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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(2):169-182; doi:10.1093/qjmam/10.2.169
© 1957 by Oxford University Press
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THE EQUILIBRIUM EQUATIONS OF THE INEXTENSIONAL THEORY FOR THIN FLAT PLATES

D. G. ASHWELL

( University College Cardiff )

This paper supplements recent work by Mansfield and Kleeman (1, 2) on the bending of inextensible flat plates. The functions of the membrane forces in the plates are described, and the existence of shearing forces concentrated along their free edges is deduced. Equations of equilibrium are obtained, from which the magnitudes of the membrane stresses (except near the edges), and of the edge-shears, may be estimated. A new form of the differential equation for the deformation of such a plate is given in terms of the edge of regression of the developable surface into which it deforms. The accuracy to be expected from the theory, when applied to practical plates, is discussed.


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