1 Approximate Probabilistic Optimization Using Exact-Capacity-Approximate-Response-Distribution

There are two major barriers in front of probabilistic structural design. First, uncertainties associated with errors in structural and aerodynamic modeling and quality of construction are not well characterized as statistical distributions and insufficient information may lead to large errors in probability calculations. Second, probabilistic design is computationally expensive because repeated stress calculations (typically finite element analysis) are required for updating probability calculation as the structure is being re-designed. Targeting these two barriers, we propose a probabilistic design optimization method, where the probability of failure calculation is confined to failure stresses, to take advantage of the fact that statistical characterization of failure stresses is required by Federal Aviation Administration (FAA) regulations. The stress distribution is condensed into a representative single value thereby eliminating the need for expensive stress distribution calculation, so a probabilistic optimization problem is transformed into a semi-deterministic optimization problem. Since the procedure starts from the deterministic optimum, a small number of iterations is expected, and a reliability analysis is required only once in each iteration. The proposed method provides approximate sensitivity of failure probability with respect to design variables, which is essential in risk allocation. The method is demonstrated with (i) a beam problem with two failur