An Effective Method for Multi-Layered Media with Cracks and Cavities

Problems for elastic multi-layered media with cracks and/or cavities arise in material science, construction designing and rock mechanics. An efficient method to solve these problems is proposed. Its efficiency is provided by employing problems' geo metrical feature: layers present a chain-like system. This allows use of the Green function by means of Fourier transform and sweep-method, and applying it to three quite similar problems for undamaged layers. Having the Green function, one reduces the problem for damaged layers to solution of integral equation (singular or hypersingular) which is defined only on surfaces of cracks and cavities and can be solved by conventional bound ary element method. All the key formulae are presented in explicit form.