Page 403 - Mechanics Analysis Composite Materials

388 Mechanics and analysis of composite materials
winding, an opening of radius ro is formed at the shell apex. However, the analysis
of Eq. (8.65) for rl that determines the minimum distance from the meridian to the
z-axis (see Fig. 8.7) shows that PI is equal to ro only if a shell has an open polar hole
(curve 4 in Fig. 8.6). For a pressure vessel whose polar hole is closed, TI >ro and the
equality takes place only for 4 = 0, Le., when TI = ro = 0. In real vessels, polar holes
are closed with rigid polar bosses shown in Fig. 8.8. The meridian of the shell under
consideration can be divided into two segments. For RZr>b, the meridian
corresponds to curve 3 in Fig. 8.6 for which T =pr0/2 and q = 0. In Fig. 8.7 this
segment of the meridian is shown with a solid line. The meridian segment b>r>ro,
where the shell touches the polar boss, corresponds to curve 4 in Fig. 8.6 for which
T = 0. In Fig. 8.7, this segment of the meridian is indicated with the dashed line.
Radius b in Figs. 8.7 and 8.8 can be set as the coordinate of an inflection point of
this curve determined by the condition z”(r = b) = 0. Differentiating Eq. (8.65) and
taking q = 0 for the closed polar opening we get

Because the segment (b - ro) is relatively small, we can assume that the contact
pressurePIbetween the shell and the boss is uniform. Then, from the condition of
boss equilibrium (the hole in the boss is closed), we have

Fig. 8.7. Combined meridian of the pressure vessel dome.

Fig. 8.8. Isotensoid dome with a polar boss.