Closed-form integration of singular terms for constant, linear and quadratic boundary elements. II: SV-P wave propagation.

*(English)*Zbl 0973.74087Summary: Part I of these two related papers [the authors, ibid. 23, No. 8, 671-681 (1999; Zbl 0968.74077)] considered the analytical evaluation of singular integral for anti-plane boundary elements, the results of which were then applied to the evaluation of scattering problem involving SH waves. This second part provides an extension of these results to the more complicated case of in-plane boundary elements, and presents their application to scattering problems involving SV-P waves. First, the singular integrals for constant, linear and quadratic boundary elements are evaluated in closed form. Thereafter, the formulation is used to model cylindrical inclusions in a two-dimensional elastic medium under the action of dynamic in-plane (plane-strain) line sources. Finally, the boundary element method results are compared with known analytical solutions for these problems.

##### 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; constant boundary elements; boundary element formulation; shear waves; scattering; SV-P waves; singular integrals; quadratic boundary elements; cylindrical inclusions; two-dimensional elastic medium; line sources
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\textit{A. J. B. Tadeu} et al., Eng. Anal. Bound. Elem. 23, No. 9, 757--768 (1999; Zbl 0973.74087)

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##### References:

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