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