Brief Review on the Use of Complex Variables and Conformal Mapping for Elastic Plate Problems—Application to Buckling of Sandwich Plates

2020 ◽  
pp. 971-977
Author(s):  
Paritosh Biswas ◽  
Bapi Karmakar
Keyword(s):  
Conformal Mapping ◽  
Elastic Plate ◽  
Complex Variables ◽  
Sandwich Plates

A Point Dislocation Interacting with an Elliptical Hole Located at a Bi-Material Interface

2012 ◽  
Vol 151 ◽  
pp. 75-79 ◽  
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe ◽  
P.B.N. Prasad
Keyword(s):  
Conformal Mapping ◽  
Unit Circle ◽  
Half Plane ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Complex Stress ◽  
Complex Variables ◽  
Material Interface ◽  
Rational Mapping ◽  
Point Dislocation

The problem of a point dislocation interacting with an elliptical hole at the interface of two bonded half-planes is studied. Complex stress potentials are obtained by applying the methods of complex variables and conformal mapping. A rational mapping function that maps a half plane with a semi-elliptical notch onto a unit circle is used for mapping the bonded half-planes. The solution derived can serve as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

THEORY OF BRILLOUIN SCATTERING BY AN ISOTROPIC ELASTIC PLATE

1984 ◽  
Vol 45 (C5) ◽  
pp. C5-103-C5-107
Author(s):  
D. R. Tilley ◽  
E. L. Albuquerque ◽  
M. C. Oliveros
Keyword(s):  
Elastic Plate ◽  
Brillouin Scattering

Generation of ao waves in sandwich plates

2002 ◽  
Vol 90 ◽  
pp. 42-42
Author(s):  
D. Osmont ◽  
D. Barnoncel ◽  
M. Dupont
Keyword(s):  
Sandwich Plates

A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

2020 ◽  
pp. 1-15
Author(s):  
Jianqi Li ◽  
Yu Zhou ◽  
Jianying Li
Keyword(s):  
Magnetic Field ◽  
Conformal Mapping ◽  
Permanent Magnet ◽  
Flux Density ◽  
Analytical Method ◽  
Electromotive Force ◽  
Analytical Calculation ◽  
Air Gap ◽  
Permanent Magnet Machines ◽  
Peak Value

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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