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Probabilistic Engineering Mechanics, Volume 28, April 2012, Pages 18-29
Andre Teofilo Beck, Wellison Jose de Santana Gomes
Department of Structural Engineering, Sao Carlos School of Engineering, University of Sao Paulo 13566-590 Sao Carlos, SP, Brazil
Abstract
In this paper, the effects of uncertainty and expected costs of failure on optimum structural design are investigated, by comparing three distinct formulations of structural optimization problems. 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 grossly neglects parameter uncertainty and its effects on structural safety. 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 probabilities used as constraints in the analysis. Risk optimization (RO) increases the scope of the problem by addressing the compromising goals of economy and safety. This is accomplished by quantifying the monetary consequences of failure, as well as the costs associated with construction, operation and maintenance. RO yields the optimum topology and the optimum point of balance between economy and safety. Results are compared for some example problems. The broader RO solution is found first, and optimum results are used as constraints in DDO and RBDO. Results show that even when optimum safety coefficients are used as constraints in DDO, the formulation leads to configurations which respect these design constraints, reduce manufacturing costs but increase total expected costs (including expected costs of failure). When (optimum) system failure probability is used as a constraint in RBDO, this solution also reduces manufacturing costs but by increasing total expected costs. This happens when the costs associated with different failure modes are distinct. Hence, a general equivalence between the formulations cannot be established. Optimum structural design considering expected costs of failure cannot be controlled solely by safety factors nor by failure probability constraints, but will depend on actual structural configuration.
Additional Information
Defying failure is the primary challenge of the structural engineer. It sounds paradoxical, but in order to achieve successful design, the structural engineer must think about and account for all possible failure modes of a structure. This is no different in structural optimization. However, a review of the literature shows that many structural optimization authors pretend to be minimizing costs while neglecting the expected costs of failure. This article describes what one misses in solving structural optimization problems when expected consequences of failure (risks) are not taken into account.
