A semi-analytic solution for multiple curved cracks emanatingfrom circular hole using singular integral equation

摘要

This paper provides an elastic solution for an infinite plate containing multiple curved edgecracks emanating from a circular hole. A fundamental solution is suggested, which repre-sents a particular solution for a concentrated dislocation in an infinite plate with the trac-tion free hole. The generalized image method and the concept of the modified complexpotentials are used in the derivation of the fundamental solution. After using the funda-mental solution and placing the distributed dislocations at the prospective sites of cracks,a singular integral equation is formulated. The singular integral equation is solved by usingthe curve length method in conjunction with the semi-opening quadrature rule. By takingan additional point dislocation at the hole center, the number of the unknowns is equal tothe number of the resulting algebraic equations. This is a particular advantage of the sug-gested method. Finally, several numerical examples are given to illustrate the efficiency ofthe method presented. Numerical examinations are carried out and sufficient accurateresults have been found.