  Optimal design under uncertainty has gained much attention in the past ten
years due to the ever increasing need for manufacturers to build robust systems
at the lowest cost. Reliability-based design optimization (RBDO) allows the
analyst to minimize some cost function while ensuring some minimal performances
cast as admissible failure probabilities for a set of performance functions. In
order to address real-world engineering problems in which the performance is
assessed through computational models (e.g., finite element models in
structural mechanics) metamodeling techniques have been developed in the past
decade. This paper introduces adaptive Kriging surrogate models to solve the
RBDO problem. The latter is cast in an augmented space that "sums up" the range
of the design space and the aleatory uncertainty in the design parameters and
the environmental conditions. The surrogate model is used (i) for evaluating
robust estimates of the failure probabilities (and for enhancing the
computational experimental design by adaptive sampling) in order to achieve the
requested accuracy and (ii) for applying a gradient-based optimization
algorithm to get optimal values of the design parameters. The approach is
applied to the optimal design of ring-stiffened cylindrical shells used in
submarine engineering under uncertain geometric imperfections. For this
application the performance of the structure is related to buckling which is
addressed here by means of a finite element solution based on the asymptotic
numerical method.
