Archive of Applied Mechanics

, Volume 65, Issue 1, pp 2–12 | Cite as

Regularized computation of interior displacements and stresses by BEM

  • C. Fiedler
Originals
  • 26 Downloads

Summary

The computation of interior displacements and stresses with the boundary element method (BEM) often requires the evaluation of nearly singular integrals. These integrals arise from the singular behaviour of the kernel functions in the Somigliana identity and the Somigliana stress identity. Treating them numerically in a standard way leads to inaccuracy near the boundary. This effect is always present in the calculation of field variables near the boundary and is called ‘boundary layer effect’. In this paper regularization procedures are proposed which consist of an indirect evaluation of singular integrals and a special coordinate transformation. The proposed procedures eliminate the boundary layer effect for both, the calculation of displacements and stresses. In a numerical example of elastostatics the developed strategies are shown to work. Due to the generality of the proposed procedures they can be extended to any standard boundary element formulation for problems with bounded domains.

Key words

Boundary element method regularization stress analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balaš, J.;Sládek, J.;Sládek, V.: Stress analysis by Boundary Element Method. Amsterdam: Elsevier 1989Google Scholar
  2. 2.
    Brebbia, C. A.;Telles, J. C. F.;Wrobel, L. C.: Boundary Element techniques. Berlin: Springer 1984Google Scholar
  3. 3.
    Crotty Sisson, J. M.: Accurate interior point computations in the boundary integral equation method. Computer Meth. Appl. Mech. Engng. 79 (1990) 281–307Google Scholar
  4. 4.
    Cruse, T. A.;Suwito, W.: On the Somigliana stress identity in elasticity. Comput. Mech. 11 (1993) 1–10Google Scholar
  5. 5.
    Cruse, T. A.;VanBuren, W.: Three-dimensional elastic stress analysis of a fracture specimen with an edge crack. Int. J. Fract. Mech. 7 (1971) 1–15Google Scholar
  6. 6.
    Fiedler, C.: On the evaluation of field variables in elastostatics and elastodynamics with the Boundary Element Method (in german). Doctoral dissertation, Hamburg: Univ. of the Federal Armed Forces 1993Google Scholar
  7. 7.
    Gaul, L.;Fiedler, C.: Improved calculation of field variables in the domain based on BEM. Engineering Analysis with Boundary Elements 11 (1993) 257–264Google Scholar
  8. 8.
    Ghosh, N.;Rajiyah, H.;Ghosh, S.;Mukherjee, S.: A new Boundary Element Method formulation for linear elasticity. Trans. ASME/J. Appl. Mech. 53 (1986) 69–76Google Scholar
  9. 9.
    Guiggiani, M.;Krishnasamy, G.;Rudolphi, T. J.;Rizzo, F. J.: A general algorithm for the numerical solution of hypersingular boundary integral equations. Trans. ASME/J. Appl. Mech. 59 (1992) 604–614Google Scholar
  10. 10.
    Hayami, K.;Brebbia, C. A.: Quadrature methods for singular and nearly singular integrals in 3-D Boundary Element Method. In: Brebbia, C. A. (ed.) Boundary Elements X, Vol. 1, pp. 237–264. Southampton: Computational Mechanics Publ. 1988Google Scholar
  11. 11.
    Kisu, H.;Kawahara, T.: Boundary Element analysis system based on a formulation with relative quantity. In: Brebbia, C. A. (ed.) Boundary Elements X, Vol. 1, pp. 111–121. Southampton: Computational Mechanics Publ. 1988Google Scholar
  12. 12.
    Lachat, J. C.;Watson, J. O.: Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostics. Int. J. Num. Meth. Engng. 10 (1976) 991–1005Google Scholar
  13. 13.
    Okada, H.;Rajiyah, H.;Atluri, S. N.: Non-hyper-singular integral representations for velocity (displacement) gradients in elastic/plastic solids (small or finite deformations). Comput. Mech. 4 (1989) 165–175Google Scholar
  14. 14.
    Sládek, V.;Sládek, J.: Three-dimensional crack analysis for an anisotropic body. Appl. Math. Modelling 6 (1982) 374–380Google Scholar
  15. 15.
    Sládek, V.;Sládek, J.: Elimination of the boundary layer effect in BEM computation of stresses. Communications in Appl. Num. Meth. 7 (1991) 539–550Google Scholar
  16. 16.
    Telles, J. C. F.: A self-adaptive co-ordinate transformation for efficient numerical evaluation of general Boundary Element integrals. Int. J. Num. Meth. Engng. 24 (1987) 959–973Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • C. Fiedler
    • 1
  1. 1.Institut für MechanikUniversität StuttgartStuttgartGermany

Personalised recommendations