Design Strategy with a Class of Structural Reliability Models of High Dimension
The reliability-based optimization of structural systems with reliability models of high dimension is considered. The design process is written as a two-level nonlinear constrained optimization problem. The top-level includes the overall optimization in the design variables, whereas the sublevel problem corresponds to the failure probability estimates. Attention is directed toward problems in which the structural system is modeled as a series system of a large number of secondary failure elements. The problem of calculating the system failure probability is transformed to calculating the failure probability of the secondary failure events. It is assumed that the secondary failure events are relatively simple to describe and characterized by their design points. The probability content of the individual secondary failure events is approximated by a first-order estimate. The interaction of the secondary failure events is considered by an efficient importance sampling technique that is integrated into the optimization process. Several issues regarding the numerical implementation of the methodology are addressed. The feasibility of the proposed method is demonstrated by the optimization of a steel column loaded by a set of axial loads with stability and material failure modes.