一类带约束的二维弱奇异积分方程的一般解及其应用*

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.

General Solution of a 2-D Weak Singular Integral Equation with Constraint and Its Applications

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.