Even with the low computational cost of PANDA2 analyses, they cannot be used

directly in the MCS that requires a large number of analyses (thousands to millions).

Instead, response surface approximations are employed. For the reliability-based design

optimization, analysis response surface approximation (ARS) is fitted to the most critical

margin in the isogrid panel in terms of both geometric design variables and the material

properties, both of which are modeled by random variables. Using the ARS, the

probability of failure at every design point can be calculated inexpensively by MCS

based on the fitted polynomials. A design response surface approximation (DRS) is then

fit to the probability of failure in order to filter out noise generated by MCS. The details

of reliability analyses and design optimization using Monte Carlo simulation combined

with response surface approximation (Qu et al., 2000) were introduced chapter three. Due

to the high nonlinearity of probability of failure and safety index in the design space, a

probabilistic sufficiency factor approach (Qu and Haftka, 2003) is used instead of the

probability of failure in the design optimization, as shown in detail in chapter six.

Example problems of the reliability-based design of isogrid stiffened panels are

presented.

 Aluminum Isogrid Panel Design Example

 An isogrid panel design problem is taken from Lamberti et al. (2003) to

demonstrate the reliability-based design methodology.

Reliability-Based Design Problem Formulation

 Isogrid stiffened panel are cylindrical shells that have rectangular blade stiffeners

positioned along the circumferential and +60o directions to the circumferential directions

as shown in Figure 1. The tank barrel to be optimized is stiffened externally with J-

shaped ring stiffeners, and internally with a blade-shaped isogrid oriented