Page 174 - Mechanics Analysis Composite Materials

Chapter 4. Mechanics of a composite layer I59

Substitution of Eqs. (4.87) and integration yields

U3
12 -
M = BIIh-0' (4.89)
+
V = ah[B41~BM(&+vi)] . (4.90)

These forces and moment should satisfy the equilibrium equation that follows from
Fig. 4.27, i.e.,

PI= 0. V'= 0, MI= V . (4.91)

Solution of the first equation is P = F = aah. Then, Eq. (4.88) gives
E2 = --(e2 + . (4.92)
B14
BI I
The second equation of Eqs. (4.91) shows that V = Cl, where CI is a constant of
integration. Then, substituting this result into Eq. (4.90) and eliminating E? with the
aid of Eq. (4.92) we get

(4.93)

where 844 =BM -B14B41.
Taking in the third equation of Eqs.(4.91) V = CI and substituting M from
Eq. (4.89) we arrive at the following equation for 81:

Integration yields

M + M'dr
V dx
Fig. 4.27. Forces and moments acting on the strip element.