Design and Stress Analysis of Extraterrestrial ... - The Black Vault

Equations (5.74), (5.75), (5.76) should be fulfilled by the
equations of shell deformations.
Let us examine shell deformation.
As already indicated, the
geometry of a shell is wholly determined by the radius of curvature
of the arc of the meridian RI, by the second principal radius R2,
and by angle 0 between the normal to the middle surface and the
axis of symmetry. The shape of the middle surface after deformation
is called the elastic surface of the shell. It can be characterized
by three projections of the full displacement of point A onto the
x-, y-, and z-axes. Let us designate these projections it, v, and w,
respectively (see Fig. 5.49).
AAB
dxd
d
Fig. 5.51.
Finding the radial deformation of anl elemlent.
The x-axis and the di•splacement of' u are directed atlong the ta4ngvent
to the arc of the meridian, y and z along the tangent to •'. aoc c
the circle, and z and w along the normal. '7ef If shell rm,,t'3r if
axisymmetrAc, displacement od v vanishes.
F.We shall express the deformation arising in the shell In terti.
displacements of u, v, and w. We find the componento of d.,forr..a:' ic.
CX,
C cxy
Cy., and yxy in the middle surface and designate them %c.' Co),
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