Multiple and Periodic Notch Problems of Elastic Half-Plane by Using Bie Based on Green's Function Method

Abstract

This paper provides a modified complex potential for the fundamental solution, which is composed of a principal part and a complementary part. The suggested complex potential satisfies the traction free condition along the boundary of half-plane in advance. After using the Somigliana identity or the Betti's reciprocal theorem between the physical field and the field of the fundamental solution, a complex variable boundary integral equation (BIE) for the notch problem in elastic half-plane is obtained. A compact derivation for the BIE is presented. By using the BIE, multiple notch problems of elastic half-plane can be solved numerically. In the method, there is no limitation for the configuration of notches. Many problems with the elliptic notch or the square notch are solved successfully. For the periodic notch problem, the remainder estimation technique is suggested. This technique provides an effective way for the solution of periodic notch problem.