Energy absorption homogenization-based crashworthiness design framework of VRB-VS tubular structure under transverse impact with engineering application

To fully realize the potential of tubular structures in lightweight design, a variable-thickness rolled blanks (VRB) and variable strength (VS) hot-stamping forming process is proposed to produce the VRB-VS tubes with circular cross-section, which demonstrate significant promise for a broad spectrum of engineering applications, such as automotive seat frames and mobile elevating work platforms, among others. The complicated interacting mechanisms between multiple design variables and crashworthiness indices introduce great challenges during substantial optimization design of VRB-VS tubular structures to balance design efficiency and crashworthiness performance under transverse impact. The inherent conflict arises from a dual-aspect paradox in crashworthiness design: the ambiguous relationships between design variables and crashworthiness responses, and the sensitivity gradient divergence observed across different design schemes, collectively necessitating prolonged design iterations that substantially escalate the development cycle duration and associated costs of automotive components. To overcome these challenges, a dual-field quantification framework, comprising the normalized internal energy density (IED) and its spatial gradient variance (δIED), is proposed to investigate the mechanisms underlying the spatial homogeneity of energy absorption. The framework establishes a functional mapping between design variables and crashworthiness indices via a surrogate model constructed using the response surface method, which facilitates sensitivity analysis and supports subsequent structural parametric investigations. Sensitivity analysis results indicate that the thickness of VRB thick zone (t0) and the strength of high-strength zone (σs0) have the greatest impact on crashworthiness indices, whereas the midpoint of thickness transition zone (pt) and the midpoint of strength transition zone (ps) show relatively minor effects. Finally, a design criterion for homogenizing the IED distribution is proposed to guide the structural design of tubular components, and has been successfully applied to a VRB-VS rear seat, achieving both excellent crashworthiness and significant mass reduction. Hot-stamping forming for circular tube with continuous changes in thickness and strengthDesign criteria aimed at homogenizing structural internal energy density distributionUnified framework for crashworthiness design of anti-intrusion tubular component in carMore uniform internal energy density distribution indicates better crashworthiness index Hot-stamping forming for circular tube with continuous changes in thickness and strength Design criteria aimed at homogenizing structural internal energy density distribution Unified framework for crashworthiness design of anti-intrusion tubular component in car More uniform internal energy density distribution indicates better crashworthiness index