An efficient coupled numerical method for reliability-based design optimization of steel frames

Abstract

The paper proposes an efficient coupled numerical method for reliability-based design optimization (RBDO) of steel frames. In this RBDO problem, the objective function is to minimize the weight of the whole steel frame. Design variables are cross sectional areas of beams and columns which are considered as discrete variables and chosen from the sets of wide-flange shape steel sections provided by the American Institute of Steel Construction (AISC). Random variables relate to the material properties and applied loads. Probabilistic constraints of ultimate load limits and serviceability limits are defined following the specifications for structural steel buildings by AISC. For analyzing the behavior of steel frames, the finite element method for frame structures is utilized. For searching the optimal solution of RBDO problems, an efficient coupled numerical method by combining the Single-Loop Deterministic Method (SLDM) and the Improved Differential Evolution (IDE) is proposed to give the method called SLDM-IDE. In the SLDM-IDE, all of the probabilistic constraints are converted to the approximate deterministic constraints. This helps transform the RBDO problem into an approximate deterministic optimization problem which can be solved by standard optimization algorithms. This helps reduce significantly the computational cost for solving the original RBDO problem. Three numerical examples are conducted, and obtained results are compared with those of previous publications to demonstrate the robustness and efficiency of the proposed approach.