Hypersingular integral equations on curved boundaries

  • Roland Maucher
Conference paper


According to the Babuska plate paradox it is impossible to approximate a circular hinged plate by a polygonal one, [1], and to expect at the same time that the solution converges to the exact solution. Therefore an exact representation of the circular boundary is required. But using the exact representation of the boundary causes a decisive difference to the straight boundary: the occuring singular integrals cannot be determined analytical anymore. The paper presents a method to calculate the singular integrals numerically and three numerical examples will demonstrate the accuracy of the boundary integral technique for various boundary conditions.


Singular Integral Collocation Point Quadrature Rule Circular Boundary Kirchhoff Plate 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    I. Babuška, J. Pitkäranta, The plate paradox for hard and soft simple support, SIAM J. Math. Anal. Vol. 21 (1990), pp 551–576MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    F. Hartmann, Introduction to boundary elements, Springer Verlag 1989MATHCrossRefGoogle Scholar
  3. [3]
    B. Knöpke, The hypersingular integral equation for the bending moments m xx, m xy and m yy of the Kirchhoff plate, Computational Mechanics Vol. 15 (1994), pp 19–30MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    R. Kieser, Über einseitige Sprungrelationen und hypersinguläre Operatoren in der Methode der Randelemente, doctoral thesis, University of Stuttgart 1991Google Scholar
  5. [5]
    M. Guiggani, Direct evaluation of hypersingular integrals in 2D BEM, Notes on numerical fluid mechanics, Vol. 33, Vieweg Verlag, Braunschweig 1992Google Scholar
  6. [6]
    J. Hildenbrand, G. Kuhn, Numerical treatment of finite pari integrals in 2-D boundary element analysis with application in fracture mechanics, Computational Mechanics Vol. 13 (1993), pp 55–67MathSciNetMATHGoogle Scholar
  7. [7]
    D. F. Paget, A Quadrature rule for finite-part integrals, BIT, Vol. 21 (1981), pp 212–220MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    H. R. Kutt, Quadrature rules for finite-part integrals, WISK 178 CSIR special report 1975Google Scholar
  9. [9]
    D. Elliott, On the approximate evaluation Hadamard finite- part integrals, IMA Journal of Num. Analysis Vol. 14 (1994), pp 485–500MATHCrossRefGoogle Scholar
  10. [10]
    K. Beyer, Die Statik im Stahlbetonbau, Springer Verlag 1987, reprintGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Roland Maucher
    • 1
  1. 1.Universität Gesamthochschule KasselKasselGermany

Personalised recommendations