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The 3‐D elastodynamic boundary element method: semi‐analytical integration for linear isoparametric triangular elements
Author(s) -
Davey K.,
Rasgado M. T. Alonso,
Rosindale I.
Publication year - 1999
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/(sici)1097-0207(19990320)44:8<1031::aid-nme539>3.0.co;2-t
Subject(s) - mathematics , singular integral , quadrature (astronomy) , boundary element method , mathematical analysis , cauchy principal value , gaussian quadrature , numerical integration , line integral , displacement (psychology) , boundary value problem , nyström method , integral equation , finite element method , physics , neumann boundary condition , cauchy boundary condition , optics , thermodynamics , psychology , psychotherapist
A semi‐analytical integration scheme is described in this paper which is designed to reduce the errors incurred when integrals with singular integrands are evaluated numerically. This new scheme can be applied to linear triangular elements for use in steady‐state elastodynamic BEM problems and is particularly useful for predicting displacement to high accuracy, close to surfaces for a spectrum of frequencies. The scheme involves the application of Taylor expansions to formulate the integrals into two parts. One part is regular and is evaluated numerically and the other part is singular but sufficiently simple to enable its transforma tion into a line integral. The line integral is solved numerically using Gauss–Legendre quadrature. This approach caters for all the integral types that appear in steady‐state elastodynamic boundary elements but, in particular, no special treatment is required for the evaluation of the Cauchy principal value singular integrals. Numerical tests are performed on a simple test‐problem for which a known analytical solution exists. The results obtained using the semi‐analytical approach are shown to be considerably more accurate than those obtained using standard quadrature methods. Copyright © 1999 John Wiley & Sons, Ltd.