Page 372 - Mechanics Analysis Composite Materials

Chapter I. Environmental, special loading, and manufacturing effects 351

where

As follows from Eqs. (7.75) and (7.76), E and K do not depend on x and y.
To find the in-plane displacementswe should integrate Eqs. (7.28) which acquire
the form

Referring the panel to coordinates x and y shown in Fig. 7.49 and assuming that
u(x = 0,y = 0) = 0 and v(x = 0,y = 0) = 0 we get

u = 8-TrX, 0 = &,.TY . (7.77)
0
0
Now consider Eqs. (7.24) in which V, = 5.= 0. Thus, yxT = yJ,T = 0, and Eqs. (7.30)
yield 8, = -&/ax, 8, = -aw/ay. The plate deflection can be found from
Eqs. (7.29) which reduce to

Assuming that w(x = 0,y = 0) = 0, &(x = 0,y = 0) = 0, = 0,y = 0) = 0 we can
write the result of integration as

w = -+(K~T~+ K,T~) (7.78)
.
To present thus obtained solution in an explicit form, consider, for the sake of
brevity, material with zero Poisson’s ratios (v12 = v21 = 0). Then, Eqs. (7.75)-(7.78)
yield

X

/
JY

Fig. 7.49. Deformed shape of a cross-ply antisymmetric panel.