constraint is expressed as a limit P" (i.e., P"=10-4) On the probability of failure, P. The
probability of failure is based on first-ply failure according to the maximum strain failure
criterion. The four design variables are the ply angles Bi and 6, and their stack-thickness
tl and tz. Reliability-based optimization seeks the lightest structure satisfying the
reliability constraint.
The twelve random variables are four elastic properties (El, E2, G12, and Cl12), two
coefficients of thermal expansion (al and a2), five ply strain allowables (sin, E1, E2u, Ez21
and ylu), and the stress-free temperature of the material (Tzero). The mean values of the
strain limits are shown in Table 5-1 except for EZu, which is 0.0154. Table 5-2 shows the
coefficients of variation (CV) of the random variables that are assumed to be normally
distributed and uncorrelated. Those CVs are obtained based on limited test data provided
to us by the manufactures, and are intended only for illustration. The mean value of the
stress-free temperature is 3000F. The mean values of other random variables change as
function of temperature and are given in chapter four.
Table 5-1. Strain allowablesa for IM600/133 at -4230F
Strain 8/< ey' sy, es' Y12"
Allowables 0.0103 -0.0109 0.0110 or 0.0154b -0.0130 0.0138
a Strains include residual strains calculated from the stress-free temperature of 3000F
b The value 0.0110 is obtained from the extreme value 0.0154 divided by a safety factor
of 1.4
Table 5-2. Coefficients of variation (CV) of the random variables
Random 1
variables ~~'GZ~ ~ Z ~ eo61 1EE11
CV 0.035 0.035 0.030 0.06 0.09