Generalized method of images in the crack analysis

摘要

A new and effective method has been developed for the analysis of cracks in elastic bodies, subjected to arbitrary loading, as well as for the analysis of crack interactions. The cases of flat cracks of arbitrary shape inside a transversely isotropic elastic half-space and inside a layer are considered. Governing integral equations are derived by the introduction of quasi-images of the cracks. The idea of images was originally used at the beginning of the century by Lord Kelvin for the solving of lectrostatics problems. The new method allows one to obtain a complete solution, defining all stresses and displacements in the whole body, not only in the plane of the crack. For the first time, an exact formulation of a crack problem in a layer is given for the case where the crack is not located in the middle plane of the layer.