薄壁方管轴向压溃的相似性研究

Study on the similarity of axial crushing of thin-walled square tubes

薄壁方管由于其几何特性导致相似性研究中,厚度无法与长度、宽度按照同一比例进行结构缩放,从而产生几何畸变,造成传统的相似律失效。为了解决这一问题,基于轴压冲击问题的响应方程、能量守恒方程,采用方程分析和量纲分析,推导了受轴压冲击作用下理想弹塑性薄壁方管几何畸变时动态响应的相似律。讨论了缩比模型与原型选取同种和不同种材料时的速度比例因子,并在理想弹塑性材料的基础上进一步修正了考虑应变率、应变硬化效应时的速度比例因子。建立有限元模型验证了畸变模型相似律的有效性。结果表明,缩比模型在采用提出的受轴压冲击薄壁方管的相似律进行缩放后,能够准确预测原型的载荷、能量等动态响应,相似性较好。

Due to their geometric characteristics,in the similarity study of thin-walled square tubes,the thickness cannot be scaled in the same scaling factor as the length and width,resulting in geometric distortion and failure of the traditional similarity law.In order to solve this problem,firstly,based on the response equation and energy conservation equation of the axial pressure impact problem,the similarity law of dynamic response of ideal elastic-plastic thin-walled square tubes with geometric distortion under axial compression impact load was derived using equation analysis and dimensional analysis.Then,velocity scaling factors of the scaled model and the prototype was discussed when selecting the same and different materials,and velocity scale factors considering strain rate and strain hardening effect were further modified on the basis of the ideal elastoplastic material.Finally,finite element models were established to verify the validity of the similarity law of the distortion model.The results show that scaled models can accurately predict the dynamic response of the prototype,such as load and energy,after scaling with the proposed similarity law of thin-walled square tubes impacted by axial compression,and the similarity is good.