# Hypersingular integral equations on curved boundaries

• Roland Maucher
Conference paper

## Abstract

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.

## Keywords

Singular Integral Collocation Point Quadrature Rule Circular Boundary Kirchhoff Plate
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## References

1. [1]
I. Babuška, J. Pitkäranta, The plate paradox for hard and soft simple support, SIAM J. Math. Anal. Vol. 21 (1990), pp 551–576
2. [2]
F. Hartmann, Introduction to boundary elements, Springer Verlag 1989
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 19–30
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 55–67
7. [7]
D. F. Paget, A Quadrature rule for finite-part integrals, BIT, Vol. 21 (1981), pp 212–220
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 485–500
10. [10]
K. Beyer, Die Statik im Stahlbetonbau, Springer Verlag 1987, reprintGoogle Scholar