基于最小二乘法的Lagrange方法在衰减冲击波中的研究

Study on Lagrange Analysis with Least Squares in Attenuating Waves

在已知粒子速度的情况下,采用现有Lagrange分析方法求解动力学方程仍有不足。针对这一情况,将反解法和自洽检验法相结合,提出了基于最小二乘法的Lagrange反解法。该方法的理论精度能够实现应力沿路径线的M(M为迹线数)阶导数恒为零,并且能够满足自洽检验法。通过对一组混凝土的实验数据进行处理,并将处理结果与实验结果以及传统Lagrange反解法进行对比,比较结果表明,该方法不仅使得迹线函数能够很好地反应各物理量沿迹线的变化性态,而且还能够适当减小偶然误差。

The existing reactive flow Lagrange analysis methods are still inadequate to solve the particle velocity history from a series of gauges embedded in material. Based on this point, a new Lagrange analysis method combined the inverse analysis with self-consistent examination was presented. The theoretical accuracy of this method can achieve that the M-order partial derivative of the stress equals zero,and the self-consistent examination is satisfied. Besides, this method is applied to process the experimental data of the light gas gun. Comparing results of this method, experimental data and the traditional inverse analysis results, it turns out that this method not only makes the particle-line function reflecting the behavior of various physical quantities along the particle-line, but also reduces the accidental error of the particle-line.