Modification of singular integral equations of planar problems of elasticity theory for an arbitrary multiply connected domain with a rectilinear cut

1992 ◽  
Vol 60 (1) ◽  
pp. 1274-1279
Author(s):  
P. N. Osiv
Keyword(s):  
Elasticity Theory ◽  
Integral Equations ◽  
Singular Integral ◽  
Connected Domain ◽  
Singular Integral Equations ◽  
Multiply Connected Domain ◽  
Multiply Connected

scholarly journals STABILITY OF SYSTEMS OF SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNEL

T-Comm ◽  
2020 ◽  
Vol 14 (9) ◽  
pp. 48-55
Author(s):  
Aleksey V. Yudenkov ◽  
◽  
Aleksandr M. Volodchenkov ◽  
Liliya P. Rimskaya ◽  
◽  
...  
Keyword(s):  
Elasticity Theory ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
System Stability ◽  
Strength Analysis ◽  
Fredholm Integral Equations ◽  
Cauchy Integral ◽  
Mean Square Stability ◽  
The Absolute

Singular Cauchy integral equations have been widely used for mathematical simulation of the actual physical and technical systems. They are considered universal at every level of simulation beginning with quantum field theory and up to strength analysis of the underground constructions. Therefore investigating system stability of such models under perturbation of their absolute terms and coefficients appears an urgent scientific task. The aim of the study is to show various aspects of stability of singular Cauchy integral sets of equations which are generalizing simulation models of the primal problems of the elasticity theory for homogeneous isotropic bodies. The methods of study are based on the properties of the Cauchy singular integral, on the general theory of Fredholm operators. When in use, systems of the singular integral equations are reduced to a set of Fredholm integral equations of the second kind and a set of the boundary value problems for analytic functions. The key results of the study are the following: development of the general determination method of the system index for singular integral equations, proof of the system stability against perturbations of the absolute terms of the set. Against perturbations of the boundary coefficients, the singular integral system is unstable. Demonstration of the stability of the singular integral Cauchy sets generalizing primal problems of the elasticity theory appears a significantly new result. The research of singular integral equations sets has been performed conducted on the space of functions satisfying the Holder condition. However the main research results prove to be true if we operate random functions converting in mean square. Stability of singular integral equations sets against perturbations of the absolute terms lays a foundation for calculus of approximations in real world tasks of defining the built-in stress of an elastic complex body.

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna
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