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