Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions
type: Item
instance of: scholarly article
title: Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions
zbMATH Open document ID: 0806.73073
DOI: 10.1016/0045-7825(93)90171-S
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1995-02-20T00:00:00Z
review text: This paper is an extension of the boundary integral equation (BIE) formulation developed by the authors recently for three-dimensional acoustic problems [Comput. Methods Appl. Mech. Eng. 96, No. 2, 271-287 (1992; Zbl 0754.76072)] to radiation and scattering of elastic waves. They employ the \textit{A. J. Burton} and \textit{G. F. Miller} [Proc. R. Soc. Lond., Ser. A 323, 201-210 (1971; Zbl 0235.65080)] composite BIE formulation using a linear combination of the conventional BIE and the hypersingular BIE to furnish unique solutions at all frequencies for external elastic wave problems. The authors derive systematically a weakly singular form of the hypersingular BIE before any discretization. The derived BIE are applied to time-harmonic scattering from a traction- free spherical void which is impinged upon by a plane longitudinal incident wave. Since the regularized hypersingular BIE requires the boundary density of the displacement vector to be \(C^ 1\) continuous, the authors employ \(C^ 1\) continuous elements, namely, the Overhauser elements and the non-conforming quadratic elements. Analysis of the numerical results is presented.
Mathematics Subject Classification ID: 74S15
Mathematics Subject Classification ID: 74J20
zbMATH DE Number: 473266
zbMATH Keywords: regularization
zbMATH Keywords: composite formulation
zbMATH Keywords: weakly singular form
zbMATH Keywords: traction- free spherical void
zbMATH Keywords: \(C^ 1\) continuous elements
zbMATH Keywords: Overhauser elements
zbMATH Keywords: non-conforming quadratic elements
author: Y. J. Liu
author: Frank J. Rizzo
reviewed by: Vladimir Sladek
MaRDI profile type: Publication
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full work available at URL: 0045-7825(93)90171-s
OpenAlex ID: W1975720513
description: scientific article; zbMATH DE number 473266