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The Quarterly Journal of Mechanics and Applied Mathematics 1966 19(3):371-386; doi:10.1093/qjmam/19.3.371
© 1966 by Oxford University Press
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SOME VARIATIONAL PRINCIPLES IN PLATE BENDING PROBLEMS

L. S. D. MORLEY

( Royal Aircraft Establishment Farnborough )

Variational principles are derived for plate bending problems where the boundary is either part clamped and part simply supported or where the boundary tractions are prescribed. This latter case is of particular significance for problems which occur in the constructional industry.

The biharmonic problem is reduced to the consideration of two successive variational problems each associated with the simpler Laplace equation. The variational principles are derived for the class of functions which are harmonic and are not subjected to any boundary conditions. Care is taken so that the principles are valid in the presence of discontinuous behaviour such as occurs at corner points.


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