| 变形弹性杆边值问题的流型法 |
| |
| 引用本文： | 殷先军,洪正平. 变形弹性杆边值问题的流型法[J]. 青岛大学学报(自然科学版), 2010, 23(3): 5-8. DOI: 10.3969/j.issn.1006-1037.2010.03.002 |
| |
| 作者姓名： | 殷先军 洪正平 |
| |
| 作者单位： | 1. 中央财经大学应用数学学院,北京,100081
2. 山东师范大学物理与电子科学学院,山东济南,250014 |
| |
| 摘 要： | 从描述弹性棒变形的数学模型出发,讨论了二阶常微分方程的边值问题,给出了确定此类问题多解性和分支的一种新方法——流型法。利用流型法将二阶常微分方程边值问题解的个数转化为确定末端流型与由边界条件确定的直线的交点问题,进而画出边值问题解的分支图,结合常用的数值解法,便可比较容易的求出边值问题的数值解。
|
| 关 键 词： | 边值问题 流型法 轨线 |
Manifold Method for Boundary Value Problem of Deformed Elastic Bar |
| |
| YIN Xian-jun,HONG Zheng-ping. Manifold Method for Boundary Value Problem of Deformed Elastic Bar[J]. Journal of Qingdao University(Natural Science Edition), 2010, 23(3): 5-8. DOI: 10.3969/j.issn.1006-1037.2010.03.002 |
| |
| Authors: | YIN Xian-jun HONG Zheng-ping |
| |
| Affiliation: | 1.School of Applied Mathematics,Central University of Finance and Economics,Beijing 100081,China;2.College of Physics and Electronics,Shandong Normal University,Jinan 250014,China) |
| |
| Abstract: | For discussion of the mathematical model describing the deformation of the elastic circular bar as gripper and spring element,a two-point boundary value problem of ordinary differential equations of order two was mainly studied in this paper.A new method,namely manifold method,was developed for multiplicity and bifurcation of the solutions.With the aid of manifold method combined with some convenient numerical approaches,the problem of finding the solutions of boundary value problem of ordinary differential equations of order two is turned into the one of determining the intersections of the end manifold with the horizontal line defined by the boundary condition,and then the bifurcation diagram can be obtained. |
| |
| Keywords: | boundary value problem elastic deformation manifold method orbit |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
