On the effects of uncertainty on optimum structural design / Estudo do efeito de incertezas na otimização estrutural
AUTOR(ES)
Wellison José de Santana Gomes
DATA DE PUBLICAÇÃO
2010
RESUMO
In this study the effects of uncertainty on optimum structural design are investigated, by comparing three distinct formulations of a structural optimization problem. Such effects can be quantified in terms of failure probabilities and risk, or expected costs of failure. Deterministic Design Optimization (DDO) allows one the find the shape or configuration of a structure that is optimum in terms of mechanics, but the formulation do not consider explicitly parameter uncertainty and its effects on structural safety. As a consequence, safety of the optimum structure can be compromised, in comparison to safety of the original structure. Reliability-based Design Optimization (RBDO) has emerged as an alternative to properly model the safety-under-uncertainty part of the problem. With RBDO, one can ensure that a minimum (and measurable) level of safety is achieved by the optimum structure. However, results are dependent on the failure probability used as constraint in the analysis. Risk optimization increases the scope of the problem, by addressing the compromising goals of economy and safety, and allowing one to find a proper point of balance between these goals. This is accomplished by quantifying the costs associated to construction, operation and maintenance of the structure, as well as the monetary consequences of failure. Experience shows that structural optimization problems can have multiple local minima. With the objective of finding the global minimum in all studied problems, two heuristic optimization methods are used in this study: genetic algorithms and particle swarm optimization. Aiming at efficiency, two methods with mathematical foundations are also considered: the methods of Powel and Polak-Ribiere. Finally, looking for a compromise between reliability (capacity to find the global minimum) and efficiency, four hybrid algorithms are constructed, combining the four methods just cited. The study investigates the effects of uncertainty on optimum structural design by comparing solutions obtained via the different formulations of the optimization problem. The paper presents some case studies, highlighting the differences in the optimum designs obtained with each formulation. The study leads to a better understanding of the limitations of each formulation in the solution of structural optimization problems. The investigation shows that, in general, the optimum structure can only be found by the most comprehensive formulation: risk optimization or RBRO. The study shows that DDO only leads to the optimum structure if an optimum safety coefficient is used as constraint for each individual failure mode. In a similar way, the investigation shows that when the costs associated to distinct failure modes are different, the RBDO formulation only leads to the optimum structural design if an optimum failure probability is specified as constraint for each failure mode of the structure.
ASSUNTO(S)
estruturas-confiabilidade structures-optimization hybrid algorithms structures-reliability estruturas-otimização algoritmos híbridos
