一种基于H-R变分的杂交广义元方法

杨森森; 马永其; 冯伟

doi:10.3879/j.issn.1000-0887.2013.03.007

一种基于H-R变分的杂交广义元方法

doi: 10.3879/j.issn.1000-0887.2013.03.007

¹上海大学上海市应用数学和力学研究所,上海 200072;²上海大学理学院力学系,上海 200444

基金项目: 上海市科委基金资助项目（11231202700）

详细信息

作者简介:
杨森森(1984—),男,湖北人,硕士生(E-mail: derwillezurmacht12@163.com);马永其(1966—),男,宁夏人,副教授,博士(通讯作者.E-mail: mayq@staff.shu.edu.cn).

中图分类号: O34
计量
- 文章访问数: 1613
- HTML全文浏览量: 84
- PDF下载量: 1128
- 被引次数: 0
出版历程
- 收稿日期: 2013-01-16
- 修回日期: 2013-01-29
- 刊出日期: 2013-03-15

A Hybrid Generalized Element Method Based on H-R Variational Principle

¹Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China;²Department of Mechanics, Shanghai University, Shanghai 200444, P.R.China

摘要

摘要: 基于HellingerReissner变分原理，通过构造合适的应力场函数使其能更方便和更准确地得到节点上的应力值，同时结合广义有限元构造广义位移插值的方法，在不提高单元节点数目的前提下提高位移场函数的阶次，从而提高其求解精度．这种方法能同时灵活地构造应力场和位移场，在同等精度条件下能占用较少内存和求解更少的方程数目，计算结果也显示了这种方法的有效性和很高的计算精度．
- 杂交元 /
- Hellinger-Reissner变分原理 /
- 广义有限元法 /
- 节点位移插值函数 /
- 应力函数
Abstract: Combining HellingerReissner variational principle and the way of constructing displacement interpolation function of generalized finite element method to construct stress field and displacement field independently, through the suitable stress field could get a more precise stress value of node conveniently, and in the same time to increase the order of displacement function without increasing the number of element’s nodes, in this way a more accurate result was got. This method combines the above two methods of flexibility of constructing the stress field and displacement field, meanwhile, using less memory and equations on the same condition compared with some other methods, and the results also show that of efficiency and higher presicion.
- hybrid element /
- HellingerReissner variational principle /
- generalized finite element method /
- nodal displacement interpolation function /
- stress function

HTML全文

参考文献(17)

[1]	卞学鐄.有限元法论文选[M].北京:国防工业版社, 1980.(Pian T H H. Collected Papers of Finite Element Method [M].Beijing: National Defence Industry Press, 1980.(in Chinese))
[2]	Babuska I, Osborn J E.Generalized finite element methods: their performance and their relation to mixed methods[J]. SIAM Journal of Numerical Analysis , 1983, 20(3): 510-535.
[3]	Babuska I, Melenk J M.The partition of unity method[J]. International Journal for Numerical Method in Engineering , 1997, 40(4):727-758.
[4]	Melenk J M, Babuska I.The partition of the unity finite element method: basic theory and applications[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1/4): 289-314.
[5]	Duarte C A, Babuska I, Oden J T.Generalized finite element methods for threedimensional structural mechanics problems[J]. Computer & Structures , 2000, 77(2):215-232.
[6]	Strouboulis T, Babuska I, Copps K.The design and analysis of the generalized finite element method[J]. Computer Methods in Applied Mechanics and Engineering , 2000, 181(1/3):43-69.
[7]	梁国平,何江衡.广义有限元方法——一类新的逼近空间[J].力学进展,1995, 25(4): 562565.(LIANG Guo-ping, HE Jiang-heng.Generalized finite element method—a new finite element space[J]. Advances in Mechanics , 1995, 25(4):562565.(in Chinese))
[8]	栾茂田, 田荣, 杨庆.广义节点有限元法[J].计算力学学报, 2000, 17(2):192-200.(LUAN Mao-tian, TIAN Rong, YANG Qing.Generalizednode finite element method based on manifold concept[J]. Chinese Journal of Computational Mechanics , 2000, 17(2):192-200.(in Chinese))
[9]	田荣, 栾茂田, 杨庆.高阶形式广义节点有限元法及其应用[J].大连理工大学学报, 2000, 40(4):492-495.(TIAN Rong, LUAN Mao-tian, YANG Qing.Highorder generalizednode finite element method[J]. Journal of Dalian University of Technology , 2000, 40(4):492-495.(in Chinese))
[10]	邵国建, 刘体锋.广义有限元及其应用[J].河海大学学报（自然科学版）, 2002, 30(4): 28-31.(SHAO Guo-jian, LIU Ti-feng.Generalized finite element and its application[J]. Journal of Hohai University(Natural Sciences) , 2002, 30(4):28-31.(in Chinese))
[11]	石根华.数值流形方法与非连续变形分析[M].裴觉民译.北京:清华大学出版社,1997.(SHI Gen-hua. Numerical Manifold Method and Discontinuous Deformation Analysis [M].PEI Juemin Transl.Beijing: Tsinghua University Press, 1997.(in Chinese))
[12]	李录贤, 刘书静, 张慧华, 陈方方, 王铁军.广义有限元方法研究进展[J].应用力学学报,2009, 26(1):96-108.(LI Lu-xian, LIU Shu-jing, ZHANG Hui-hua, CHEN Fang-fang, WANG Tie-jun.Researching progress of generalized finite element method[J]. Chinese Journal of Applied Mechanics , 2009, 26(1):96108.(in Chinese))
[13]	Duarte C A, Hamzeh O N, Liszka T J, Tworzydlo W W.A generalized finite element method for the simulation of threedimensional dynamic crack propagation[J].Computer Methods in Applied Mechanics and Engineering , 2001, 190(15/17):2227-2262.
[14]	彭自强, 李小凯, 葛修润.广义有限元法对动态裂纹扩展的数值模拟[J].岩土力学与工程学报, 2004, 23(18):31323137.(PENG Zi-qiang, LI Xiao-kai, GE Xiu-run.Numerical simulation of dynamic crack propagation with generalized finite element method[J]. Chinese Journal of Rock Mechanics and Engineering , 2004, 23(18):3132-3137.(in Chinese))
[15]	章青, 刘宽, 夏晓舟, 杨静.广义扩展有限元法及其在裂纹扩展分析中的应用[J].计算力学学报, 2012, 29(3):427-432.(ZHANG Qing, LIU Kuan, XIA Xiao-zhou, YANG Jing.Generalized extended finite element method and its application in crack growth analysis[J]. Chinese Journal of Computational Mechanics , 2012, 29(3):427432.(in Chinese))
[16]	田宗漱, 卞学鐄.多变量变分原理与多变量有限元方法[M].北京：科学出版社, 2011.(TIAN Zhong-shu, Pian T H H. Multivariable Variation Principle and Multivariable Finite Element Method [M].Beijing: Science Press, 2011.(in Chinese))
[17]	卓家寿.弹塑性力学中的广义变分原理[M].北京:中国水利水电出版社, 2002.(ZHUO Jia-shou. Generalized Variatiational Principle of ElasticPlastic Mechanics [M].Beijing: China Water Power Press, 2002.(in Chinese))