一种与时间步长相关的奇异单元细分法-《郑州大学学报(工学版)》

文章信息/Info

Author(s):: Lee Yuan 1; Zhang Jianming 2; Zhong Yudong 2; Qian Hongtao 3; 1. School of Computer and Information Engineering, Henan Normal University; 2. School of Mechanical and Vehicle Engineering, Hunan University; 3. Department of Mechanical Engineering, Henan Institute of Technology

Keywords:: time domain boundary element method; elastic dynamics; singular integral; unit subdivision; volatility front

摘要:: 奇异积分是边界元法求解物理问题时的难点之一，其精度对计算结果的准确性有很大影响，单元细分是解决奇异积分的关键。针对动态分析问题，提出了一种与时间步长相关的单元细分法。与传统单元细分法相比，该方法不仅考虑了源点在单元中的位置，同时考虑了波动前沿的位置，能够反映出被积核函数的分段特性，从而能够更加准确地模拟纵波和横波对单元积分的影响。两个算例验证了该方法的准确性及其对计算精度的影响，研究结果表明：对于存在奇异性的第一个分析步，该方法比传统方法的结果误差减小了15.5%。

Abstract:: The singular integral was one of the difficult problems for the Boundary Element Method to solve the physical problems. Its precision had great influence on the accuracy of the calculation result. Element subdivision was the key to solve the singular integral. Aiming at the problem of dynamic analysis. An element subdivision method related to time-step length was proposed. Compared with the traditional method, this method not only considerd the position of the source point in the cell, but also the position of the wave front, which could reflect the segmentation characteristic of the kernel function. Therefore it could more accurately simulate the impact of longitudinal wave and shear wave on the integral of the element. In this paper, the accuracy of the method and its effect on the calculation accuracy were verified by two examples. The results showed that the error was 15.5% less than that of the traditional method for the first analysis step with singularity.