Analytical Stress Analysis of Elastic Composites with Cracks. Final Report

摘要

The elastostatic axisymmetric problem of a sphere, containing a centrally located penny-shaped crack, embedded in a dissimilar matrix subject to far field loads is solved. First the problem of a cracked sphere is solved by using Boussinesq stress-functions. Two coordinate systems - oblate spheroidal for representing the crack surface and spherical polars for the spherical surface - are used to satisfy boundary conditions. Integral representations and transformations of harmonic functions are used to relate stress-functions in the two coordinate systems. This procedure leads to a system of algebraic equations which are solved, for axisymmetric tractions on both the surfaces. This solution is then used to obtain the solution of the original problem. A new representation of the solution for the axisymmetric problem of a crack in an infinite medium is also presented. (ERA citation 05:007498)