CONTINUITY AND COLLOCATION EFFECTS IN THE BOUNDARY ELEMENT METHOD

CONTINUITY AND COLLOCATION EFFECTS IN THE BOUNDARY ELEMENT METHOD The presence of singularities in the integral operators of the boundary element methods requires that the density functions must satisfy certain continuity requirements if the displacements and stresses are to be bounded. Quite often the continuity conditions, particularly on the derivatives of the density functions, are relaxed at the element ends for the sake of simplicity in approximating the unknown density functions. In this paper, a numerical study on the effects of satisfying or violating the continuity requirements and the effect of the boundary condition collocating point on three different BEM formulations is presented. Two are indirect formulations using force singularities and displacement discontinuity singularities, and the third is Rizzo's direct formulation. The two integral operators in the direct BEM appear individually in the two different formulations of the indirect BEM. This makes it possible to study the numerical error and other problems in each integral operator and the interaction of the two integral operators in the direct BEM. The impact of the study on numerical modelling for the three BEM formulations is presented in the paper. © 1997 by John Wiley & Sons, Ltd. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

CONTINUITY AND COLLOCATION EFFECTS IN THE BOUNDARY ELEMENT METHOD

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Publisher
Wiley
Copyright
Copyright © 1997 John Wiley & Sons, Ltd.
ISSN
0029-5981
eISSN
1097-0207
D.O.I.
10.1002/(SICI)1097-0207(19970530)40:10<1877::AID-NME143>3.0.CO;2-K
Publisher site
See Article on Publisher Site

Abstract

The presence of singularities in the integral operators of the boundary element methods requires that the density functions must satisfy certain continuity requirements if the displacements and stresses are to be bounded. Quite often the continuity conditions, particularly on the derivatives of the density functions, are relaxed at the element ends for the sake of simplicity in approximating the unknown density functions. In this paper, a numerical study on the effects of satisfying or violating the continuity requirements and the effect of the boundary condition collocating point on three different BEM formulations is presented. Two are indirect formulations using force singularities and displacement discontinuity singularities, and the third is Rizzo's direct formulation. The two integral operators in the direct BEM appear individually in the two different formulations of the indirect BEM. This makes it possible to study the numerical error and other problems in each integral operator and the interaction of the two integral operators in the direct BEM. The impact of the study on numerical modelling for the three BEM formulations is presented in the paper. © 1997 by John Wiley & Sons, Ltd.

Journal

International Journal for Numerical Methods in EngineeringWiley

Published: May 30, 1997

References

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