Parametric Cross-Section Design and Crashworthiness Optimization of High-Strength Steel Double-Cell Roll-Formed Tubes Under Lateral Bending

Lightweight design and crashworthiness of protective structures are critical for battery safety in electric vehicles (EVs). This study addresses the limited research on cross-sectional shape design of high-strength steel double-cell roll-formed tubes (DCRFTs), widely used in EV bumper beams, battery boxes, and electric bus frames. A parametric design method is proposed based on three parameters: middle flange offset (o), upper deflection angle (α), and lower deflection angle (β). Under the constraints of constant cross-sectional height and enclosed area, this method systematically generates diverse shapes, including square, trapezoid, hexagon, re-entrant hexagon, and various hybrid shapes. Validated finite element models were employed to analyze the deformation modes and crashworthiness of DP980 steel DCRFTs under idealized lateral three-point bending with simple supports. The results indicated that the re-entrant hexagon section reduced maximum deformation (Disp) by 2.95%, peak crushing force (PCF) by 9.53%, and improved crushing force efficiency (CFE) by 13.88% compared to the baseline square section. The parametric study and sensitivity analysis confirmed that the offset (o) was the most critical parameter, contributing over 80% of the variance in Disp, PCF, and CFE. Multi-objective optimization using an RBF surrogate model and the NSGA-II algorithm yielded Pareto optimal solutions. Compared to the baseline, three representative solutions achieved Disp reductions of 11.83–25.10% and CFE improvements of 15.63–22.26%, each with distinct trade-offs among objectives. This work establishes a methodological framework for parametric cross-section design of roll-formed profiles; its extension to realistic boundary conditions will further facilitate practical EV protective structure design.