Based on hyper-singular integral equations of the inclined crack in the half-plane,through appropriate variable replacements and equation collocations,establish the linear equations.

The problem of the crack parallel to the free boundary in a half-plane body, with the distributed loads only at the crack surface is discussed in this paper.

The edge internal branch crack problems for half-plane in antiplane elasticity are solved with complex potentials and singular integral equation approach.

By using of complex variable function and integral equation method, the antiplane multiple holes and cracks problem of half plane region is considered in this paper.

On the basis of half plane equations, this paper presents a principle named"multiple half plane" to study the intersection of line segments and describes a principleto determine whether two line segments intersect.

Using the Cauchy Integral Method of complex variable, the fundamental solutions of complex stress functions due to a concentrated force or moment acting on an arbitrary point in an anisotropic half plane were derived when the straight line boundary of the half plane was free or fixed.

Let ρ>1,if the function was analytic in the right half-plane,and was not continuous on the boundary,satisfying,then some analogous results could be obtained.