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Existence and uniqueness in the theory of bending of elastic plates

Published online by Cambridge University Press:  20 January 2009

Christian Constanda
Christian Constanda
Affiliation:
University of Strathclyde, Glasgow, Scotland
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Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]

In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 47 - 56
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1.Naghdi, P. M., The theory of shells and plates (Handbuch der Physik VIa/2, Springer-Verlag, Berlin-Heidelberg-New York, 1978).Google Scholar
2.Constanda, C., Uniqueness in the theory of bending of elastic plates (to appear).Google Scholar
3.Kellog, O. D., Foundation of potential theory (Springer-Verlag, Berlin, 1929).CrossRefGoogle Scholar
4.Kupradze, V. D., Potential methods in the theory of elasticity (Israel Program for Scientific Translations, Jerusalem, 1965).Google Scholar
5.Muskhelishvili, N. I., Singular integral equations (P. Noordhoff, Groningen, 1951).Google Scholar