Page 163 - Mechanics Analysis Composite Materials

148 Mechanics and analysis of composite materials

Z

Fig. 4.18. A composite layer consisting of a system of unidirectional plies with the same orientation.

Fig. 4.19. An anisotropic outer layer of a composite pressure vessel. Courtesy of CRISM.

equations for the global coordinate frame x, y, z (see Fig. 4.18). To do this, we
should transfer stresses 01, 02, 212, 213, 223 acting in the layer and the corresponding
strains EI, ~2, y12, 713, 723 into stress and strain components a,, a-v, zxv, z,,, zM and E,,
E,", y,.", y,,, y,, using Eqs. (2.8), (2.9) and (2.21), (2.27) for coordinate transformation
of stresses and strains. According to Fig. 4.18, directional cosines, Eqs. (2.1), of
such transformation are (we take x' = 1, y' = 2,z' = 3)

I,, = c, I+ = s, 19, = 0,
If, = -s, If? = c, fvl, = 0, (4.66)
I*, = 0, I?,, = 0, lyi = 1 ,

where c = cos 4 and s = sin 4. Using Eqs. (2.8) and (2.9) we get