Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics
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In this paper, a shape optimization problem is formulated by introducing a tracking-type cost functional to match a desired rotation pattern, and shape sensitivity analysis is rigorously performed for the nonlinear problem by means of a new shape-Lagrangian formulation adapted to nonlinear problems.Abstract:
The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to smooth the rotation pattern of the rotor. A shape optimization problem is formulated by introducing a tracking-type cost functional to match a desired rotation pattern. The magnetic field generated by permanent magnets is modeled by a nonlinear partial differential equation of magnetostatics. The shape sensitivity analysis is rigorously performed for the nonlinear problem by means of a new shape-Lagrangian formulation adapted to nonlinear problems.read more
Citations
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References
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Olaf Schenk,Klaus Gärtner +1 more
TL;DR: Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsympetric matrices from real world applications.
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Jan Sokołowski,Jean-Paul Zolésio +1 more
TL;DR: This book is motivated largely by a desire to solve shape optimization problems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems.
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Optimal Shape Design for Elliptic Systems
TL;DR: The techniques of the calculus of variation and of optimization proved to be successful for several optimal shape design problems however these remain expensive both in the qualification of the engineers required to understand the method and in computing time.
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An unfitted finite element method, based on Nitsche's method, for elliptic interface problems
Anita Hansbo,Peter Hansbo +1 more
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New Cartesian grid methods for interface problems using the finite element formulation
Zhilin Li,Tao Lin,Xiao-Hui Wu +2 more
TL;DR: New finite element methods based on Cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients, and these new methods can be used as finite difference methods.