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Approximate Solutions of Boundary Value Problems in Potential Theory with Applications to Electrostatics and Elastostatics

Published online by Cambridge University Press:  20 January 2009

W. E. Williams
W. E. Williams
Affiliation:
Department of Applied Mathematics, The University, Liverpool
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Summary

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A simple approximate formula is obtained for the capacity of the condenser formed by a “small” conductor placed inside a much larger one. The formula involves a constant whose choice is, to a certain extent, arbitrary and it is shown that, for problems involving spheroids inside cylinders and between parallel plates, the constant may be found in a simple fashion so as to give very accurate results. A similar formula is obtained for the loss in potential energy due to a crack or cavity in a circular beam or a thick plate. For the particular cases of the boundary value problems considered which have been treated by other means very close numerical agreement is obtained between those results and ones deduced in the present paper.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 2 , December 1964 , pp. 89 - 101
Copyright
Copyright © Edinburgh Mathematical Society 1964

References

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