[52–3] Conformal Mapping Related to Torsional Rigidity, Principal Frequency, and Electrostatic Capacity

1982 ◽  
pp. 285-292
Author(s):  
G. Szegö
Author(s):  
Dorin Bucur ◽  
Ilaria Fragala

We prove that, in the class of convex polygons with a given number of sides,  the regular $n$-gon is optimal for some shape optimization problems involving the torsional rigidity, the principal frequency of the Laplacian, or the logarithmic capacity.


2018 ◽  
Vol 457 (2) ◽  
pp. 1153-1172 ◽  
Author(s):  
Giuseppe Buttazzo ◽  
Serena Guarino Lo Bianco ◽  
Michele Marini

Author(s):  
Jianqi Li ◽  
Yu Zhou ◽  
Jianying Li

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.


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