Investigation of a Basic Plane Interface Problem of Statics for Elastic Mixtures

2003 ◽  
Vol 10 (4) ◽  
pp. 729-744
Author(s):  
K. Svanadze
Keyword(s):  
Contact Problem ◽  
Integral Equations ◽  
Plane Interface ◽  
Interface Problem ◽  
Two Dimensional ◽  
Type Analysis ◽  
Fredholm Type ◽  
System Of Integral Equations ◽  
Displacement Vectors ◽  
Basic Plane

Abstract The two-dimensional interface problem of statics of elastic mixtures is investigated when differences between displacement vectors and stress vectors are given on the contact curve. For this problem special potentials with complex densities are constructed and by means of them the contact problem is reduced to a system of integral equations of Fredholm type. Analysis of the equations obtained is given.

Axisymmetric Stressed State of Uniformly Layered Space with Periodic Systems of Internal Disc-Shaped Cracks and Inclusions

2020 ◽  
pp. 25-40
Author(s):  
V.N. Hakobyan ◽  
H.A. Amirjanyan ◽  
K.Ye. Kazakov
Keyword(s):  
Integral Equations ◽  
Periodic System ◽  
Crack Extension ◽  
Integral Transform ◽  
Contact Stresses ◽  
Circular Disc ◽  
System Of Equations ◽  
Axisymmetric Stress State ◽  
Fredholm Type ◽  
System Of Integral Equations

Using the Hankel integral transform, we construct discontinuous solutions for the problem of the axisymmetric stress state of a piecewise homogeneous, uniformly layered space, obtained by alternately connecting two heterogeneous layers of the same thickness. The space on the middle planes of the first heterogeneous layer contains a periodic system of circular disc-shaped parallel cracks, and on the middle planes of the second layer has a periodic system of circular disc-shaped parallel rigid inclusions. The determining system of equations is obtained in the form of a system of integral equations with kernels of the Weber --- Sonin type with respect to the crack extension and tangent contact stresses acting on the facial surfaces of rigid inclusions. With the help of rotation operators, the resulting determining system of equations is reduced to a system of integral equations of the second kind of Fredholm type. The equation solution is constructed by the method of mechanical quadratures. A numerical analysis was carried out and regularities were revealed in the variation of the intensity factors of rupture stresses, crack extension and contact stresses under the inclusions depending on the physical and mechanical and geometrical characteristics of the problem

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

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