Page 280 - Mechanics Analysis Composite Materials

Chapter 5. Mechanics of laminates 265
IdV - 2a2wN+ pw =p , (5.105)

where

For the cylinder under study, a' = 14/R2 and o2= 139/R2. Because p > a, the
solution of Eq. (5.105) can be written in the following form:

4
w = CnFn(x) + wp , (5.106)
11=1
where Cnare constants of integration, and

To analyze the local effects in the vicinity of the cylinder end, e.g., x = 0 (the stress
state of the cylinder at a distance from its ends is presented above), we should take
C3 = 0 and C4 = 0 in Eq. (5.106) which reduces to

(5.107)
w = CIfi (x) + CZF2(x)+wp '
To differentiate the functions entering this solution, the following relationships can
be used:
F( = -(tFz +rFI), F2/ = tfi - rFz,

F: = (r2- ?)FI + 2rtF2, F: = (3- t2)F2 - 2rtfi,
F,"' = -r(? - 32)F1+ t(? - 3?)fi,
FY = -r(? - 3?)F2 - t(t2 - 3r')B .

Constants of integration CI and CZentering Eq. (5.107) should be found from the
boundary conditions at x = 0. As follows from Figs. 5.24 and 5.25,

where M, is specified by Eqs. (5.104) and (5.107), while V, can be found from the
second equilibrium equation in Eqs. (5.93).
For the cylinder under study, the final expressions for strains and rotation angle
are