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Computational Mechanics

, Volume 24, Issue 2, pp 90–99 | Cite as

Numerical implementation of the integral-transform solution to Lamb's point-load problem

  • H. G. Georgiadis
  • D. Vamvatsikos
  • I. Vardoulakis
Article

Abstract

The present work describes a procedure for the numerical evaluation of the classical integral-transform solution of the transient elastodynamic point-load (axisymmetric) Lamb's problem. This solution involves integrals of rapidly oscillatory functions over semi-infinite intervals and inversion of one-sided (time) Laplace transforms. These features introduce difficulties for a numerical treatment and constitute a challenging problem in trying to obtain results for quantities (e.g. displacements) in the interior of the half-space. To deal with the oscillatory integrands, which in addition may take very large values (pseudo-pole behavior) at certain points, we follow the concept of Longman's method but using as accelerator in the summation procedure a modified Epsilon algorithm instead of the standard Euler's transformation. Also, an adaptive procedure using the Gauss 32-point rule is introduced to integrate in the vicinity of the pseudo-pole. The numerical Laplace-transform inversion is based on the robust Fourier-series technique of Dubner/Abate-Crump-Durbin. Extensive results are given for sub-surface displacements, whereas the limit-case results for the surface displacements compare very favorably with previous exact results.

Keywords

Numerical Evaluation Challenging Problem Exact Result Numerical Implementation Surface Displacement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • H. G. Georgiadis
    • 1
  • D. Vamvatsikos
    • 1
  • I. Vardoulakis
    • 1
  1. 1.Mechanics Division, National Technical University of Athens, 5, Heroes of Polytechnion Ave., Zographou, GR-15773, GreeceGR

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