 2008.
  • [31] M. Masmoudi, J. Pommier, and B. Samet. The topological asymptotic expansion for the Maxwell equations and some applications. Inverse Problems, 21(2):547–564, 2005.
  • [32] M. Hintermüller, A. Laurain, and A. A. Novotny. Second-order topological expansion for electrical impedance tomography. Advances in Computational Mathematics, 36(2): 235–265, 2012.
  • [33] S. Osher and J.A. Sethian. Front propagating with curvature dependent speed: algorithms based on hamilton-jacobi formulations. Journal of Computational Physics, 78: 12–49, 1988.
Como citar:

Canelas, Alfredo; Novotny, Antonio A.; Roche, Jean R.; "TOPOLOGICAL DERIVATIVES AND A LEVEL SET APPROACH FOR AN INVERSE ELECTROMAGNETIC CASTING PROBLEM", p. 2262-2274 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18780

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