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Sensitivity-Based Topology and Shape Optimization with Application to Electric Motors

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Frontiers in PDE-Constrained Optimization

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 163))

Abstract

In many industrial applications, one is interested in finding an optimal layout of an object, which often leads to PDE-constrained shape optimization problems. Such problems can be approached by shape optimization methods, where a domain is altered by smooth deformation of its boundary, or by means of topology optimization methods, which in addition can alter the connectivity of the initial design. We give an overview over established topology optimization methods and focus on an approach based on the sensitivity of the cost function with respect to a topological perturbation of the domain, called the topological derivative. We illustrate a way to derive this sensitivity and discuss the additional difficulties arising in the case of a nonlinear PDE constraint. We show numerical results for the optimization of an electric motor which are obtained by a combination of two methods: a level set algorithm which is based on the topological derivative, and a shape optimization method together with a special treatment of the evolving material interface which assures accurate approximate solutions to the underlying PDE constraint as well as a smooth final design.

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Authors and Affiliations

  1. Graz University of Technology, Institute of Applied Mathematics, Graz, Austria

    Peter Gangl

Authors
  1. Peter Gangl
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Correspondence to Peter Gangl .

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Editors and Affiliations

  1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, USA

    Harbir Antil

  2. Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, USA

    Drew P. Kouri

  3. Corporate Strategic Research, ExxonMobil Research and Engineering Company, Annandale, NJ, USA

    Martin-D. Lacasse

  4. Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, USA

    Denis Ridzal

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Gangl, P. (2018). Sensitivity-Based Topology and Shape Optimization with Application to Electric Motors. In: Antil, H., Kouri, D.P., Lacasse, MD., Ridzal, D. (eds) Frontiers in PDE-Constrained Optimization. The IMA Volumes in Mathematics and its Applications, vol 163. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8636-1_9

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