Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels

摘要

Optimal design under uncertainty has gained much attention in the past tenyears due to the ever increasing need for manufacturers to build robust systemsat the lowest cost. Reliability-based design optimization (RBDO) allows theanalyst to minimize some cost function while ensuring some minimal performancescast as admissible failure probabilities for a set of performance functions. Inorder to address real-world engineering problems in which the performance isassessed through computational models (e.g., finite element models instructural mechanics) metamodeling techniques have been developed in the pastdecade. This paper introduces adaptive Kriging surrogate models to solve theRBDO problem. The latter is cast in an augmented space that "sums up" the rangeof the design space and the aleatory uncertainty in the design parameters andthe environmental conditions. The surrogate model is used (i) for evaluatingrobust estimates of the failure probabilities (and for enhancing thecomputational experimental design by adaptive sampling) in order to achieve therequested accuracy and (ii) for applying a gradient-based optimizationalgorithm to get optimal values of the design parameters. The approach isapplied to the optimal design of ring-stiffened cylindrical shells used insubmarine engineering under uncertain geometric imperfections. For thisapplication the performance of the structure is related to buckling which isaddressed here by means of a finite element solution based on the asymptoticnumerical method.