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

Dependence (5.104) is plotted in Fig. 5.60a. Pre'ernted also
are the result of the analysis of a plate which can be displaced it,
a radial direction (without ';urn) and the result of analysis accorJill
to formulas for a rigid plate.
Thus, maximum bend of the membrane and pressure p are connected
by a cubic dependence. With small bends the term containing the
third power of ratio w 0 /h can be disregarded; dependence (5.1011)
converts to the earlier presented dependences for a £'igid plate.
The curves in Fig. 5.60a show that with a growth in bend the
rigidity of a flexible plate increases. With bends of w/h > 1 the
plate should be assumed flexible.
However, this method of analyzing deflections Qf a flexible pt.f,-
is not universal. It has good agreeme,- with precis( calc:lat.ion
and practice when w/h < 4.
The method requires refinement if the deflections exceed this
value. Actually, when examining the elastic surface of a olate,
as deflections increase we can note a displacement of the [2.ih-r
point toward the contour and at the limit its agreement .:iill ,:.t
attachment, which contradict, the oasic assumption conct:.,.1ng th,
similarity of large bends to benas of a rigid plat,-.
f oc ( r)3
05-7).)
We can pr-scribe the 3hape, of the elast ic surface [n tbh f,.r.
This expression differs from expression (5.103) by the fact t'..,t
here, instead of the exponent 3, there is introduced an undeterm.Lne.,
index z which can be determined each time as a function ol uhe
specific relationship between load and plate thickness.
SJthe transformations, we .,býain
I nEh4-- pb
th ) "a k3
A IfWO -LA3ly-0)3 h-3
On'ittinv
ka" 5. 0""
623
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