Truss topology optimization considering uncertainties in the applied loads and progressive collapse

Resumo

The progressive collapse is a phenomenon that has received increasing attention from engineers and
researchers in recent years. The study of optimal structural design considering load redistribution due to the
progressive failure of elements is recent. In this context, this paper deals with the topology optimization of truss
structures, considering uncertainties in the applied loads and the progressive collapse of elements. The optimal
topologies are determined following the ground structure approach. Uncertainties are included in the optimization
problem through the RBDO (Reliability Based Design Optimization) and RO (Risk Optimization) formulations.
Progressive collapse is incorporated into the analyses by considering load redistribution after member failure. The
PSO algorithm is applied to solve optimization problems. System reliability is evaluated using the Monte Carlo
Simulation method with stratified sampling. In RO problems, the costs of hyperstatic and isostatic failures are
differentiated and solutions are obtained for different costs. The results suggest that the RBDO formulation leads
to isostatic optimal topologies, since there is no incentive for the permanence of hyperstatic elements in the final
solution. On the other hand, in the RO formulation, hyperstatic structures are among the optimal solutions,
indicating that this formulation is the most appropriate for dealing with problems including progressive collapse.