SEMIANALYTICAL SOLUTIONS TO GRIFFITH FRACTURE UNDER VARIABLE-PRESSURE

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 approxima ted by a polynomial and solutions are then obtained by Fourier transfo rm. The expressions for the components of stress and displacement due to the opening of a crack under an uniform internal pressure are deriv ed as a special case example to illustrate the use of the derived solu tions. They are in agreement with solutions derived by other methods p ublished in the literature. However, it is very difficult, if not impo ssible, to obtain exact analytical solutions when the distribution of the variable internal pressure becomes more complex. The derived semia nalytical solutions establish the basis for a more efficient algorithm to obtain numerical solutions in such cases.