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The Quarterly Journal of Mechanics and Applied Mathematics 1987 40(3):339-363; doi:10.1093/qjmam/40.3.339
© 1987 by Oxford University Press
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AN ELASTIC CIRCULAR CYLINDER WITH DISPLACEMENT PRESCRIBED AT THE ENDS—AXIALLY SYMMETRIC CASE

M. ROBERT and LEON M. KEER

( Department of Engineering Science and Applied Mathematics, Northwestern University Evanston, Illinois 60201, USA )

The problem of a linear elastic cylinder with a stress-free curved surface and prescribed displacements at the plane ends is solved by the development in terms of eigenvalue expansions. Then, a biorthogonality relationship for the axially symmetric case is obtained, which is seen to have convergence difficulties. These are surmounted through use of a Galerkin approach, which yields a more diagonally dominant system. To obtain results at the plane ends special techniques have to be developed that correctly incorporate the singular behaviour there.


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