On the Construction of the Boundary Integral Representation and Connected Integral Equations for Homogeneous Problems of Plane Linear Elastostatics

  • M. Pignolé
Conference paper
Part of the Boundary Elements book series (BOUNDARY, volume 3)

Abstract

Four fundamental identities are established. They rest on addition to the interior problem (resp. exterior) of an exterior problem (resp. interior) and consideration of displacement and tension jumps across the boundary, connected with these two problems. Two of these identities express, according to these jumps, displacements and stresses everywhere in both the interior and exterior domains. The two others respectively connect the previous jumps to a boundary displacement or tension linear combination.

We obtain the true boundary integral equations by introducing boundary conditions into these identities.

Two ways of discretisation are shown.

Keywords

Lution Reso Pentech 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baldino, R. R. (1979 and 1980) An integral equation solution of the mixed problem for the Laplacian in R3. Part 1 and 2. Rapports internes 48 et 54, Centre de Math. Appl., Ecole Polytechnique, Palaiseau-France.Google Scholar
  2. Banerjee, P. K. (1976) Integral equation methods for analysis of piece-wise non-homogeneous three dimensional elastic solids of arbitrary shape. Int. J. Mech. Sci., 18: 293–303.CrossRefMATHGoogle Scholar
  3. Brebbia, C. A. and Walker, S. (1978) Introduction to boundary element methods. Recent advances in boundary element methods, Pentech Press, Plymouth and London, 293–303.Google Scholar
  4. Chaudonneret, M. (1978) Calcul des concentrations de contraintes en élastoviscoplasticité. Publication O.N.E.R.A. 1978–1, Chatillon-France.Google Scholar
  5. Cruse, T. A. (1977) Mathematical foundations of the boundary-integral equation method in solid mechanics. AFOSR-TR 77-1002, Pratt and Whitney Aircraft Group, United Technologies Corporation, East Hartford, Connecticut 06108.Google Scholar
  6. Hartmann, F. (1980) The complementary problem of finite elastic bodies. New developments in boundary element methods, CML Publications, Southampton, 229–246.Google Scholar
  7. Lachat, J. C. (1975) A further development of the boundary integral technique for elastostatics. Thesis, University of Southampton.Google Scholar
  8. Nedelec, J. C. (1977) Cours de l’école d’été d’analyse numérique CEA-IRIA-EDF.Google Scholar
  9. Pignolé, M. (1980) Une méthode intégrale directe pour la résolution de problèmes d’élasticité. Applications aux problèmes plans. Thèse, Université de Bordeaux I.Google Scholar
  10. Schwartz, L. (1973) Théorie des distributions. Hermann, Paris.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • M. Pignolé
    • 1
  1. 1.Laboratoire de Mécanique PhysiqueUniversité de Bordeaux IFrance

Personalised recommendations