Dynamic Stresses near Cracks in Anisotropic Bodies at Longitudinal Shear

The elasticity problem of an anisotropic body with cracks under the action of time-varying loads and harmonic waves is studied at the antiplane dynamic consideration. To solve the problem, the basic equations are reduced to the consideration of dynamic problems for some isotropic material. The obtained equations were solved using the Laplace integral transformation. Laplace transforms are found on the basis of the method of integral equations and are reduced to solving hypersingular integral equations. A numerical method for solving the obtained equations using the quadrature method is proposed. The Laplace inversion is performed numerically on the basis of pre-regularized formulas that allow the calculation of stresses with controlled accuracy. A study of the stress concentration near cracks under dynamic loads and falling waves was performed.