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