In this study, the parameters of concave expanded flanges of beam-column connections of steel frames are optimized based on the effects of different sizes of concave expanded flanges on the fracture performance. Firstly, two beam-column connection models with concave expanded flanges are built and analyzed under cyclic loads, which have the same conditions as the specimens during the previous test. Secondly, the validity of the numerical simulation models is verified through analyzing the hysteretic behaviors of the connections with concave expanded flanges, such as the plastic hinge position, the hysteresis curves, the skeleton curves, the stiffness degradation, the ductility coefficient, and the energy dissipation capacity. Thirdly, in order to comprehensively evaluate the fracture status of metal materials, the relevant fracture evaluation index (the stress triaxiality ratio (Rσ), plastic equivalent strain index (PI), and cracking index (RI)) are introduced. Afterwards, eighteen numerical simulation models with differences in the length la of the reinforced section, the length lb of the transition section, and the width c of the reinforced section were analyzed. Finally, the parameters of the concave expanded flanges of the beam-column connections are optimized based on the results of the three fracture evaluation index.