Page 272 - Mechanics Analysis Composite Materials

Chapter 5. Mechanics of laminates 257
The final result is obtained under the assumption that the strain is small (E: << 1).
Consider the case of axial compression. Free body diagram for the laminate
element shown in Fig. 5.20 yields (see Fig. 5.19)

P
N,-=--, N,.=O.
27LR .
As a result, the constitutive equations from Eqs. (5.74) that we need to use for the
analysis of this case become
P
-
0
BIIE,+ B12t: = -- B2 I tt +822~:= 0 , (5.76)
271R’
M, = Clle: + &E&, M,* = c21t: + CZZ&Y, (5.77)
where

The first two equations, Eqs. (5.76), allow us to find strains, i.e.,

(5.79)

where B = BllB22 - BI2B?l and 821 = BIZ.
Bending moments can be determined with the aid of Eqs. (5.77). Axial moment,
My,has reactive nature in this problem. Nonsymmetric laminate in Fig. 5.20 tends
to bend in the xz-plane under axial compression of the cylinder. However, the
cylinder meridian remains straight at a distance from its ends. As a result, a reactive
axial bending moment appears in the laminate. Circumferential bending moment,

Fig. 5.20. Forces and moments acting on an element of the cylinder under axial compression.