Singular Integral Equations for Some Contact Problems of Elasticity Theory for Bodies with Cracks

2019 ◽  
pp. 65-138 ◽  
Author(s):  
Oleksandra Datsyshyn ◽  
Volodymyr Panasyuk
Keyword(s):  
Elasticity Theory ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Contact Problems

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.

Contact of Coated Systems Under Sliding Conditions

2006 ◽  
Vol 128 (4) ◽  
pp. 886-890 ◽  
Author(s):  
Lifeng Ma ◽  
Alexander M. Korsunsky ◽  
Kun Sun
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Contact Problems ◽  
Sliding Contact ◽  
Integration Scheme ◽  
Singular Behavior ◽  
Contact Conditions ◽  
Numerical Integration Scheme ◽  
Traction Distribution

The contact of coated systems under sliding conditions is considered within the framework of elasticity theory with the assumption of perfect bond between coating and substrate. Formulation is introduced in the form of a system of coupled singular integral equations of the second kind with Cauchy kernels that describe contact problems for coated bodies under complete, semi-complete and incomplete contact conditions. Accurate and efficient numerical method for the solution of sliding contact problems is described. Explicit results are presented for the interpolative Gauss-Jacobi numerical integration scheme for singular integral equations of the second kind with Cauchy kernels. The method captures correctly both regular and singular behavior of the traction distribution near the edges of contact. Several cases of sliding contact are considered to demonstrate the validity of the method.

scholarly journals APPLICATION OF SINGULAR INTEGRAL EQUATIONS IN SOLVING SOME CONTACT PROBLEMS IN THEORY OF ELASTICITY

2019 ◽  
Vol 1 (1) ◽  
pp. 46-55
Author(s):  
V. Gavdzinski ◽  
◽  
M. El–Sheikh ◽  
E. Maltseva ◽  
◽  
...  
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Contact Problems ◽  
Theory Of Elasticity

scholarly journals Regularity of the minimiser of one-dimensional interaction energies

2020 ◽  
Vol 26 ◽  
pp. 27
Author(s):  
M. Kimura ◽  
P. van Meurs
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Matrix Theory ◽  
Singular Integral Equations ◽  
Contact Problems ◽  
Nonlocal Interaction ◽  
Interaction Energies ◽  
Fredholm Type ◽  
Dimensional Interaction ◽  
Regularity Results

We consider both the minimisation of a class of nonlocal interaction energies over non-negative measures with unit mass and a class of singular integral equations of the first kind of Fredholm type. Our setting covers applications to dislocation pile-ups, contact problems, fracture mechanics and random matrix theory. Our main result shows that both the minimisation problems and the related singular integral equations have the same unique solution, which provides new regularity results on the minimiser of the energy and new positivity results on the solutions to singular integral equations.

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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