THE TRANSFORMATION FOR AN ARBITRARY HOLE IN AN INFINITE PLATE OF ELASTIC MATERIAL
Jean Dollimore · The Quarterly Journal of Mechanics and Applied Mathematics · 1963
An infinite plate of elastic material contains a small unstressed central slit, the plate being subjected to a loading at infinity. The principal stresses are required in the region exterior to the slit. The boundary of the slit is mapped onto the unit circle on another plane, using a power series mapping function which is fitted to the data defining the slit by a least squares method. This, together with some further constraints, results in a set of equations which are solved by numerical methods. We consider in detail the particular case of a bone shaped slit which is defined continuously. In this case, coefficients in the power series are calculated with the aid of an electronic digital computer.