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**Multi-domain BEM for two-dimensional problems of elastodynamics.**
*(English)*
Zbl 0631.73067

An advanced implementation of the boundary element technique for the periodic and transient dynamic analyses of two-dimensional elastic or viscoelastic solids of arbitrary shape and connectivity is presented. For transient dynamic analysis the problem is first solved in the Laplace transform space and then the time domain solutions are obtained by numerical inversion of transformed domain solutions. The present analysis is capable of treating very large, multi-domain problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces. With the help of this substructuring capability, problems related to the layered media and soil-structure interaction can all be analyzed. This paper also introduces a new type of element called ‘enclosing element’, which has been developed and used to model the infinitely extending boundaries of a half-space or a layered medium. A number of numerical examples are presented, and through comparisons with available analytical and numerical results, the accuracy, stability and efficiency of the present analysis are established.

### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

65R20 | Numerical methods for integral equations |

74H45 | Vibrations in dynamical problems in solid mechanics |

65R10 | Numerical methods for integral transforms |

### Keywords:

dynamic reciprocal theorem; boundary element technique; periodic; transient dynamic analyses; two-dimensional elastic; viscoelastic solids; arbitrary shape; connectivity; Laplace transform space; time domain solutions; numerical inversion; very large, multi-domain problems; substructuring; layered media; soil-structure interaction; enclosing element### Software:

LINPACK
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\textit{S. Ahmad} and \textit{P. K. Banerjee}, Int. J. Numer. Methods Eng. 26, No. 4, 891--911 (1988; Zbl 0631.73067)

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