Reliability index based strategy for the probability-damage approach in fail-safe design optimization (β-PDFSO)

This research proposes a new formulation for fail-safe size optimization, considering the probability of occurrence of each failure scenario and the random structural parameters as sources of uncertainty. Essentially, the fail-safe reliability-based design optimization is reformulated, where the term "damaged structure" coalesces information of the whole set of damaged configurations. Thus, a single random reliability index is defined, representing the reliability of a limit-state of the damaged structure, which accounts for the safety level of the entire set of damaged configurations. The method provides the optimum design for which the reliability indices of the damaged structure are achieved at the confidence level the designer demands. The first application example corresponds to an academic analytical problem. The second and third application examples correspond to practical engineering cases: a 2D truss structure with stress constraints as well as the tail section of an aircraft fuselage with stress and buckling constraints. Results show a considerable reduction of the objective function compared to the fail-safe RBDO, which could lead to oversized designs. In this sense, mass savings up to 13.6% are achieved for the industrial-like application example.