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

I
"I II
when xd = b ,•=
Eafl, a (h- a) (2a + b)
2 (1
2(-I
1:• 3-0a
o If the Phell has little thickness, we assume b : (I + m)a, where
nm is a small quantity. ,Sub'stituting this value into formulas a
and co and disregarding the highest orders of quantity in, we find
L
wheni r aý :--2(I-) 2J '
LM
when r = b ---- a 1 2M.
I (1 3
If we disregard quantity 2m/3,
we. shall arrive at the same valutes
for circular strespses as were ob'tained fo:' a. cylindrical zhell and
for a tpin plate with attached edges.:
Analysis of flexible plates
By flexible we mean those plates which'are free and under the ac~ion ýf
external forces noticeably change their s'iape witnout disrupting
the elastic pro~erties of the material. U'Jually, such plates have
a valup for parameter w/h > 1.
The dlfl'frence between such plates and those examined above l.!o•
in the fazt that to of the bendihg stresses are acddI ttiJ',- 17
compressive stresses of the middle surface, due to large defli•otiD,,
(Fig. 5.57a).
In deriving the basic equations examined below, we retain the
hypothesis of tne Invariability of the normal to the m~ddle ;urface
and the. problem is solved within the limits of el:taicity.
Let us set up steady-state equaticns for a plate element. t. witcn
we shall give two meridional artrc two conlc zectio:,,, .,itth
*I ,
" I.