Litvin O. The research of the fields of stresses and displacements near thin elastic inclusions under steady state oscillations

The thesis is dedicated to solution of 3D time-harmonic problems for an infinite elastic solid with a spatial crack under crack-face loading or incident waves. The problem is reduced to the boundary integral equations (BIEs) relative to dynamic crack opening displacements. The analytical small parameter method is developed to solve the BIEs under conditions of low-frequency regimes and shallow cracks. The analysis is carried out for the stress intensity factors in the vicinity of crack along the spheroidal and cylindrical surfaces under time-harmonic pressure and longitudinal plane wave diffraction. The formulas are derived for the calculations of wave scattering amplitudes and cross-sections in the far zone in terms of BIEs solutions. The influence of spheroidal crack curvature on the scattering amplitudes are studied for different time-harmonic perturbations.