Page 88 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics of a unidirectional ply 73

(3.47)

Displacements can be determined with the aid of Eqs. (3.19), (3.21) and (3.25).
Changing .Y for 2 =x/a we get

For the first fiber (n = l), we have

Substituting Eq. (3.42) into these equations we arrive at

(n=2,3,4, ...,k) , (3.48)

(3.49)

To determine coefficients Ci, we should apply the boundary conditions and write
Eqs. (3.23) and (3.24) in the explicit form-using Eqs. (3.47)-(3.49). Substituting S,,
from Eq. (3.43) and 1.i from Eq. (3.41) we get

Bi 2n - 1
2citan sin- 2 Oi =O (n = 2,3,4, ...,k),
i: I

Introducing new coefficients
Oi
Di=Cjtan- , (3.50)
2
we arrive at the final form of the boundary conditions, Le.,

(3.51)

(3.52)