Interface Crack Problem for Electroelastic Body

2000 ◽  
Vol 7 (2) ◽  
pp. 231-244
Author(s):  
L. Bitsadze
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Displacement Vector ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Representation Formula ◽  
Potential Method ◽  
Integral Representation Formula ◽  
Homogeneous Plane ◽  
Special Integral

Abstract A two-dimensional crack problem in the Comninou formulation is investigated for a piecewise homogeneous plane. Applying a special integral representation formula for the displacement vector the problem is reduced to a system of singular integral equations. The system is analysed and its solvability is proved using the potential method and the theory of singular integral equations.

scholarly journals Localized boundary-domain singular integral equations of the Robin type problem for self-adjoint second-order strongly elliptic PDE systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Otar Chkadua ◽  
Sergey Mikhailov ◽  
David Natroshvili
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Singular Integral ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Representation Formula ◽  
Potential Method ◽  
Factorization Method ◽  
Variable Coefficients ◽  
Second Order

AbstractThe paper deals with the three-dimensional Robin type boundary-value problem (BVP) for a second-order strongly elliptic system of partial differential equations in the divergence form with variable coefficients. The problem is studied by the localized parametrix based potential method. By using Green’s representation formula and properties of the localized layer and volume potentials, the BVP under consideration is reduced to the a system of localized boundary-domain singular integral equations (LBDSIE). The equivalence between the original boundary value problem and the corresponding LBDSIE system is established. The matrix operator generated by the LBDSIE system belongs to the Boutet de Monvel algebra. With the help of the Vishik–Eskin theory based on the Wiener–Hopf factorization method, the Fredholm properties of the corresponding localized boundary-domain singular integral operator are investigated and its invertibility in appropriate function spaces is proved.

Application of Singular Integral Equations in the Boundary Value Problems of Electroelasticity

2002 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
L. Bitsadze
Keyword(s):  
Boundary Value Problems ◽  
Existence Theorem ◽  
Integral Equations ◽  
Singular Integral ◽  
Boundary Value ◽  
Three Dimensional ◽  
Singular Integral Equations ◽  
Potential Method ◽  
Uniqueness And Existence ◽  
Symbolic Matrix

Abstract The purpose of this paper is to consider the three-dimensional versions of the theory of electroelasticity for a transversally esotropic body. Applying the potential method and the theory of singular integral equations, the normality of singular integral equations corresponding to the boundary value problems of electroelasticity are proved and the symbolic matrix is calculated. The uniqueness and existence theorem for the basic BVPs of electroelasticity are given.

scholarly journals Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded Materials

2020 ◽  
Vol 12 (1) ◽  
pp. 43
Author(s):  
Youn-Sha Chan ◽  
Edward Athaide ◽  
Kathryn Belcher ◽  
Ryan Kelly
Keyword(s):  
Integral Equations ◽  
Functionally Graded Materials ◽  
Singular Integral ◽  
Mixed Mode ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Mixed Mode Fracture ◽  
Graded Materials

A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

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

Singular integral equations in the bound-state problem

1965 ◽  
Vol 35 (3) ◽  
pp. 913-932 ◽  
Author(s):  
G. Cosenza ◽  
L. Sertorio ◽  
M. Toller
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Bound State ◽  
State Problem ◽  
Bound State Problem

scholarly journals Methods of solution of singular integral equations

2012 ◽  
Vol 6 (1) ◽  
pp. 15 ◽  
Author(s):  
Aloknath Chakrabarti ◽  
Subash Chandra Martha
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations
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