Semianalytical Solutions to Griffith Fracture Under Variable Pressure

Abstract

The stresses and displacements in the vicinity of a Griffith crack in a semiinfinite two-dimensional elastic medium subjected to a variable internal pressure are analyzed by polynomial approximation and Fourier transform, and semianalytical solutions to the governing differential equations are formulated. The variable internal pressure is approximated by a polynomial and solutions are then obtained by Fourier transform. The expressions for the components of stress and displacement due to the opening of a crack under an uniform internal pressure are derived as a special case example to illustrate the use of the derived solutions. They are in agreement with solutions derived by other methods published in the literature. However, it is very difficult, if not impossible, to obtain exact analytical solutions when the distribution of the variable internal pressure becomes more complex. The derived semianalytical solutions establish the basis for a more efficient algorithm to obtain numerical solutions in such cases.