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Extended Peridynamics and Parameter Optimization Study Based on Moving Least Squares Method
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2021-03-01 , DOI: 10.1155/2021/2595170
Jingwei Xu 1, 2 , Wei Hou 3 , Shoucheng Luan 2 , Shuting Mao 3 , Guowei Liu 2 , Pengfei Ma 1
Affiliation  

Based on the theory of peridynamics, the least squares and the moving least squares method are proposed to fit the physical information at nondiscrete points. It makes up for the shortcomings of the peridynamic method that only solves the discrete nodes and cannot obtain the physical information of other blank areas. The extended method is used to fit the one-way vibration problem of the rod, and the curve of the displacement of a nondiscrete node in the rod is extracted with time. The fitted displacement results are compared with the theoretical results to verify the feasibility of the fitting method. At the same time, the parameters in the fitting of the moving least squares method are optimized, and the effects of different tight weight functions and influence ranges on the results are analyzed. The results show that when the weight function is a power exponential function, the fitting effect increases with the decrease in the coefficient. When the weight function is a cubic spline weight function, a better fitting effect is obtained. And in the case of ensuring the fitting result, the affected area should be reduced as much as possible, and the calculation efficiency and precision can be improved.

中文翻译:

基于移动最小二乘法的扩展周动力学和参数优化研究

基于周动力学理论,提出了最小二乘法和移动最小二乘法来拟合非离散点的物理信息。它弥补了仅解决离散节点而无法获得其他空白区域物理信息的周边动力学方法的缺点。使用扩展方法来拟合杆的单向振动问题,并随时间提取杆中非离散节点的位移曲线。将拟合的位移结果与理论结果进行比较,以验证拟合方法的可行性。同时,优化了移动最小二乘法拟合中的参数,并分析了不同紧权函数和影响范围对结果的影响。结果表明,当权重函数为幂指数函数时,拟合效果随着系数的减小而增大。当权重函数为三次样条权重函数时,可获得更好的拟合效果。并且在确保拟合结果的情况下,应尽可能减小患处,并可以提高计算效率和精度。
更新日期:2021-03-01
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