首页 | 本学科首页   官方微博 | 高级检索  
     检索      

基于单位分解法的无网格数值流形方法
引用本文:李树忱,程玉民.基于单位分解法的无网格数值流形方法[J].力学学报,2004,36(4):496-500.
作者姓名:李树忱  程玉民
作者单位:上海大学上海市应用数学和力学所
摘    要:在数值流形方法和单位分解法的基础上,提出了无网格数值流形方法. 无网格数值流形 方法在分析时采用了双重覆盖系统,即数学覆盖和物理覆盖. 数学覆盖提供的节点形成求解 域的有限覆盖和单位分解函数;而物理覆盖描述问题的几何区域及其域内不连续性. 与原有 的数值流形方法相比,无网格数值流形方法的数学覆盖形状更加灵活,可以用一系列节点的 影响域来建立数学覆盖和单位分解函数,具有无网格方法的特性,从而摆脱了传统的数值流 形方法中网格所带来的困难. 与无网格方法相比,由于采用了有限覆盖技术,试函数的构造 不受域内不连续的影响,克服了原有的无网格方法在处理不连续问题时所遇到的困难. 详细推导了无网格数值流形方法的试函数和求解方程,最后给出了算例,验证了该方法的正 确性.

关 键 词:数值流形方法  单位分解法  无网格方法  有限覆盖技术  不连续性
修稿时间:2003年11月13

Meshless numerical manifold method based on unit partition
Li Shuchen Cheng Yumin.Meshless numerical manifold method based on unit partition[J].chinese journal of theoretical and applied mechanics,2004,36(4):496-500.
Authors:Li Shuchen Cheng Yumin
Institution:Li Shuchen Cheng Yumin Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China
Abstract:In this paper the meshless numerical manifold method is presented based on the numerical manifold method and the partition of unity method. In meshless numerical manifold method, two cover systems are employed. The mathematical cover system provides the nodes for forming finite covers of the solution domain and the partition of unity functions, and the physical cover system describes geometry of the domain of the problem and the discontinuous surfaces in the domain. The shape function in this method is formed by the partition of unity and the finite cover technology, so the shape functions cannot be affected by discontinuous domain, and crack problems can be treated better. To local problems, the shape functions are more effective than other method. So the method can avoid the disadvantages in other meshless methods in which the tip of the discontinuous crack is not considered. Comparing with the conventional numerical manifold method, the shape of the finite cover can be selected easily. And the finite covers and the partition of unity functions are formed with the influence domains of a series of nodes. So the meshless manifold method has some advantages of the meshless and gets rid of the disadvantage of the mesh in the numerical manifold method. Comparing with the conventional meshless method, finite cover technology is used in the method, and then the test functions cannot be influenced by the discontinuity in the solving domain. And this method can conquer some difficulties in the conventional meshless methods for the problems with a discontinuous domain. The test function and the equations of the meshless numerical manifold method are obtained in detail. And a numerical example is given and it shows the method in this paper is correct.
Keywords:numerical manifold method  partition of unity  meshless method  finite cover technology  discontinuity
本文献已被 CNKI 维普 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》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号