extrapolation problem was solved, and the side constraints are set as the range of the ARS

shown in Table 5-3. The error of 0.000012 is much lower than the allowable failure

probability of 0.0001.

 Table 5-6 compares the reliability-based optimum with the three deterministic

optima from chapter 4 and their failure probabilities. The optimal thickness increased

from 0.100 to 0.120, while the failure probability decreased by about one order of

magnitude.

Table 5-6. Comparison of reliability-based optimum with deterministic optima
Optimal Design Laminate Failure probability Allowable
 [81, 62, tl, t2] thickness from MCS of ARS probability of
 (degree and inch) (inch) 1,000,000 samples failure

 [24.89, 25.16, 0.015, 0.015] 0.120 (0.120) 0.000055 0.0001

 [0.00, 28.16, 0.005, 0.020] 0.100 (0.103) 0.019338a
 Deterministic
 [27.04, 27.04, 0.010, 0.015] 0.100 (0.095) 0.000479
 optima
 [25.16, 27.31, 0.005, 0.020] 0.100 (0.094) 0.000592
a This deterministic optimum is out of the range of the analysis response surfaces; the
 probability of failure was calculated by Monte Carlo simulation based on another set of
 analysis response surfaces.

Refining the Reliability-Based Design

 The reliability-based designs in Table 5-6 show that the ply angles close to 250

offer designs with low failure probability. Furthermore, good designs require only a

single ply-angle allowing simplification of the configuration of the laminate from

[f 6,/ B O]s to [f B ]s. Table 5-7 shows the failure probabilities of some chosen designs

calculated with Monte Carlo simulation using ARS. The laminates with ply-angles of

240, 250, and 260 offer lower probabilities of failure than the rest. These three laminates

will be further studied.