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A boundary integral equation method for radiation and scattering of elastic waves in three dimensions
Author(s) -
Rizzo F. J.,
Shippy D. J.,
Rezayat M.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210110
Subject(s) - mathematical analysis , mathematics , gaussian quadrature , gravitational singularity , boundary value problem , scattering , cauchy distribution , cauchy principal value , integral equation , quadratic equation , quadrature (astronomy) , geometry , nyström method , physics , mixed boundary condition , cauchy boundary condition , optics
A vector boundary integral equation (BIE) formulation and numerical solution procedure is presented for problems of three‐dimensional elastic wave radiation and scattering from arbitrarily shaped obstacles. The formulation is explicitly in terms of surface traction and displacement, rather than wave potentials, and the BIE on which numerical work is based is written in a form entirely free of Cauchy principal value integrals. Indeed, the subsequent computational process, based on quadratic isoparametric boundary elements, renders all integrals free of singularities, so that ordinary Gaussian quadrature may be used. Numerical examples include scattering from spherical surfaces and radiation from a cube.