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

We find here deformation cx, Cy, Yxy in layers which are distance 7
from the middle surface. Let us assume the hypothesis of the
invariability of the normal, assuming that the points on the normal
to the middle surface remain on the same normal after deformation.
Then the disolacement of the point which is
/
/
distance z from the mlddle
surface will differ from u and v by quantities z(pw/ax) and z
(0.a/0y) (Fig. 5.54).
Thus,
uz=u-Z -; vz='v-z T; wz=w,
where uz, vz, wz are the displacements of the point which -is dis-r(t•,
z fromn the middle surface.
In addition, at this point we should assume, instead of HR and R
the quantities R 1
+ z and R2 + z and, accordingly,
R 1 R 1 0 R? 2 + ZR 2 P 2 J
Here from expressions (5.77), (5.79), (5.79., we easl'v Itnd, L,
components of deformation in all layers of thu ,Aiell. For this V.
substitute, instead of' u, v, and w, the quantities uz, V , and i"
Finally, keeping the first powers of z, we obtain
I Ow + u
Oy2 U id R.hv22 1 a
O~' R 2 2 2 ROJ ()X
C'
- 21,07