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The Quarterly Journal of Mechanics and Applied Mathematics 1958 11(3):326-350; doi:10.1093/qjmam/11.3.326
© 1958 by Oxford University Press
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ON THE VARIATION OF POISSON'S RATIO IN THE SOLUTION OF ELASTIC PROBLEMS

R. J. KNOPS

( Department of Mathematics, University of Nottingham )

Assuming that the solution is known to a three-dimensional elastic boundary-value problem for a particular Poisson's ratio, equations are established which enable the general solution to be deduced from the known one. The known solution need not necessarily correspond to a real Poisson's ratio; an infinite value, for example, reduces the problem to one in Potential Theory. As illustrations of the method three problems are discussed, one dealing with a semi-infinite body whose plane boundary is rigidly fixed, and two with cones loaded at the vertex. The solutions to the cone problems appear to be new.


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