THE EQUILIBRIUM OF AN: ISOTROPIC ELASTIC PLATE. 
(i) Permanent mode. 
aoe. oe oe oe) 
l-o 2 dz\du dy 
eee as 
[=e 2 dy\ dx dy 
ae o As =) 
- eer Nike la 
where 
d (dU , dV -( =) 
Ma 1- =) 
wast mH) a bee dy\dy da | 
d (dU .adV d (dU | 
)_ ac ae _— Ans ait NO, pee es (0) 
2 (= ; 7) c “(5 di 
Put 
1 /dU JdvV 1 e ge 
i = = + 
Se l-o\dx dy | 
We k e a =) = (2 a _ 
aye aa dy dx 
Then 
dA , dil _6 dA dll _g 
dx dy i Pi Serine dn «ds 
and « 
da a_ gf aA _dll_y 
dy dx ds dn 
Also 
a du. dv 
ee Ee 5 ae 
~_ 2p = (+) 
dy dx 
The components of traction parallel to the axes are 
X = lea + may; Y slay + myy. 
These are easily transformed into 
em 2u( 1A +1 mI — a) X=? p(-U+ma +5"). 
ds d 
Hence 
fiu= 1X + mY =2p( A ie 12) 
y ds ds 
i= —mX+1Y = 2p - +i + m2) 
ds ds 
also nz = 0 
or > dq p 
26) (4 - aq _ p 
a-a(a- 4-2) 
dsp 
TRANS. ROY. SOC. EDIN., VOL. XLI. PART I. (NO. 8). 
32 
209 
