1.
Introduction and Summary
.—This paper deals with the elastic stability of a corrugated plate under thrust along its generators. Besides the assumption, common to all such problems, that the plate is thin, it is supposed that the depth of a bay (
d
, fig. 1) is a small multiple of
h
, the semi-thickness, and that the transverse expansion that is the usual accompaniment of a longitudinal thrust, is prevented by a thrust in a perpendicular direction. The equations derived in §§ 2-7 are then soluble, and the critical stress in any case can be found from an equation expressing that an infinite determinant is zero. The numerical work that has been done has been limited to the two cases in which
d
= 10
h
and
d
= 5
h
, respectively. As a preliminary, in §§ 8-11, it has been supposed that σ, Poisson’s ratio, is zero. The equations are greatly simplified by this supposition, and results can easily be obtained which are a valuable guide to the more complicated arithmetic of the normal case in which σ does not vanish. In particular, this preliminary work is used to find the “favourite type of distortion” (that possible under the least stress) in the other case: it can be seen that the favourite types are the same whether a is or is not zero. The necessary exploration is therefore done for σ = 0, and the arithmetic in the more practical case, in which we suppose that σ = ¼, is confined to the calculation of stresses causing definite modes of distortion.
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