Page 399 - Mechanics Analysis Composite Materials

384 Mechanics and analysis of composite materials

This equation allows us to determine the shell thickness at the equator (r =R), hR,
matching GIor rs2 with material strength characteristics.
As was already noted, the shells under study can be made laying up fabric tapes of
variable width, ~(r),along the shell meridians. The tape width can be linked with
the shell thickness, h(r), as

kw(r)S = 2nrh(r) , (8.56)

where k is the number of tapes in the shell cross-section (evidently, k is the same for
all the cross-sections) and 6 is the tape thickness. Substituting h(r) from Eq. (8.52)
we get

Consider the second special case - a shell made by winding of unidirectional
composite tapes at angles *4 with respect to the shell meridian. The tape width, WO,
does not depend on r, and its thickness is 6. Then, equation similar to Eq. (8.56) can
be written as

where k is the number of tapes with angles +$ and -4. Thus, the shell thickness is
kWO6
h(r) =
2nrcos 4(r) *
It can be expressed in terms of the thickness value at the shell equator h~ =
h(r = R) as

R COS (PR
h(r) = hR (8.57)
rcos 4(r) '

where 4R= &(r=R). It should be noted that this equation is not valid for
r < 1-0+WO,Le., in the shell area close to the polar opening where tapes are
completely overlapped.
Substituting h(r) from Eq. (8.57) into Eq. (8.51) we arrive at the following
equation for the tape orientation angle:

d4 sin4[n-(l -n)cos2q5]
r--.
dr cos (b[ 1 - (1 - n)cos2 $1 =