Closed-form integration of singular terms for constant, linear and quadratic boundary elements. I: SH wave propagation.

*(English)*Zbl 0968.74077Summary: One of the most important aspects in the application of boundary element techniques to wave propagation problems is the accurate representation of the singular terms at the points of application of virtual loads. It is current practice to carry out this task by means of numerical quadrature. This paper presents an analytical evaluation of the singular integrals for constant, linear and quadratic boundary elements involving SH waves, the results of which are then used to model inclusions in a two-dimensional acoustic medium illuminated by dynamic anti-plane line sources. Finally, the BEM results are compared with known analytical solutions for cylindrical inclusions.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

74J10 | Bulk waves in solid mechanics |

74J20 | Wave scattering in solid mechanics |

##### Keywords:

linear boundary elements; SH wave propagation; elastic inclusions; scattering; constant boundary elements; analytical evaluation of singular integrals; quadratic boundary elements; two-dimensional acoustic medium; dynamic anti-plane line sources
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\textit{A. J. B. Tadeu} et al., Eng. Anal. Bound. Elem. 23, No. 8, 671--681 (1999; Zbl 0968.74077)

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##### References:

[1] | Wong, H.L.; Trifunac, M.D., Surface motion of a semi-elliptical alluvial valley for incident plane SH-waves, Bull seismic soc am, 64, 1389-1403, (1974) |

[2] | Lee, V.W.; Karl, J.A., Diffraction of SV waves by underground circular, cylindrical cavities, Soil dynamics earthquake engng, 11, 445-456, (1992) |

[3] | Lee, V.W.; Wu, X., Application of the weighted residual method to diffraction by 2D canyons of arbitrary shape: II incident P, SV and Rayleigh waves, Soil dynamics earthquake engng, 13, 365-375, (1994) |

[4] | Kausel E. Forced vibrations of circular foundations in layered media. MIT Research Report 74-11. Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1974. |

[5] | Sanchez-Sesma, F.J., Site effects on strong ground motion, Soil dynamics earthquake engng, 6, 124-132, (1987) |

[6] | Dravinski, M.; Mossessian, T.K., Scattering of plane harmonic P, SV and Rayleigh waves by dipping layers of arbitrary shape, Bull seismic soc am, 77, 212-235, (1987) |

[7] | Pedersen, H.A.; Sanchez-Sesma, F.J.; Campillo, M., Three-dimensional scattering by two-dimensional topographies, Bull seismic soc am, 84, 1169-1183, (1994) |

[8] | Beskos, D.E., Wave propagation through ground, (), 359 |

[9] | Hall, W.S., Integration methods for singular boundary element integrands, (), 219 |

[10] | Kawase, H., Time-domain response of a semi-circular canyon for incident SV, P and Rayleigh waves calculated by the discrete wavenumber boundary element method, Bull seismic soc am, 78, 1415-1437, (1988) |

[11] | Tadeu, A.J.B.; Kausel, E.; Vrettos, C., Modelling and seismic imaging of buried structures, Soil dynamics earthquake engng, 15, 387-397, (1996) |

[12] | Tadeu AJB. Modelling and seismic imaging of buried structures. PhD thesis. M.I.T., Department of Civil Engineering, Cambridge, Massachusetts, 1992. |

[13] | Pao, Y.H.; Mow, C.C., Diffraction of elastic waves and dynamic stress concentrations, (1973), Crane and Russak |

[14] | Manolis, G.D.; Beskos, D.E., Boundary element methods in elastodynamics, (1988), Unwin Hyman |

[15] | Tadeu AJB, Santos PFA. Performance of higher order elements in the analysis of a two-dimensional acoustic medium. BEM 21, Oxford, UK, 1999. |

[16] | Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1964), Dover New York, pp. 480-484 |

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