Spectral relationships of the integral equation with logarithmic kernel in some different domains

2014 ◽  
Vol 4 (3) ◽  
pp. 610-622
Author(s):  
M. I. Youssef ◽  
M. A. Abdou
Keyword(s):  
Integral Equation ◽  
Contact Problem ◽  
Potential Theory ◽  
Fredholm Integral Equation ◽  
Theory Of Elasticity ◽  
Theory Method ◽  
Logarithmic Kernel ◽  
Special Cases ◽  
Plane Theory Of Elasticity ◽  
Potential Theory Method

In this work, the Fredholm integral equation (FIE) with logarithmic kernel is investigated from the contact problem in the plane theory of elasticity. Then, using potential theory method (PTM), the spectral relationships (SRs) of this integral equation are obtained in some different domains of the contact. Many special cases and new SRs are established and discussed from this work.

scholarly journals An asymptotic model for solving mixed integral equation in some domains

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Mohamed Abdella Abdou ◽  
Hamed Kamal Awad
Keyword(s):  
Integral Equation ◽  
Potential Function ◽  
Theory Of Elasticity ◽  
Asymptotic Model ◽  
Logarithmic Function ◽  
Integral Term ◽  
Special Cases ◽  
Generalized Potential ◽  
Carleman Function ◽  
Axisymmetric Problems

Abstract In this paper, we discuss the solution of mixed integral equation with generalized potential function in position and the kernel of Volterra integral term in time. The solution will be discussed in the space $$L_{2} (\Omega ) \times C[0,T],$$ L 2 ( Ω ) × C [ 0 , T ] , $$0 \le t \le T < 1$$ 0 ≤ t ≤ T < 1 , where $$\Omega$$ Ω is the domain of position and $$t$$ t is the time. The mixed integral equation is established from the axisymmetric problems in the theory of elasticity. Many special cases when kernel takes the potential function, Carleman function, the elliptic function and logarithmic function will be established.

The Elasto-Electric Field for a Rigid Conical Punch on a Transversely Isotropic Piezoelectric Half-Space

1999 ◽  
Vol 66 (3) ◽  
pp. 764-771 ◽  
Author(s):  
W.-Q. Chen ◽  
T. Shioya ◽  
H.-J. Ding
Keyword(s):  
Exact Solution ◽  
Electric Field ◽  
Potential Theory ◽  
Half Space ◽  
Piezoelectric Effect ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Theory Method ◽  
Elementary Functions ◽  
Potential Theory Method

This paper exactly analyzes the problem of a rigid conical punch indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to include the piezoelectric effect. By using the previous results of pure elasticity, exact solution is derived. It is found that all the elastoelectric variables are expressed in terms of elementary functions. Numerical results are finally performed.

Sign in / Sign up

Export Citation Format

Share Document