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The Quarterly Journal of Mechanics and Applied Mathematics 1952 5(4):462-465; doi:10.1093/qjmam/5.4.462
© 1952 by Oxford University Press
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RELAXATION METHODS. A THREE-DIMENSIONAL MECHANICAL ANALOGY

D. C. VAUGHAN

( Messrs. L. G. Mouchel and Partners, Ltd. 38 Victoria Street, London, S.W. 1 )

An analogy is established between the approximate mathematical solution to any three-dimensional finite difference equation, obtained by relaxation methods, and the deflexions, in an arbitrarily chosen direction, of the nodes of a corresponding, suitably loaded and tensioned, weightless, elastic three-dimensional net.

The analogy is valid for any form of space lattice, but three regular forms are of particular use.


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