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工程力学  2015 

对有限覆盖无网格法中悬挂节点的研究

DOI: 10.6052/j.issn.1000-4750.2014.01.0046, PP. 80-86

Keywords: 无网格伽辽金法,节点布置,悬挂节点,前处理,背景积分,精度

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Abstract:

当前基于Galerkin法的无网格法都只在域内和边界上布置节点。基于无网格方法背景网格独立于节点布置这一性质,该文探讨了无网格域外布置悬挂节点的可行性,提出了一种统一的、均匀的无网格节点布置方案,并设计了相应的背景网格方案,称为有限覆盖无网格法。通过数值算例讨论了悬挂节点对精度的影响,在此基础上讨论了悬挂节点的数目、节点影响域的形状、尺寸以及背景积分方案等对求解精度的影响,并给出了推荐的做法。算例结果表明,悬挂节点能够显著提高求解精度,尤其是边界附近的应力精度。

References

[1]  Lucy L B. A numerical approach to the testing of the fission hypothesis [J]. The Astronomical Journal, 1977, 82: 1013―1024.
[2]  Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods [J]. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229―256.
[3]  Liu W K, Jun S, Zhang Y F. Reproducing kernel particle methods [J]. International Journal for Numerical Methods in Fluids, 1995, 20(8/9): 1081―1106.
[4]  Atluri S, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics [J]. Computational Mechanics, 1998, 22(2): 117―127.
[5]  Gu Y, Chen W, Zhang C Z. Singular boundary method for solving plane strain elastostatic problems [J]. International Journal of Solids and Structures, 2011, 48(18): 2549―2556.
[6]  Fu Z J, Chen W, Yang H T. Boundary particle method for Laplace transformed time fractional diffusion equations [J]. Journal of Computational Physics, 2013, 235: 52―66.
[7]  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)
[8]  Nguyen V, Rabczuk T, Bordas S, Duflot M. Meshless methods: A review and computer implementation aspects [J]. Mathematics and Computers in Simulation, 2008, 79(3): 763―813.
[9]  Lu H, Chen J S. Adaptive Galerkin particle method [M]// Griebel M, Schweitzer M A. Meshfree methods for paatial differential equations [J]. Berlin Heidelberg: Springer, 2003, 251―265.
[10]  Le C V, Askes H, Gilbert M. Adaptive element-free Galerkin method applied to the limit analysis of plates [J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37/38/39/40): 2487―2496.
[11]  Rabczuk T, Belytschko T. Adaptivity for structured meshfree particle methods in 2D and 3D [J]. International Journal for Numerical Methods in Engineering, 2005, 63(11): 1559―1582.
[12]  彭翀, 袁会娜, 张丙印. 无网格自动加密方法及其在土体裂缝分析中的应用[J]. 工程力学, 2013, 30(6): 231―235. Peng Chong, Yuan Huina, Zhang Bingyin. Automatic node refinement for meshfree method and its application in soil crack analysis [J]. Engineering Mechanics, 2013, 30(6): 231―235. (in Chinese)
[13]  Shi G H. Manifold method of material analysis [C]. Minneapolis, Minnesota: Transactions of the 9th Army Conference on Applied Mathematics and Computing, 1991: 57―76.
[14]  田荣. 连续与非连续变形分析的有限覆盖无单元方法及其应用研究[D]. 大连: 大连理工大学, 2000. Tian Rong. Finite-cover-based element-free method for continuous and discontinuous deformation analysis with applications in geotechnical engineering [D]. Dalian: Dalian University of Technology, 2000. (in Chinese)
[15]  樊成. 有限覆盖 Kriging 插值无网格法及其在岩体断裂中的应用研究[D]. 大连: 大连理工大学, 2007. Fan Cheng. Kriging interpolation meshless method based on finite cover technique and its application in fracture analyses of rock mass [M]. Dalian: Dalian University of Technology, 2007. (in Chinese)
[16]  Tiago C, Pimenta P M. An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations [J]. Engineering Analysis with Boundary Elements, 2008, 32(6): 494―511. Dolbow J, Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods [J]. Computational Mechanics, 1999, 23(3): 219―230.
[17]  Liu G R. Meshfree methods: moving beyond the finite element method [M]. New York: CPC Press, 2009: 201―210.
[18]  Timoshenko S P, Goodier J N, Abramson H N. Theory of elasticity [J]. Journal of Applied Mechanics, 1970: 37―888.
[19]  朱伯芳. 有限单元法原理与应用[M]. 北京: 中国水利水电出版社, 2009: 146―150.
[20]  Zhu Bofang. The principle of finite element method and its application [M]. Beijing: China Water Power Press, 2009: 146―150. (in Chinese)

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