Page 184 - Mechanics Analysis Composite Materials

Chapter 4. Mechanics of u composite luyer 169

Total stresses in Eqs. (4.1 10) and (4.111) should satisfy equilibrium equations,
Eqs. (2.5), which yield for the problem under study

(4.113)

where I = 1: 2, 3.
To simplify the problem, assume that the additional stresses 01 and cr2 do not
depend on z, i.e., that they are uniformly distributed through the thickness of
longitudinal plies. Then, Eqs. (4.113), upon substitution of Eqs. (4.1 IO) and
(4.111) can be integrated with respect to z. The resulting stresses should satisfy
the following boundary and interface conditions (see Fig. 4.37):

Finally, using Eq. (4.112) to express 01 in terms of 02 we arrive at the following
stress distribution (Vasiliev et al., 1970):

(4.114)

where

ZI =z-hl -ha, 22=z+hl +hZ, and ()'=d()/dx.

Thus, we need to find only one unknown function: 02(x). To do this, we can use the
principle of minimum strain energy (see Section 2.1 1.2) according to which function
oz(x) should deliver the minimum value of

(4.1 15)