Integrated Reliability-Based Optimal Design of Structures

In conventional optimal design of structural systems the weight or the initial cost of the structure is usually used as objective function. Further, the constraints require that the stresses and/or strains at some critical points have to be less than some given values. Finally, all variables and parameters are assumed to be deterministic quantities. In this paper a probabilistic formulation is used. Some of the quantities specifying the load and the strength of the structure are modelled as random variables, and the constraints specify that the reliability of the structure has to exceed some given value. The reliability can be measured from an element and/or a systems point of view. A number of methods to solve reliability-based optimization problems has been suggested, see e.g. Frangopol [I]. Murotsu et al. (2], Thoft-Christensen & Sørensen (3] and Sørensen (4).
For structures where the reliability decreases with time it is often necessary to design an inspection and repair programme. For example the reliability of offshore steel structures decreases with time due to corrosion and development of fatigue cracks. Until now most inspection and repair strategies are based on experience rather than on rational investigations, see e.g. Jubb [5] and Dunn [6]. As a result it can be expected that inspection and repair of the structure on the above-mentioned bases are not only uneconomic, but perhaps also unsatisfactory from a safety point of view.
In chapter 2 of this paper reliability-based optimal design is discussed. Next, an optimal inspection and repair strategy for existing structural systems is presented. An optimization problem is formulated , where the objective is to minimize the expected total future cost of inspection and repair subject to the constraint that the reliability at any time is acceptable (see Thoft-Christensen & Sørensen (7]). The reliability is estimated using first-order reliability methods, Thoft-Christensen & Murotsu (8] and Madsen et al. (9]. Finally, integration of the optimal inspection/repair strategy and the reliability-based optimal design problem is considered. A practically usable procedure to solve the described integrated optimization problem is presented and demonstrated on an offshore structure.