XV
ON THE DISTRIBUTION OF STRESS IN AN
ELASTIC RIGHT CIRCULAR CYLINDER
(Schlömilch's Zeitschrift für Math. u. Physik, 28, pp. 125-128, 1884.)
A HOMOGENEOUS elastic right circular cylinder is bounded by
two rigid planes perpendicular to its axis. Let pressures be
applied to its curved surface at any desired inclination to it,
and let them be independent of the coordinate parallel to the
axis and act perpendicularly to that axis. Then the distribu-
tion of stress in the interior can be expressed in a finite form
so remarkably simple that it may be of interest in spite of the
narrow limits of the problem.
Let F be the pressure on the element ds of the curved
surface, and f its direction. Further, let M, be the component
in direction n of the pressure on a plane element parallel to
the axis of the cylinder, and the normal to which has the
direction n. Let (m, n) denote the angle between the direc-
tions m and n; the radius vector joining the element
considered to the element ds of the curved surface; p the
perpendicular let fall on the axis of the cylinder from the
element ds; and R the radius of the cylinder. With this
notation
M,
=
-
p cos (n,m) +
1
2
cos (fr) cos (n,r) cos (m,r)
F
ds,
r
(1).
π
p =
2RT
F cos (f,r)ds.