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Boundary integral Equations Method in two- and three-dimensional problems of elastodynamics

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Abstract

In this paper the boundary integral equations method (BIEM) are considered for elastodynamic initial boundary value problems. It's known two approaches are discerned for account time. First of one is a combination of BIEM with Laplace (Fourier) transformation. This approach was suggested and realized by Cruse T.E. and Rizzo F. J. By them BIE in Laplace transformation space were obtained, investigated and some concrete problems were solved. This method was developed also by Manolis G. D., Beskos D. and other scholars for some dynamic problems solving.

The second approach using retarding potentials was considered by Brebbia C. A., Fujiki K., Fukui T., Kato S., Kishima T., Kobayashi S., Nishimura N., Niwa Y., Manolis G. D. Mansur W.J. (for 2D elastodynamics), Chutoryansky N.M. (for 3D elastodynamics). Detailed review of abroad scholars elaborating BIEM was made by Beskos D. [7].

This paper discusses BIEM for 2 and 3D elastodynamics on the base of the second approach. The fundamental solutions, integral representations and boundary integral equations are constructed by means distributions theory for the general case of anisotropic elastic media. It's suggested some new results concerning special regularization of singularities on the wave fronts of the integral equations kernels. The illustrative numerical examples 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 rectangular forms in 2 and 3D cases. These results show quite stability of the elaborating algorithm.

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Authors and Affiliations

  1. Institute of Pure and Applied Mathematics, Pushkin str., 125, 480021, Almaty, Kazakhstan (Former SU)

    L. A. Alekseyeva & G. K. Zakir'yanova

  2. Institute of Mechanics and Machine-Science, Abai str., 31, Almaty, 480091, Kazakhstan (Former SU)

    Sh. A. Dildabayev & A. B. Zhanbyrbayev

Authors
  1. L. A. Alekseyeva
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  2. G. K. Zakir'yanova
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  3. Sh. A. Dildabayev
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  4. A. B. Zhanbyrbayev
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Communicated by S. N. Atluri, 7 December 1995

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Alekseyeva, L.A., Zakir'yanova, G.K., Dildabayev, S.A. et al. Boundary integral Equations Method in two- and three-dimensional problems of elastodynamics. Computational Mechanics 18, 147–157 (1996). https://doi.org/10.1007/BF00350533

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