X.Y. Lin

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

This paper provides an elastic solution for an infinite plate containing multiple curved edge cracks emanating from a circular hole. A fundamental solution is suggested, which represents a particular solution for a concentrated dislocation in an infinite plate with the traction free hole. The generalized image method and the concept of the modified complex potentials are used in the derivation of the fundamental solution. After using the fundamental 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 using the curve length method in conjunction with the semi-opening quadrature rule. By taking an additional point dislocation at the hole center, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. Finally, several numerical examples are given to illustrate the efficiency of the method presented. Numerical examinations are carried out and sufficient accurate results have been found.

Singular integral equation method for contact problem for rigidly connected punches on elastic half-plane

In the contact problem of a rigid flat-ended punch on an elastic half-plane, the contact stress under punch is studied. The angle distribution for the stress components in the elastic medium under punch is achieved in an explicit form. From obtained singular stress distribution, the punch singular stress factor (abbreviated as PSSF) is defined. A fundamental solution for the multiple flat punch problems on the elastic half-plane is investigated where the punches are disconnected and the forces applied on the punches are arbitrary. The singular integral equation method is suggested to obtain the fundamental solution. Further, the contact problem for rigidly connected punches on an elastic half-plane is considered. The solution for this problem can be considered as a superposition of many particular fundamental solutions. The resultant forces on punches are the undetermined unknowns in the problem, which can be evaluated by the condition of relative descent between punches. Finally, the resultant forces on punches can be determined, and the PSSFs at the corner points can be evaluated. Numerical examples are given.