Abstract In a real-world loading case (e.g., car crash accidents), energy-absorbing components are subject to oblique loads at various uncertain angles. This paper aims to investigate the behavior of such components under three-dimensional (3D) oblique loads in deterministic and probabilistic loading conditions. In this way, some square tubes are tested experimentally, and results are utilized to validate numerical models. To apply the 3D oblique load, a special test setup is designed, constructed, and installed on a universal tensile testing machine. Hammersley method is employed to design sample points. ABAQUS software is used for the finite element modeling and analysis. GEvoM software is implemented for mapping design variables onto crashworthiness characteristics including energy absorption (EA) and peak crush force (PCF). Both deterministic and reliability-based robust design (RBRD) optimizations are performed, and their results are compared with each other. The primary outcome of this research is the effect of incidence angles on the energy-absorbing characteristics, as well as some remarkable trade-off design points obtained from various multiple-criteria decision-making (MCDM) methods. It was discovered that the obtained design points of probabilistic study, which satisfied the reliability constraint, were roughly 60% more robust than deterministic points.

中文翻译：

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概率3D斜向载荷下薄壁管耐撞性多目标优化

摘要 在实际载荷情况下（例如，车祸事故），吸能部件会受到各种不确定角度的倾斜载荷。本文旨在研究此类组件在确定性和概率加载条件下的三维 (3D) 倾斜载荷下的行为。通过这种方式，对一些方管进行了实验测试，并利用结果来验证数值模型。为了施加 3D 倾斜载荷，需要在万能拉伸试验机上设计、构建和安装特殊的测试装置。Hammersley 方法用于设计样本点。ABAQUS软件用于有限元建模和分析。GEvoM 软件用于将设计变量映射到耐撞特性，包括能量吸收 (EA) 和峰值挤压力 (PCF)。执行确定性和基于可靠性的稳健设计 (RBRD) 优化，并将它们的结果相互比较。这项研究的主要成果是入射角对能量吸收特性的影响，以及从各种多标准决策 (MCDM) 方法中获得的一些显着的权衡设计点。结果发现，概率研究获得的满足可靠性约束的设计点比确定性点的稳健性大约高 60%。以及从各种多标准决策（MCDM）方法中获得的一些显着的权衡设计点。结果发现，概率研究获得的满足可靠性约束的设计点比确定性点的鲁棒性大约高 60%。以及从各种多标准决策（MCDM）方法中获得的一些显着的权衡设计点。结果发现，概率研究获得的满足可靠性约束的设计点比确定性点的鲁棒性大约高 60%。