ABSTRACT
For a planar crack the basic boundary conditions are stated in the first section. The necessary edge behaviour as well as uniqueness condition are discussed. The boundary condition for punch or indentation problem are stated clearly. Using the representation theorem in Chapter 1, the mixed-boundary value problem for planar crack and indentation on use of the Green’s function yield the two-dimensional singular integro-differential equation in case of a planar crack, and a simple two-dimensional integral equation for punch problem is derived. As a limiting case, the corresponding one-dimensional singular integral equation for indentation as well as hyper singular integral equation for line crack problem are derived. In the rest of this chapter, various general methods for solving two-dimensional singular integral equations for elliptic disk-shaped planar body are discussed. Also included is a discussion of a one-dimensional singular equation.
