Solution of a 2-D Weak Singular Integral Equation with Constraint

Yun Tian-quan

Volume 16 Issue 5

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Article Navigation > Applied Mathematics and Mechanics > 1995 > 16(5): 415-420

Yun Tian-quan. Solution of a 2-D Weak Singular Integral Equation with Constraint[J]. Applied Mathematics and Mechanics, 1995, 16(5): 415-420.

Citation:

Yun Tian-quan. Solution of a 2-D Weak Singular Integral Equation with Constraint[J]. Applied Mathematics and Mechanics, 1995, 16(5): 415-420.

Citation:

Yun Tian-quan. Solution of a 2-D Weak Singular Integral Equation with Constraint[J]. Applied Mathematics and Mechanics, 1995, 16(5): 415-420.

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Solution of a 2-D Weak Singular Integral Equation with Constraint

Yun Tian-quan

Department of Mechanics, South China University of Technology, Guangzhou 510641, P. R. China

Received Date: 1994-03-15
Rev Recd Date: 1994-12-10
Publish Date: 1995-05-15

Abstract

Abstract

In this paper, the solution of a 2-D weak singular integral equation of tire first kind subjected to constraint is found and listed p=p(r,θ)={2/[π²k(φ₀]}√F(r,θ)-c_*(0≤r≤r_*) where(s,φ)is a local polar coordhrating with orighr at M(r,θ),(r,θ)is the global polar coordinating with origin at O(0,0):k and F are given continuous functions;φ₀ and C are constant;F(r_*,θ)=c_*(const.)is the boundary contour of considering range Q. The method used can be extended to 3-D cases.
- Radon transform,
- Abel integral equation,
- range,
- theorem of integral mean value of function,
- contact problem,
- Hertz’s solution

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References(6)

References

[1]	S.P.Timoshenko and J.N.Goodiar,Theory of Elasticity,MdGraw-Hill Book Co.,New York(1970),414.
[2]	Yun Tian-quan,Solution of Hertz's contact problem by Radon transform,Proc.2nd Int.Conf.on Nonlinear Mech.,(Edited by Chien Wei-zang et al.),Beijing(1993),215-218.
[3]	Yun Tian-quan,Asymptotic solution of small parametered 2-D integral equation arising form contact problem of elasticity based on the solution of a 2-D integral equation,Proceedings of AMS.
[4]	Yun Tian-quan,The exact integral equation of Hertz's contact problem,Appl.Math.and Mech.(English Ed.),12,2(1991),181-185.
[5]	G.T.Herman,The fundamentais of computerized tomography,Image Reconstruction from Projections,Academic Press,INC,New York(1980).
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