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The Quarterly Journal of Mechanics and Applied Mathematics 1958 11(2):159-171; doi:10.1093/qjmam/11.2.159
© 1958 by Oxford University Press
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SOME MIXED BOUNDARY VALUE PROBLEMS IN ISOTROPIC THIN PLATE THEORY

G. M. L. GLADWELL

( University College London )

The mixed boundary value problems with which the paper deals are problems in which the plate is clamped along part of the boundary and is either free, or subject to specified bending moment and shear, along the remainder. Complex variable analysis, and especially the techniques evolved by Muskhelishvili (1) and (2) are used throughout. First the general boundary conditions for the problems are stated and reduced to a suitable form and then, using known results for plates with fully clamped boundaries, the boundary conditions are reduced to non-homogeneous Hilbert problems—the kind of problem treated in Muskhelishvili's book (2). Special attention is given to the case of point loading in the interior of the plate, and to the case when part of the boundary is subject to constant bending moments and shears.


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