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, ψ) is a local polar coordinating with 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\(Q_; g\left( w \right) = {{F(r,\theta )} \mathord{\left/ {\vphantom {{F(r,\theta )} {\left[ {\pi k\left( {\psi _0 } \right)} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {\pi k\left( {\psi _0 } \right)} \right]}};{\text{ }}g' = {{dg} \mathord{\left/ {\vphantom {{dg} {dw;{\text{ }}w = N - r^2 }}} \right. \kern-\nulldelimiterspace} {dw;{\text{ }}w = N - r^2 }}\sin ^2 \left( {\theta + \psi _0 } \right);{\text{ }}\psi _0 \) and N are mean values. The solution shown in type(2.19) of[1] is a special case of the above 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.