受轴向冲击薄壁圆管的几何畸变相似律研究

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.