负高斯曲率曲面薄壁管吸能特性研究

为设计出具备优良吸能特性的薄壁结构，提出一种新型负高斯曲率曲面圆形横截面薄壁管(negative Gaussian curvature surface circular tube, NGC-C)。利用经验证的有限元分析方法对其进行轴向动态冲击模拟，提取各项性能指标，借助复杂比例评估法(complex proportion assessment, COPRAS)将其与传统薄壁吸能结构进行了综合性能对比。采用拉丁超立方抽样法从设计空间中提取样本点并获取各样本点对应性能响应值，建立代理模型。基于该代理模型，借助改进非支配排序遗传算法(non-dominated sorting genetic algorithm, NSGA-Ⅱ)对其进行了多目标优化设计。结果表明：NGC-C综合性能优于传统薄壁吸能结构，经优化后比吸能提高了16.47%，有效压溃长度降低了12.40%，质量减少了20.18%。将负高斯曲率曲面形态引入薄壁管构型，能够提高薄壁管的耐撞性和轴向抗变形能力。

Study on energy absorption characteristics of thin-walled tubes with negative Gaussian curvature

In order to design a lightweight thin-walled structure with high specific energy absorption and high stiffness, a new type of circular cross-section thin-walled tube with negative Gaussian curvature (negative Gaussian curvature surface circular tube, NGC-C) is proposed and studied in this paper. The finite element analysis method verified by previous experimental data is used to simulate the axial dynamic impact, and various performance indexes such as specific energy absorption and effective crushing length are extracted. The comprehensive performance of the thin wall energy absorption structure with zero Gaussian curvature and positive Gaussian curvature is compared with the complex proportional assessment method (complex proportion assessment, COPRAS). The Latin hypercube sampling method is used to extract 20 sample points from the design space and obtain the corresponding performance response values of each sample point, and the polynomial fitting method is used to establish the proxy model. Based on the agent model, the multi-objective optimization design is carried out by using the improved non dominated sorting genetic algorithm (non-dominated sorting genetic algorithm, NSGA-Ⅱ). The results show that the comprehensive performance of the thin-walled circular tube with negative Gaussian curvature is better than that of all kinds of non-negative Gaussian curvature thin-walled energy absorbing structures, especially in that it has the minimum effective crushing length. The goodness of fit of the established proxy models is higher than 98%, which can better reflect the relationship between structural design variables and performance response. After optimization, the specific energy absorption of thin-walled circular tubes with negative Gaussian curvature is increased by 16.47 %, the effective crushing length is reduced by 12.4 %, and the mass is reduced by 20.18 %. To sum up: introducing the negative Gaussian curvature surface shape into the thin-walled tube configuration can reduce the structural quality and improve the crashworthiness of the thin-walled tube, provide a new idea for the design of the thin-walled energy absorbing structure, and can be applied to the energy absorbing scenarios such as the automobile energy absorbing box.