Probability-damage approach for fail-safe design optimization (PDFSO)

Abstract

Fail-safe design often leads to oversized structures as the design must be able to behave properly for the different accidental situations that could undergo throughout their lifespan. The existing research about structural optimization applied to fail-safe design does not contemplate the idea of having accidental situations with different probabilities of occurrence. This means that the structure must satisfy the design constraints in the damaged structure regardless of whether one accidental situation is much more likely than another. The objective of this research is to formulate a new optimization strategy to get fail-safe structures with minimum weight taking into account the available data about the probability of occurrence associated to each partial collapse. A multi-model probabilistic optimization problem is defined and applied to two structures: a 2D truss structure with stress constraints as well as the tail section of an aircraft fuselage with stress and buckling constraints.

Topology Optimization of Strength-Safe Continuum Structures Considering Random Damage

“…If the two models are equivalent, the dual problem can be solved instead of the primal problem. Therefore, the dual sequence quadratic programming is utilized to solve the model (17) in order to improve the solution's efficiency. The dual model looks like this:…”

“…Wang et al [16] introduced the minimization of von Mises stress of damaged structure into the optimization objective, and proposed two topological optimization objectives: the worst-case formulation and the mean-performance formulation, which effectively alleviated the stress concentration problem caused by local failure. Because of the different probabilities of different damages, Cid et al [17] developed a new optimization strategy to avoid unnecessary structural performance loss caused by low-probability damage. They analyzed different preset damage conditions of the structure, introduced the probability of each damage in the optimization model, and defined the multi-model probabilistic optimization problem.…”

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

“…Finally, Cid et al [10] formulated the probability-damage approach for fail-safe design optimization (PDFSO). That research incorporates a source of uncertainty that had not been taken into account in fail-safe optimization approaches until then.…”

“…In the civil engineering field, companies have reported accidental situations applied to cable-stayed bridges, in which the accidental situation where three adjacent cables break due to an impact of a vehicle is less probable than the breakage of a single cable. To address this aspect, a new methodology, denoted as probability-damage approach for fail-safe design optimization (PDFSO) was proposed by Cid et al [10], where the probability of occurrence of each damage scenario was contemplated as a new source of uncertainty into the deterministic fail-safe optimization problem. In that strategy, the main novelty was to define a new probabilistic formulation where the set of responses from the damaged configurations associated with the same limit-state are transformed into a single probabilistic constraint.…”