受轴向冲击薄壁圆管的几何畸变相似律研究

对于受轴向冲击载荷作用的薄壁圆管动态响应的相似律问题，由于圆管的薄壁特性导致厚度无法与高度和半径按相同的比例进行结构缩放，从而产生模型的几何畸变，此时传统的相似律已无法描述原型与畸变模型之间的动态响应规律。基于薄壁圆管轴向冲击问题的控制方程，通过能量守恒和量纲分析，推导了考虑几何畸变条件下轴向冲击载荷作用的理想弹塑性薄壁圆管动态响应的相似律。通过在给定应变与应变率区间上建立比例模型预测的流动屈服应力与原型流动屈服应力的最佳逼近关系，将几何畸变相似律进一步推广至包含应变率和应变硬化的材料。通过数值方法验证了提出的几何畸变模型相似律的适用性。分析结果表明，提出的考虑厚度畸变的受轴向冲击薄壁圆管的相似律可用于预测原型结构的冲击动态响应，并显著降低比例模型与原型结构平均载荷和能量的偏差。

Study on the scaling law of geometrically-distorted thin-walled cylindrical shells subjected to axial impact

In scaling the dynamic responses of thin-walled cylindrical shells subjected to axial impact loading, the thickness cannot be adjusted according to the same scale as the radius and height due to the thin wall characteristics. Hence, geometrically-distorted models would be used, and the traditional scaling law cannot describe the relationship between the dynamic responses of the prototype and the geometrically-distorted model. In this paper, the scaling law for this case was derived for elastic-ideal plastic thin-walled cylindrical shells under axial impact loading. For strain hardening and strain-rate hardening material, based on the average load, deformation energy, and displacement of the shell in the axisymmetric deformation mode, the dimensionless numbers of three key design parameters, namely the stress, mass, and displacement, were obtained through the law of energy conservation. Then, the optimal approximation of the flow stress predicted by the distorted scaled model to the flow stress of the prototype was established on a given strain and strain rate interval. In this way, the derived scaling law can be applied to the case considering the coupling effects of geometric distortion, strain-rate sensitivity, and strain hardening. Finally, several finite element models of thin-walled cylindrical shell models subject to axial mass impact were established. These models use the elastic-ideal plastic material model and the general material model with strain-rate hardening and strain hardening effects. The modified impact velocity and impact mass were obtained by the present method using the geometrically-distorted model, which verified the effectiveness and correctness of the proposed scaling law. The results show that the geometrically distorted model corrected by the method proposed in this article can quite accurately predict the dynamic responses of the prototype, and significantly reduce the errors in the dynamic responses of the thin-walled cylindrical shell subjected to axial impact loading, especially the average load and deformation energy.