Analysis Response Surface Approximation
Reliability analysis of systems with multiple failure modes often employs Monte
Carlo simulation, combined with approximation to the failure evaluations. PANDA2
provides the margins of those failure modes that are critical for the stiffened panel, and
these may change during the design optimization. Consequently, it is impossible to
follow each individual failure mode, and instead the most critical safety margins for each
of the two load cases are extracted from the PANDA2 analysis report. Analysis response
surface approximations are fitted to the worst safety margins in terms of random
variables. Probability of failures for the panel system and each load cases are calculated
by performing Monte Carlo simulation using the approximation.
The deterministic optimum obtained by PANDA2 global optimization in Lamberti
et al. (2003) is shown in Table 8-4 (Lamberti et al. 2003).
Table 8-4. Deterministic Optimum
b (in) h (in) t, (in) tz (in) Weight (lb)
10.71 2.049 0.0986 0.1261 2598
Two analysis response surfaces approximations (ARS) were fitted to the critical
margins of the two load cases in terms of seven variables, which included four design
random variables, and three material random variables. Statistical design of experiment is
Latin Hypercube sampling (LHS, e.g., Wyss and Jorgensen, 1998), where design random
variables were treated as uniformly distributed variables over the range shown in Table 8-
5. Ranges for normal random variables are automatically handled by Latin Hypercube
sampling. Using the ARS, probabilities of failure are calculated by Monte Carlo
simulations