| 二维正交各向异性位势问题的高阶单元快速多极边界元法 |
| |
| 引用本文： | 李聪,胡斌,胡宗军,牛忠荣. 二维正交各向异性位势问题的高阶单元快速多极边界元法[J]. 力学学报, 2021, 53(4): 1038-1048. DOI: 10.6052/0459-1879-20-455 |
| |
| 作者姓名： | 李聪 胡斌 胡宗军 牛忠荣 |
| |
| 作者单位： | 安徽建筑大学土木工程学院,合肥230601;合肥工业大学土木与水利工程学院力学系,合肥230009 |
| |
| 基金项目： | 1)国家自然科学基金(11272111);博士启动基金(2020QDZ08) |
| |
| 摘 要： | 研制了一种适用于二维正交各向异性位势问题的高阶单元(线性单元和二次单元)快速多极边界元法.在快速多极边界元法中,源点对于远场区域的积分采用快速多极展开式计算,而对于近场区域的积分则直接进行计算.高阶单元的使用使得近场积分,尤其是奇异积分和几乎奇异积分的计算更加复杂.通过引入复数表达对其进行简化,若边界采用线性单元插值,...
|
| 关 键 词： | 位势问题 快速多极边界元法 高阶单元 几乎奇异积分 |
| 收稿时间： | 2020-12-29 |
ANALYSIS OF 2-D ORTHOTROPIC POTENTIAL PROBLEMS USING FAST MULTIPOLE BOUNDARY ELEMENT METHOD WITH HIGHER ORDER ELEMENTS |
| |
| Affiliation: | *School of Civil Engineering, Anhui Jianzhu University, Hefei 230601, China?School of Civil Engineering, Hefei University of Technology, Hefei 230009, China |
| |
| Abstract: | A new fast multipole boundary element method is proposed for analyzing 2-D orthotropic potential problems by using linear and three-node quadratic elements. In the fast multipole boundary element method, fast multipole expansions are used for the integrals on elements that are far away from the source point, and the direct evaluations are used for the integrals on elements that are close to the source point. The use of linear and three-node quadratic elements results in more complicated computations for near-field integrals, especially singular integrals and nearly singular integrals. In this paper, the complex notation is introduced to simplify the near-field integrals. If the boundary is discretized by linear elements, the near-field integrals are calculated by the analytic formulas, if the three-node quadratic element is used, a semi analytical algorithm is given to calculate the near-field integrals. Accurate evaluations of the singular integrals and nearly singular integrals on linear and three-node quadratic elements ensure that the present fast multipole boundary element method can be applied to the ultra-thin structure, which broadens the application of the fast multipole boundary element method with linear and quadratic elements. Numerical examples show that the number of elements required by the fast multipole boundary element method with linear and quadratic elements is significantly less than that with constant elements. In addition, the required CPU time is increased linearly with the increase of the number of degrees of freedom $(N)$, which demonstrates the computational efficiency is still in the complexity of $O (N)$. Therefore, the present method exhibits higher accuracy and efficiency for solving large-scale problems. |
| |
| Keywords: | |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《力学学报》浏览原始摘要信息 |
|
点击此处可从《力学学报》下载全文 |
|
