Hostname: page-component-74656f9884-54qdv Total loading time: 0 Render date: 2026-11-10T23:44:30.929Z Has data issue: false hasContentIssue false
  • English
  • Français

The boundary integral equation method with application to certain stress concentration problems in elasticity

Published online by Cambridge University Press:  17 February 2009

F. J. Rizzo  and
D. J. Shippy
D. J. Shippy
Affiliation:
Department of Engineering Mechanics, University of Kentucky, Lexington, Kentucky 40506, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The essential aspects of the Boundary Integral Equation Method for the numerical solution of elliptic type boundary value problems are presented. A numerical example for a stress concentration problem in classical elasticity in three dimensions is given along with several examples for a class of scalar problems in elastic torsion of non-cylindrical bars. Some discussion and criticism of the method itself and in comparison with widely used field methods is also presented.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 4 , April 1981 , pp. 381 - 393
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Banerjee, P. K. and Butterfield, R., Boundary elements in engineering science (McGraw-Hill, London, 1980).Google Scholar
[2]Brebbia, C., The boundary element method for engineers (John Wiley, New York, 1978).Google Scholar
[3]Clements, D. L., “A boundary integral equation method for the numerical solution of a second order elliptic equation with variable coefficients,” J. Australian Math. Society, B, Appl. Math. (to appear).Google Scholar
[4]Cruse, T. A. and Rizzo, F. J. eds. “Boundary integral equation method: computational applications in applied mechanics,” ASME AMD-Vol. 11 (1975), 1–141.Google Scholar
[5]Fairweather, G., Rizzo, F. J., Shippy, D. J. and Wu, Y., “On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method,” J. Computational physics 31, 1 (1979), 96–112.CrossRefGoogle Scholar
[6]Heise, U., “The spectra of some integral operators for plane elastostatical boundary value problems,” J. elasticity 8 (1978), 47–49.CrossRefGoogle Scholar
[7]Hess, J. L., “Review of integral equation techniques for solving potential flow problems with complicated boundaries,” Proc. Second Intl. Symp. Innovative numerical anavsis in applied engineering science (Virginia U. Press, Charlottesville, 1980), 131–143.Google Scholar
[8]Jaswon, M. A., “Integral equation methods in potential theory. I”, Proceedings of the Royal Society 273, A (1963), 23–32.Google Scholar
[9]John, F., Plane waves and spherical means (Interscience, New York, first edition, 1955).Google Scholar
[10]Kellogg, O. D., Foundations of potential theory (Dover, New York, first edition, 1953).Google Scholar
[11]Lachat, J. C. and Watson, J. O., “Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics”, Int. J. Numerical methods in engineering 10, 5 (1976), 991.CrossRefGoogle Scholar
[12]Love, A. E. H., A treatise on the mathematical theory of elasticity (Dover, New York, fourth edition, 1944).Google Scholar
[13]Lovitt, W. V., Linear integral equations (Dover, New York, 1950).Google Scholar
[14]Muskhelishvili, N. I., Singular integral equations (Noordhoff, Holland, 1953).Google Scholar
[15]Peterson, R. E., Stress concentration factors (Wiley, New York, 1974).Google Scholar
[16]Rizzo, F. J., “An integral equation approach to boundary value problems of classical elastostatics”, Quarterly of applied mathematics 25, 1 (1967), 83–95.CrossRefGoogle Scholar
[17]Rizzo, F. J., Gupta, A. K. and Wu, Y., “A boundary integral equation method for torsion of variable diameter circular shafts and related problems,” Proc. Second Intl. Symp. Innovative numerical analysis in applied engineering science (Virginia U. Press, Charlottesville, 1980), 373–380.Google Scholar
[18]Rizzo, F. J. and Shippy, D. J., “An advanced boundary integral equation method for three-dimensional thermoelasticity”, Int. J. Numerical methods in engineering 11, (1977), 1753–1768.CrossRefGoogle Scholar
[19]Rushton, K. R., “Stress concentrations arising in the torsion of grooved shafts,” Intl. J. Mechanical science 9 (1967), 697–705.CrossRefGoogle Scholar
[20]Shaw, R. P., “BIE methods applied to wave problems”, Developments in boundary element methods 1 (1979), 121–153.Google Scholar
[21]Stakgold, I., Boundary value problems of mathematical physics-volume 1 (Macmillan, New York, 1967).Google Scholar
[22]Stippes, M. and Rizzo, F. J., “A note on the body force integral of classical elastostatics,” ZAMP 28 (1977), 339–341.Google Scholar
[23]Timoshenico, S. and Goodier, J. N., Theory of elasticity (McGraw-Hill, New York, 1951).Google Scholar
[24]Vekua, I. N., New methods for solving elliptic equations (North-Holland, Netherlands, 1967).Google Scholar
[25]Watson, J. O., “Hermitian cubic boundary elements for plane elastostatics”, Proc. Second Intl. Symp. Innovative numerical analysis in applied engineering science (Virginia U. Press, Charlottesville, 1980), 403–412.Google Scholar
[26]Wu, Y., “The boundary integral equation method using various approximation techniques for problems governed by Laplace's equation”, U. S. Air Force Special Report AFOSR-TR-76–1313, Washington, DC, (1976).Google Scholar
[27]Zienkiewicz, O. C., The finite element method (McGraw-Hill, London, third edition, 1977).Google Scholar