一类带约束的二维弱奇异积分方程的一般解及其应用*
General Solution of a 2-D Weak Singular Integral Equation with Constraint and Its Applications
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摘要: 本文给出二维弱奇异积分方程作用着约束方程的比[1]为更一般的解P式中k和产是给出的连续函数;(s,φ)是原点在M(r,θ)的局部极坐标;(r,θ)是原点在O(0.0)的总体极坐标;F(r*,θ)=c*(常数)是研究域Q的边界围线∂Q:g(ω)=F(r,θ)/[πkφ0];g'=dg/dω,ω=N-r2sin2(θ+φ0);φ0,N为中值.[1]的(2.19)型的解仅为F(r,θ)=ω时上述解的特例.文中给出刚性圆锥和弹性半空间接触问题的解作为应用例子.此解较Love(1939)的解简明.Abstract: In this paper, the solution, more general than [1], of a weak singular integral equation subject to constraint is found where k and F are given continuous functions: (s,φ) is a local polar coordinatingwin origin at M(r,θ): (r,θ) is the global polar coordinating with origin at O(0,0) F(r*,θ)=c*(const.) is the boundary contour ∂Q of the considered range Q:g(ω)=F(r,θ)/[πkφ0];g'=dg/dω,ω=N-r2sin2(θ+φ0);φ0 and N are mean values. The solution shown in type (2.19) of [1] is a special case of theabove solution and only suits F(r,θ) =ω. The solution of a rigid cone contact with elastic half space, more simple and clear than Love's (1939), is given as an example of application.
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Key words:
- Radon transform /
- Abel integral equation /
- theorem mean value /
- Hertz’s solution
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[1] 云天铨,一类带约束的二维弱奇异积分方程的解,应用数学和力学,16(5) (1995),415-420. [2] G. T. Herman, Image reconstruction from projections, The fundamentals of Compulerized Tomography, Academic Press, INC., New York (1980). [3] 郭硕鸿.《电动力学》,高等教育出版社,北京(1978). [4] 王耀光等,《半微积分极谱法》,厦门大学出版社,厦门(1990) [5] S. P. Timoshenko and J. N. Goodiar, Theory of Elasticity,Mc Graw-Hill Book Co., New York (1970), 414. [6] A. E. H. Love, Boussinesq's problem for a rigid cone, Quart. J. Math. (Oxford Series),10 (1939), 161~175. [7] 云天铨,《积分方程及其在力学中的应用》,华南理工大学出版社,广州(1990), 60.
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