On structural design optimization under uncertainty and risk

Abstract

In this paper, the effects of uncertainty and risk on structural design optimization are investigated, by comparing results of Deterministic Design Optimization (DDO), Reliability-based Design Optimization (RBDO) and Reliability-based Risk Optimization (RBRO). DDO yields a structural topology (or shape) which is optimum in terms of mechanics, but does not explicitly address parameter uncertainties and their effects on structural safety. RBDO properly models safety-under-uncertainty, allowing the optimum structure to maintain an acceptable level of safety. Results, however, 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 costs associated to construction, operation and maintenance, as well as the monetary consequences of failure. RBRO yields the optimum topology and the optimum point of balance between economy and safety. 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 (including expected cost of failure). 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.