Index Of Discontinuous Connection Function In R-H Problem And Its Application

In this paper,we mainly study the boundary value theory of analytic functions.Finally the index of discontinuous connection function in R-H problem and its application on plane elastic crack in discontinuous case where equilibrium solution proved are given.Here the main work can be summarized as:1.For the continuous RH boundary value problem,to give a conjecture and prove that the Canonical function of R problem under an unbounded multi-connected region.2.The new proposition and index representation of discontinuous connection functions,which including the curve Γ is discontinuous and L,Γ are both discontinuous in RH problem are given.There will be a new definition of the canonical function,and the final solution form is obtained.3.The practical application of the discontinuous boundary on fracture mechanics and the corresponding solution are given.In order to solve the elastic equilibrium of the discontinuous boundary,we introduce the functionco(t)to represent the two unknown analytic functions φ(z)、ψ(z);then we can get the integral expression of the discontinuous boundary,thus the position of the crack can be easily determined.