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* Corresponding author 1 Optimize - Optimize-Mechanical Engineering Program 2 CALVI - Scientific computation and visualization IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l-Image, de l-Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine 3 IECN - Institut Élie Cartan de Nancy 4 Optimize - Optimize-Mechanical Engineering Program-COPPE-UFRJ

Abstract : The design of inductors in electromagnetic shaping of molten metals consists of 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. The solution of this problem correspond to the optimal design, i.e., the shape of the liquid metal is as close as possible to the target shape. 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 minimizes 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 to penetrate into 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.

Keywords : shape optimization inverse problems electromagnetic casting

Autor: Alfredo Canelas - Jean Rodolphe Roche - José Herskovits -



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