Abstract
A general solution of the elastic equations is obtained for problems of stress distributions in plates or cylinders when the bounding faces of the plates Z = ±
h
, or the flat ends of the cylinders, are free from applied normal and shear stresses. The solution is expressed either in the form of Fourier series in the co-ordinate
Z
, or in power series in
Z
, the coefficients of the series being certain functions of the
x
and
y
co-ordinates which are sufficient to satisfy boundary conditions over two bounding cylindrical surfaces normal to the planes
Z
= ±
h
. The form of the theory is greatly simplified by making use of complex combinations of stress components, and by using the complex variable
z
=
x
+
iy
. A first approximation to the part of the theory which deals with the bending of the plate yields a theory similar in character to that given recently by Reissner.
Cited by
28 articles.
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