Page 394 - Mechanics Analysis Composite Materials

Chapter 8. Optimal composite structures 379

According to the derivation of Obraztsov and Vasiliev (1989), the ratio of the layers’
thicknesses is

and elastic constants in Eqs. (8.37) are generalized as

Superscripts 1 and 2 correspond to layers with orientation angles 4I and 4:,
respectively.

8.3. Application to pressure vessels
As an example of application of the foregoing results, consider filament wound
membrane shells of revolution, that are widely used as pressure vessels, solid
propellant rocket motor cases, tanks for gases and liquids, etc. (see Figs. 4.14 and
7.43). The shell is loaded with uniform internal pressure p and axial forces T
uniformly distributed along the contour of the shell cross-section Y = ro as in
Fig. 8.4. Meridional, Nz, and circumferential, Np, stress resultants acting in the shell

Fig. 8.4. Axisymmetrically loaded membrane shell of revolution.