Two complementary methods to face with convexity issues in topology optimization problems
(2009) Compumag 2009 — Location: Florianopolis (Brésil) (22.November.2009)
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- Abstract
- To perform parameter and shape optimization, an initial topology is required which affects the final solution. Topology optimization methods have the advantage to release this constraint. They are based on a splitting of the design space into cells, in which they attempt to distribute optimally some given materials. Several convexity issues were already highlighted in topology optimization of electromagnetic devices. The optimization algorithm gets trapped in local minimizers and the final solution differs according to the initial conditions. In this paper, two main causes of this lack of convexity are studied. The first one is linked to the handling of intermediate materials, especially those that are a combination of windings and iron. The second one appears when the optimization objective is computed by a difference of magnetic energy between different positions of the rotor. The methods proposed to manage these convexity issues focus on the shape of the optimization domain of each cell. They are based on the use of parameterized hyperbolic functions to define the boundaries of the optimization domain and to modify them during the optimization process.
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Labbe, T., Dehez, B., & Glineur, F. (2009). Two complementary methods to face with convexity issues in topology optimization problems. Compumag 2009, Florianopolis (Brésil). https://hdl.handle.net/2078.5/252059