Page 277 - Mechanics Analysis Composite Materials

262 Mechanics and analysis of cornposite materials

Fig. 5.23. As can be seen interaction of the layers under axial compression of the
cylinder results in radial compression that occurs between the layers.
We now return to transverse shear stress z,, and try to determine the transverse
stresses taking into account transverse shear deformation of the laminate. To do
this, we should first specify the character of loading, e.g., assume that axial force T
in Fig. 5.19 is uniformly distributed over the cross-sectional contour of the angle-ply
layer middle surface as in Fig. 5.24. As a result we can take T = 2nRN (because the
cylinder is very thin, we neglect the radius change over its thickness).
To study the problem, we should supplement constitutive equations, Eqs. (5.74),
with the missing equation for transverse shear, Eqs. (5.20) and add the terms
including the change of the meridian curvature IC~,which is not zero any more. As a
result, we arrive at the following constitutive equations:

(5.89)

(5.90)
(5.91)
(5.92)

Forces and moments in the left-hand sides of these equations are linked by
equilibrium equations that can be written as (see Fig. 5.25)

AJ:=o, g:-v,=o, y--=o, (5.93)
N,.
I
R

Fig. 5.24. Application of the axial forces.