### Abstract

The interaction forces of the linear unbounded soil in a non‐linear soil‐structure‐interaction analysis can be calculated recursively, starting directly from the dynamic‐stiffness coefficients in the frequency domain. Two possibilities of choosing a recursive equation are discussed. The recursive equation in the frequency domain. For each frequency, the interaction force at a specific time station is expressed as a function of the corresponding interaction force at the previous time station and of the displacements at the current time station and at the two most recent past time stations. This recursive evaluation of the convolution integral. which can be derived using the z‐transformation, is rigorous. By using interpolation in the frequency domain, an approximate procedure results, which leads to a significant reduction in computational effort. The recursive equation in the time domain. By approximating the dynamic‐stiffness coefficients as the ratios of two polynomials in frequency using a curve‐fitting technique based on the least‐squares method and by applying the partial‐fraction expansion and using the z‐transformation, the recursive coefficients can be determined explicitly. Alternatively, the ratio of two polynomials can also be transformed to an ordinary differential equation together with the initial conditions. The recursive equations using interpolation in the frequency domain and based on a ratio of two polynomials lead to a reduction in the computational effort of one and up to three orders of magnitude, respectively.

Original language | English |
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Pages (from-to) | 365-376 |

Number of pages | 12 |

Journal | Earthquake Engineering & Structural Dynamics |

Volume | 18 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1989 Apr |

### ASJC Scopus subject areas

- Geotechnical Engineering and Engineering Geology
- Earth and Planetary Sciences (miscellaneous)

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## Cite this

*Earthquake Engineering & Structural Dynamics*,

*18*(3), 365-376. https://doi.org/10.1002/eqe.4290180305