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

Georgiadis, HG; Vamvatsikos, D; Vardoulakis, I

dc.contributor.author	Georgiadis, HG	en
dc.contributor.author	Vamvatsikos, D	en
dc.contributor.author	Vardoulakis, I	en
dc.date.accessioned	2014-03-01T01:14:53Z
dc.date.available	2014-03-01T01:14:53Z
dc.date.issued	1999	en
dc.identifier.issn	0178-7675	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13268
dc.subject	Exact Results	en
dc.subject	Fourier Series	en
dc.subject	Integral Transforms	en
dc.subject	Laplace Transform	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Integral equations	en
dc.subject.other	Laplace transforms	en
dc.subject.other	Problem solving	en
dc.subject.other	Lamb's point-load problem	en
dc.subject.other	Elasticity	en
dc.title	Numerical implementation of the integral-transform solution to Lamb's point-load problem	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s004660050441	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s004660050441	en
heal.language	English	en
heal.publicationDate	1999	en
heal.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.	en
heal.publisher	Springer-Verlag GmbH & Company KG, Berlin, Germany	en
heal.journalName	Computational Mechanics	en
dc.identifier.doi	10.1007/s004660050441	en
dc.identifier.isi	ISI:000082581800003	en
dc.identifier.volume	24	en
dc.identifier.issue	2	en
dc.identifier.spage	90	en
dc.identifier.epage	99	en