Page 247 - Mechanics Analysis Composite Materials

232 Mechanics and analysis of composite materials
Consider Eqs. (5.10) and (5.11). Integrating them over the layer thickness and using
Eqs. (5.12) and (5.13) we get

-e -e

-e -e
Because the actual distribution of stresses and strains according to the foregoing
reasoning is not significant, we can change them for the corresponding average
stresses and strains:

where

(5.17)

S
1
sm,= s,, =-J am,d~ . (5.18)
h2
-e
It should be emphasized that Eqs. (5.16) are not the inverse form of Eqs. (5.15).
Indeed, solving Eqs. (5.16), using Eqs. (5.18) and taking into account that

a55 =A66 I a56 = -256 9 a66 =255 I
- Am,
Am, =
A55A66 -A:6 ’

we arrive at Eqs. (5.15) in which

(5.19)

These expressions, in general, do not coincide with Eqs. (5.17).
Thus, the constitutive equations for transverse shear are specified by Eqs. (5.15),
and there exist two, in general different, approximate forms of stiffnesscoefficients -
Eqs. (5.17) and (5.19). The fact that equations obtained in this way are approximate
is quite natural because the assumed displacement field, Eqs. (5.1) and (5.2), is also
approximate.