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The Green's function of an elastic plate

Published online by Cambridge University Press:  24 October 2008

W. R. Dean
W. R. Dean
Affiliation:
University CollegeLondon
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Extract

In this paper a simple expression in finite terms is found for the small transverse displacement of a thin plane elastic plate due to a transverse force applied at an arbitrary point of the plate. The plate is clamped along the semi-infinite straight lines represented by AB, CD in Fig. 1, these lines being the only boundaries of the plate. The transverse displacement w at any point (x, y) of the plate is a biharmonic function of the variables (x, y) which vanishes together with its normal derivative at all points of the boundary. Clearly w is also a function of the coordinates (x0, y0) of the point of application of the force, and it is known ((5), p. 173) that it is a symmetrical function of the coordinate pairs (z, y) and (x0, y0); it is the Green's function associated with the differential equation and the boundary conditions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 2 , April 1953 , pp. 319 - 326
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

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