Effects of epistemic uncertainties on truss topology optimization considering progressive collapse

Resumo

The history of engineering contains many examples of structural failures. Despite being related to
diverse causes, these collapses can be attributed to the existence of uncertainties, which are usually classified as
aleatory and epistemic. In this context, optimization techniques can be employed in order to obtain optimal
structural solutions that are robust to the effects of uncertainty. Additionally, the progressive collapse phenomenon
has raised engineers' and researchers' awareness in recent years. However, there are still very few papers addressing
the optimal structural design under uncertainty considering progressive collapse. Hence, this paper aims to
investigate the effect of aleatory and epistemic uncertainties on truss topology optimization considering

progressive collapse. Uncertainties are considered in the optimization problems through the RBDO (Reliability-
Based Design Optimization) and RO (Risk Optimization) formulations. Non-structural factors, which are

epistemic in nature and can lead to progressive collapse, are considered using a formulation based on the latent
failure probability concept. Through a simple six-bar truss problem, the huge impact of epistemic uncertainties on
optimal topologies is shown. The variation of the latent failure probability indicates the existence of two transition
points in the optimal solutions, named Hyperstatic and Redundancy Thresholds. We conclude that these bounds
are mainly controlled by the magnitude of epistemic uncertainties, having a strong effect on the reliability and
costs of the optimal solutions. These results reveal something that has already been recognized in practice:
engineering structures need to be redundant in order to cope with the effect of epistemic uncertainties. Therefore,
despite being an idealized concept, the latent failure probability proves to be a simple tool to impose minimal
redundancy in optimal structural solutions.