Reliability-Based Design Optimization under Eigen-Frequency Constraints using a System Reliability Approach

Reliability-Based Design Optimization (RBDO) methodology is contemporary orientation in designing economical and safe structures. The RBDO allows us to reach effectively balanced cost-safety configurations, by controlling the structural uncertainties during the design process, which cannot be achieved by deterministic optimization. A practical formulation of the RBDO consists in minimizing the expected cost under reliability constraints. However, from numerical point of view, solving the RBDO problems is a heavy task because of the nested nonlinear procedures: mathematical programming algorithms, reliability analysis and numerical simulation of structural systems. For real engineering structures, the evaluation of reliability constraints is computationally expensive. In this paper, a new methodology of reliability-based design optimization of vibrating structures is proposed. An efficient RBDO procedure is developed in order to find the best compromise between satisfying the target system reliability and optimizing the structural cost. The proposed approach is based on the concept of the decoupled approach, where the RBDO problem is converted to several cycles of deterministic design optimization followed by the calibration of the optimal system safety factors. The originality of the present work lies in taking account for several eigen-frequencies rather than the single fundamental frequency, where the system safety factors are optimally calibrated on the basis of the overall system performance. The numerical application shows the interest and the good-standing of the proposed method.