doi:10.3850/978-981-08-7619-7_P007

ABSTRACT

In this paper, the effects of uncertainty and risk on optimum structural design are investigated by comparing three distinct formulations of structural optimization problems. Deterministic Design Optimization (DDO) allows one to find the shape or configuration of a structure that is optimum in terms of mechanics, but 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, ensuring 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. Risk optimization (RBRO) 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. Results are compared for some example problems. The broader RBRO solution is found first, and optimum results are used as constraints in DDO and RBDO. Results show that even when the optimum safety coefficients are used as constraint in DDO, the formulation leads to optimum configurations which respect these design constraints, reduce manufacturing costs but increase total expected costs. If the (optimum) system failure probability is used as constraint in RBDO, the optimum solution reduces manufacturing costs, but by increasing total expected costs. This happens when the costs associated to different failure modes are distinct.

Keywords: Structural optimization, Optimum design, DDO, RBDO, Reliability analysis, Risk optimization, Uncertainty quantification.

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