一种与时间步长相关的奇异单元细分法  

An Singular Element Subdivision Method Related to Time-Step Length

作　　者：李源[1,2] 张见明 钟玉东[2] 千红涛 LI Yuan;ZHANG Jianming;ZHONG Yudong;QIAN Hongtao(College of Computer and Information Engineering,Henan Normal University,Xinxiang 453007,China;College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410082,China;Department of Mechanical Engineering,Henan Institute of Technology,Xinxiang 453003,China)

机构地区：[1]河南师范大学计算机与信息工程学院,河南新乡453007 [2]湖南大学机械与运载工程学院,湖南长沙410082 [3]河南工学院机械工程系,河南新乡453003

出　　处：《郑州大学学报（工学版）》2019年第1期7-11,共5页Journal of Zhengzhou University（Engineering Science）

基　　金：国家自然科学基金资助项目(11702087;U1704158);河南省高等学校重点科研项目(16A520015;17A520040;17A520038);河南省自然科学基金资助项目(162300410177;182300410130);河南省科技创新人才项目(184100510003);河南省科技攻关项目(182102210362);河南省高校青年骨干教师培养计划项目(2017GGJS041);河南师范大学博士启动课题(qd15131)

摘　　要：奇异积分是边界元法求解物理问题的难点之一,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%.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 considered 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.

关 键 词：时域边界元法 弹性动力学 奇异积分 单元细分 波动前沿 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]