Advertisement

Exploiting Partial or Complete Geometrical Symmetry in Boundary Integral Equation Formulations of Elastodynamic Problems

  • Marc Bonnet
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 19)

Abstract

Procedures based on group representation theory, allowing the exploitation of geometrical symmetry in symmetric Galerkin BEM formulations of 3D elastodynamic problems, are developed. They are applicable for both commutative and noncommutative finite symmetry groups and to partial geometrical symmetry, where the boundary has two disconnected components, one of which is symmetric.

Keywords

Boundary Element Method Geometrical Symmetry Abelian Case Elastodynamic Problem Symmetry Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allgower, E. L., Georg, K., Miranda, R., Tausch, J. Numerical Exploitation of Equivariance. Z. Angew. Math. Mech., 78, 795–806 (1998).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bonnet, M. On the use of geometrical symmetry in the boundary element methods for 3D elasticity. In C.A. Brebbia (ed.), Boundary element technology VI, pp. 185–201. Comp. Mech. Publ., Southampton / Elsevier, Southampton, Boston (1991).Google Scholar
  3. 3.
    Bonnet, M., Maier, G., Polizzotto, C. On symmetric galerkin boundary element method. Appl. Mech. Rev., 51, 669–704 (1998).CrossRefGoogle Scholar
  4. 4.
    Bossavit, A. Symmetry, groups and boundary value problems: a progressive introduction to noncommutative harmonic analysis of partial differential equations in domains with geometrical symmetry. Comp. Meth. in Appl. Mech. Engng., 56, 167–215 (1986).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Eringen, A. C., Suhubi, E. S. Elastodynamics (vol II — linear theory). Academic Press (1975).Google Scholar
  6. 6.
    Lobry, J., Broche, C.H. Geometrical symmetry in the boundary element method. Engng. Anal. with Bound. Elem., 14, 229–238 (1994).CrossRefGoogle Scholar
  7. 7.
    Nedelec, J. C. Integral equations with non integrable kernels. Integral equations and operator theory, 5, 562–572 (1982).MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Serre, J. P. Linear representations of finite groups. Springer-Verlag (1977).Google Scholar
  9. 9.
    Vinberg, E. B. Linear representations of groups. Birkhäuser (1989).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Marc Bonnet
    • 1
  1. 1.Laboratoire de Mécanique des Solides (UMR CNRS 7649)Ecole PolytechniquePalaiseau CedexFrance

Personalised recommendations