The numerical solution of certain integral equations with non-integrable kernels arising in the theory of crack propagation and elastic wave diffraction

An infinite elastic medium is initially at rest in a prestressed state of plane- or anti-plane strain. At time t = 0 a plane crack comes into existence which occupies a strip parallel to the y axis and whose width varies in time. Assuming that the components of the traction are known on the crack surface it is possible to set up an integral equation on the area of the crack for the relative displacement across the crack. Although the kernel of this integral equation is non-integrable a method is found for discretizing it and a numerical method of solution is carried out. The results, which in some cases are the solutions of diffraction problems, are presented graphically.