This paper studies a boundary integral equation (BIE) for notch problems in an
elastic half-plane based on Green’s function method. The boundary along the
half-plane is traction-free. A fundamental solution is suggested, which is composed of
a principal part and a complementary part. The process for evaluating the
complementary part from the principal part is similar to the Green’s function method
for Laplace’s equation. After using the Somigliana identity or Betti’s reciprocal
theorem between the field of the fundamental solution and the physical field, the
displacements at the domain point are obtained. Letting the domain point approach
the boundary point and using the generalized Sokhotski–Plemelj formula, a BIE
of the notch problem for a traction-free half-plane boundary is obtained.
The accuracy of the suggested technique is examined. Computed results for
elliptic notches and a square notch with rounded corner are presented in the
paper.
Keywords
elasticity, elastic half-plane, notch problem, fundamental
solution, Green's function method, complex variable BIE
