iterations of DIRECT for a two dimensional space might look like Figure 8-3 (b); given
infinite iterations, DIRECT will evaluate every point in the design space. A more detailed
explanation of this procedure is given in Jones et al. (1993) and Finkel (2003).
Reliability-Based Design Optimization Using Direct Optimization with Safety
Factor Corrected by Probabilistic Sufficiency Factor
DIRECT optimizer is employed to avoid the problem that PANDA2 Superopt may
not drive the actual safety margin to zero. DIRECT optimization starts from the last
design in Table 8-20. The optimum is shown in Table 8-21. It is seen that design indeed
satisfies the reliability constraint.
Table 8-21. Design history of RBDO based on DIRECT deterministic optimization with
probabilistic sufficiency factor correct safety factor by actual safety margin
using Equation (8-4)
Safety Minimize obj ective function W while pof <0. 0001
factor for Obj ective Pof/PSF from Critical strength
strength [b, h, t,, 81, tz, 82] function: MCS of 106 failure mode
failure mode weight (lb) samples (load case 1)
S3=
[5.895, 0.9167,
1.514/1.179 'Skin transverse-
0.0005, 89.81, 1952.4 0.000100/0.999641
381=1.2837 'tensile
0.0400, 1.67]
25
* pof = probability of failure, PSF = probabilistic sufficiency factor
Summary
Reliability-based design optimization of aluminum and composite isogrid stiffened
panels is investigated. The uncertainties in the panels including both material properties
and manufacturing process variation are modeled by random variables. The reliability-
based design optimization is carried out using Monte Carlo simulation and response
surface approximation. Due to the high nonlinearity of probability of failure, probabilistic
sufficiency factor approach is employed to construct design response surface
approximation.