THE EQUILIBRIUM OF AN ISOTROPIC ELASTIC PLATE. 
Hence, putting in the values of A and B from (16), (18), 
: _ cosh Bh sinh fz 32 1 ( eo oe ) \ 
Bee 27m cos me { Bisinh 2Bh—2Bh) 4B? B?\BIB* 10h 
and similarly 
a (cosh Bh +2Bh sinh Bh) sinh Bz 32 _ 1 ( SS) ) ; 
ge e008 mo { B (sinh 2Bh — 2Bh) apn B\8h8 40h 
12. The same problem. Final form of the solution. 
We come lastly to ¢,, 6, of § 10. 
The function F requires separate formule for its expression in the three cases 
m=0, m=1, m>1, but in all cases 
F = (27/6*)J,,8p cosmwo+F,, when p<a \ 
= F,, when p>a 
where F, and F, satisfy the equations y*F,=0, y*F,=0. The values of F,, F, for the 
various cases are given in (/). 
When p<a, the term (27/6*)J,,8p cos mw of F, taken by itself in $, and 4,, would 
give 
ope Dae s(t 9 =| 
4h3 B+ B2\8h3 “ 40 h 
-2crJ »Bp COS mw . 
ee 3 nin = 69 2 
t 4n3 B+” B2\8h3~ 40 z) 
These are precisely the terms of negative degree (both in @ and in A) with signs 
changed, in the expressions for $3 and 9, given at the end of § 11. 
If, then, we take this part of ¢,, 9, along with $,, 9, we have the complete solution 
in the form 
cosh Bh sinh Bz 
al 
ee ea, Oh ON) 
+ 27 >, ( -) =e sh 26-1 JmKp COS w(KAGp KAI mBA — GyKABAS»' Ba) 
B? — x*)«h(cosh 2xh — 1) 
2 alA- 3 Gove +a 
— FB atl 
* 40k 
ak Bh+28h sinh Bh) sinh Bz 
ord 
FO aes GT — DBR) 
h sinh xh) sinh xz 
2 (cosh kh + 2x ; 
i: 2 (8? — K?)Kh(cosh 2«h — 1) 
Fy 3—2 — Dh2z272F 2 
+ me 6 27 Fy 2h? AYA 1)-3 oN oa F, 
when p<a. 
and 
¢ = Qn >, ( -) (2 cos ae tale Le G,,Kp cos Muw(Kad , Kad »Ba—-J,KaBa J, Ba) 
= «2)«h(cosh 2«h — 1) 
3 t ._, 9 
F, -—8y? oF, 
7a al? ina F,)+ Zon 
ee Cos te na esi SEED eos maxed, /xad, Ga dea ba), Ga) 
(8? — x?)kh(cosh 2xh — 1) 
3 
+i als - 589 2B, — 2h2y7F 2)- 
o, 
AO ie oe 
when p>a . 
J mkp COS mw(KAG,, KAJ Ba — GKa Bad,’ Ba) 
(33) 
(34), 
