Stress-Based Topology Optimization of Steel-Frame Structures Using Members with Standard Cross Sections: Gradient-Based Approach

This article presents a computationally efficient methodology for stress-based topology optimization of steel frame structures with cross-sectional properties that are mapped from I-beam sections of a design manual. To account for the natural variability of the data, this mapping is achieved via quantile regression to derive continuous relationships between cross-sectional area (the design variable) and other section properties. These relationships are used for deriving the gradient of structural performance, which allows using computationally efficient gradient-based optimization schemes. Three frame structures are designed using the proposed algorithm, the resulting designs are compared with traditional compliance-based topology optimization algorithms, and changes in the designs are discussed. A comparison of stress distribution within the designed structures verified the effectiveness of the proposed methodology.