三维弹性问题无网格分析的奇异杂交边界点方法

苗雨; 王元汉

三维弹性问题无网格分析的奇异杂交边界点方法

苗雨,
王元汉

华中科技大学土木工程与力学学院,武汉 430074

基金项目: 中国科学院岩土力学重点实验室资助项目(Z110507)

详细信息

作者简介:
苗雨(1979- ),男,山东人,讲师,博士(联系人.Tel:+86-27-87556934;E-mail:my_miaoyu@163.com).

中图分类号: O241
计量
- 文章访问数: 2638
- HTML全文浏览量: 114
- PDF下载量: 500
- 被引次数: 0
出版历程
- 收稿日期: 2004-12-03
- 修回日期: 2006-02-10
- 刊出日期: 2006-05-15

Meshless Analysis for Three-Dimensional Elasticity With Singular Hybrid Boundary Node Method

School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

摘要

摘要: 提出了一种求解三维线弹性问题的奇异杂交边界点方法．将修正变分原理与移动最小二乘法结合起来，利用了前者的降维优势和后者的无网格特性．使用刚体位移法处理方法中的强奇异积分，提出了一种自适应的积分方案，解决了原有的杂交边界点方法中存在的“边界层效应”．在该方法中，将基本解的源点直接布在边界上，避免了在正则化杂交边界点法中不确定参数的选取．三维弹性力学问题算例体现了这些特点．结果表明该方法与已知的精确解符合较好，同时研究了影响该方法精度的一些参数．
- 三维弹性问题 /
- 移动最小二乘 /
- 无网格法 /
- 修正变分原理 /
- 奇异杂交边界点方法
Abstract: The singular hybrid boundary node method (SHBNM) is proposed for solving threedimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ‘boundary layer effect', which is the main drawback of the original hybrid BNM, was overcomed by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3-D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.
- three-dimensional elasticity /
- moving least squares /
- meshless method /
- modified variational principle /
- singular hybrid boundary node method

HTML全文

参考文献(7)

[1]	Lucy L B.A numerical approach to the testing of the fission hypothesis[J].Astronomic Journal,1977,18(12):1013—1024.
[2]	Belytschko T,Lu Y Y,Gu L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,137(2):229—256.
[3]	Mukherjee Y X,Mukherjee S.The boundary node method for potential problems[J].International Journal for Numerical Methods in Engineering,1994,40(5):797—815.
[4]	Zhang J M,Yao Z H,Li H.A hybrid boundary node method[J].International Journal for Numerical Methods in Engineering,2002,53(5):751—763. doi: 10.1002/nme.313
[5]	Zhang J M,Yao Z H.The meshless regular hybrid boundary node method for 2D linear elasticity[J].Engineering Analysis With Boundary Elements,2003,27(3):259—268. doi: 10.1016/S0955-7997(02)00137-6
[6]	DeFigueredo T G B, Brebbia C A.A new hybrid displacement variational formulation of BEM for elastostatics[A].In: Brebbia C A, Conner J J, Eds.Advances in Boundary Elements[C].Southampton: Computational Mechanics Publication,1989,1(1):47—57.
[7]	Atluri S N, Kim H G,Cho J Y.A critical assessment of the truly meshless local Petrov-Galerkin (MLPG),and local boundary integral equation (LBIE) methods[J].Computational Mechanics,1999,24(2):348—372. doi: 10.1007/s004660050457