A fast decoupled reliability-based design optimization of structures using B-spline interpolation curves

Abstract

This paper introduces a new method for reliability-based design optimization (RBDO) of structures. In RBDO of structural problems unlike the conventional two-level approaches, sometimes it is not necessary to carry out reliability analysis for each deterministic design. The proposed method may be categorized as a decoupled method for reliable optimum design; however, it is based on the safety factor (SF) concept. To briefly describe the proposed method, a deterministic design optimization (DDO) point is obtained based on an arbitrary SF. The corresponding failure probability (P f) is then determined using Monte Carlo simulation (MCS). The P f is then compared with the targeted P f. If the relative distance error is greater than a desirable tolerance, the cubic B-spline interpolation concept is then employed as a result of which a modified SF is extracted. For the modified SF found, DDO procedure is carried out. The above procedure is iteratively repeated until convergence occurs and the reliable optimum point is found. Finally, the proposed method was applied to solving some structural problems. The obtained results were favourably in accordance with those recorded in the literature while only a fraction of P f computations was necessary.