BOUNDARY INTEGRAL-EQUATIONS METHOD IN 2-DIMENSIONAL AND 3-DIMENSIONALPROBLEMS OF ELASTODYNAMICS

In this paper the boundary integral equations method (BIEM) are consid ered for elastodynamic initial boundary value problems. It's known two approaches are discerned for account time. First of one is a combinat ion of BIEM with Laplace (Fourier) transformation. This approach was s uggested and realized by Cruse T. E. and Rizzo F. J. By them BIE in La place transformation space were obtained, investigated and some concre te problems were solved. This method was developed also by Manolis G. D., Beskos D. and other scholars for some dynamic problems solving. Th e second approach using retarding potentials was considered by Brebbia C. A., Fujiki K., Fukui T., Kato S., Kishima T., Kobayashi S., Nishim ura N., Niwa Y., Manolis G. D. Mansur W. J. (for 2D elastodynamics), C hutoryansky N. M. (for 3D elastodynamics). Detailed review of abroad s cholars elaborating BIEM was made by Beskos D. [7]. This paper discuss es BIEM for 2 and 3D elastodynamics on the base of the second approach . The fundamental solutions, integral representations and boundary int egral equations are constructed by means distributions theory for the general case of anisotropic elastic media. It's suggested some new res ults concerning special regularization of singularities on the wave fr onts of the integral equations kernels. The illustrative numerical exa mples concern the scattering of elastic waves on cavities embedded in an infinite isotropic medium. So, it's shown the numerical results of waves diffraction on the one and two cavities of arched and rectangula r forms in 2 and 3D cases. These results show quite stability of the e laborating algorithm.