## 留言板

 引用本文: 杨建军, 郑健龙. 无网格介点法：一种具有h-p-d适应性的无网格法[J]. 应用数学和力学, 2016, 37(10): 1013-1025.
YANG Jian-jun, ZHENG Jian-long. A Meshless Intervention-Point Method With h-p-d Adaptability[J]. Applied Mathematics and Mechanics, 2016, 37(10): 1013-1025. doi: 10.21656/1000-0887.370159
 Citation: YANG Jian-jun, ZHENG Jian-long. A Meshless Intervention-Point Method With h-p-d Adaptability[J]. Applied Mathematics and Mechanics, 2016, 37(10): 1013-1025.

## 无网格介点法：一种具有h-p-d适应性的无网格法

##### doi: 10.21656/1000-0887.370159

###### 作者简介:杨建军（1975—），男，讲师，博士，硕士生导师(通讯作者. E-mail: yangjianjun01@126.com);郑健龙（1954—），男，教授，博士，博士生导师，工程院院士.
• 中图分类号: O241; O343

## A Meshless Intervention-Point Method With h-p-d Adaptability

Funds: The National Natural Science Foundation of China（51478053）
• 摘要: 提出了一种新型无网格法，即无网格介点（MIP）法.MIP法采用移动最小二乘核近似，有利于提高数值方法的计算稳定性，而且算法更为简便.MIP法采用局部介点近似技术，使得这种方法不仅具有一般的h适应性，而且具有p-d适应性，从而使方法在数值实施上更具有灵活性.数值算例结果表明，MIP法具有计算简单，效率高，精度高的优点，而且显示出对多种求解问题具有广泛适用的特性.
•  [1] YANG Jian-jun, ZHENG Jian-long. Intervention-point principle of meshless method[J]. Chinese Science Bulletin,2013,58(4/5): 478-485. [2] Li S, Liu W K. Meshfree and particle methods and their applications[J]. Applied Mechanics Reviews,2002,55(1): 1-34. [3] Jensen P S. Finite difference techniques for variable grids[J]. Computers & Structures,1972,2(1/2): 17-29. [4] Perrone N, Kao R. A general finite difference method for arbitrary meshes[J]. Computers & Structures,1975,5(1): 45-57. [5] Liszka T, Orkisz J. The finite difference method at arbitrary irregular grids and its application in applied mechanics[J]. Computers & Structures,1980,11(1/2): 83-95. [6] Lucy L B. A numerical approach to the testing of the fission hypothesis[J]. The Astronomical Journal,1977,82: 1013-1024. [7] Gingold R A, Monaghan J J. Smoothed particle hydrodynamics: theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society,1977,181(3): 375-389. [8] Belytschko T, Krongauz Y, Organ D, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments[J]. Computer Methods in Applied Mechanics and Engineering,1996,139(1/4): 3-47. [9] Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements[J]. Computational Mechanics,1992,10(5): 307-318. [10] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods[J]. International Journal for Numerical Methods in Engineering,1994,37(2): 229-256. [11] Atluri S N, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics[J]. Computational Mechanics,1998,22(2): 117-127. [12] 张雄, 刘岩, 马上. 无网格法的理论及应用[J]. 力学进展, 2009,39(1): 1-36.(ZHANG Xiong, LIU Yan, MA Shang. Meshfree methods and their applications[J]. Advances in Mechanics,2009,39(1): 1-36.(in Chinese)) [13] 杨建军, 郑健龙. 移动最小二乘法的近似稳定性[J]. 应用数学学报, 2012,35(4): 637-648.(YANG Jian-jun, ZHENG Jian-long. Stability of moving least squares approximation[J]. Acta Mathematicae Applicatae Sinica,2012,35(4): 637-648.(in Chinese)) [14] Breitkopf P, Touzot G, Villon P. Double grid diffuse collocation method[J]. Computational Mechanics,2000,25(2): 199-206. [15] Timoshenko S P, Goodier J N. Theory of Elasticity [M]. 3rd ed. McGraw-Hill Book Company, 1970. [16] Onate E, Idelsohn S, Zienkiewicz O C, Taylor R L. A finite point method in computational mechanics. Applications to convective transport and fluid flow[J]. International Journal for Numerical Methods in Engineering,1996,39(22): 3839-3866. [17] 韩治, 杨海天, 王斌. 无网格伽辽金法求解轴对称问题[J]. 工程力学, 2005,22(5): 64-68.(HAN Zhi, YANG Hai-tian, WANG Bin. Solving axisymmetric problems via EFGM[J]. Engineering Mechanics,2005,22(5): 64-68.(in Chinese)) [18] 陈建桥, 梁元博, 丁亮. 无网格局部Petrov-Galerkin法求解轴对称问题[J]. 华中科技大学学报（城市科学版）, 2007,24(4): 9-12.(CHEN Jian-qiao, LIANG Yuan-bo, DING Liang. Numerical analysis of axisymmetric problems by MLPG[J]. Journal of Huazhong University of Science and Technology (Urban Science Edition),2007,24(4): 9-12.(in Chinese)) [19] 杨建军, 郑健龙. 无网格MLPG法求解轴对称弹性力学问题[J]. 工程力学, 2012,29(8): 8-13.(YANG Jian-jun, ZHENG Jian-long. Analysis of axisymmetric elasticity problems using the meshless local Petrov-Galerkin method[J]. Engineering Mechanics,2012,29(8): 8-13.(in Chinese)) [20] 程玉民, 彭妙娟, 李九红. 复变量移动最小二乘法及其应用[J]. 力学学报, 2005,37(6): 719-723.(CHENG Yu-min, PENG Miao-juan, LI Jiu-hong. The complex variable moving least-square approximation and its application[J]. Chinese Journal of Theoretical and Applied Mechanics,2005,37(6): 719-723.(in Chinese)) [21] 孙新志, 李小林. 复变量移动最小二乘近似在Sobolev空间中的误差估计[J]. 应用数学和力学, 2016,37(4): 416-425.(SUN Xin-zhi, LI Xiao-lin. Error estimates for the complex variable moving least square approximation in Sobolev spaces[J]. Applied Mathematics and Mechanics,2016,37(4): 416-425.(in Chinese))

##### 计量
• 文章访问数:  1779
• HTML全文浏览量:  77
• PDF下载量:  1321
• 被引次数: 0
##### 出版历程
• 收稿日期:  2016-05-23
• 修回日期:  2016-06-10
• 刊出日期:  2016-10-15

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈