MAPPING FLAT CRACKS ONTO PENNY-SHAPED CRACKS, WITH APPLICATION TO SOMEWHAT CIRCULAR TENSILE CRACKS

摘要

Consider a three-dimensional Homogeneous isotropic elastic solid contain-ing a flat pressurized crack, tl. The problem of finding the resulting stress distribution can be reduced to ahypersingular integral equationover.fi for the crack-opening displace-ment, Here, this equation is transformed into a similar equation over a circular region D using a conforanal mapping between and D. This new equation is then regularized analytically by using an appropriate expansion method (Fourier series in the azimuthal direction and series of orthogonal polynomials in the radial direction), Analytical results for regions that are approximately circular are also obtained. The method will generalize to other scalar problems and td vector problems (such as shear loading of the crack),.