A non‐probabilistic reliability‐based design optimization method for structures based on interval models

Abstract

AbstractA non‐probabilistic reliability optimization method for structures with uncertain‐but‐bounded variables was presented. Based on the interval model description for the uncertain‐but‐bounded parameters, the non‐probabilistic reliability index was used to measure the structural reliability. The optimal design was formulated as a nested two‐loop optimization problem. For a nonlinear function, a number of constraints that satisfied the non‐probabilistic reliability index were treated as the serial system, and the feasible region of the uncertain parameters was determined by the target non‐probabilistic reliability index. The inner optimization method for solving a number of non‐probabilistic reliability indices was transformed into the problem of minimizing the functions within the feasible range. For a linear function, the non‐probabilistic reliability optimization problem can be transformed into a deterministic optimization problem. The high computational cost of determining the non‐probabilistic reliability was greatly reduced. Three numerical examples were presented to illustrate the efficiency of the proposed method.