基于FETI的非协调等几何分析

祝雪峰; 胡平; 马正东; 刘炜

doi:10.3879/j.issn.1000-0887.2013.08.001

基于FETI的非协调等几何分析

doi: 10.3879/j.issn.1000-0887.2013.08.001

¹大连理工大学汽车工程学院工业装备结构分析国家重点实验室,辽宁大连116024;²密歇根大学机械工程系,Ann Arbor 美国 48105;³北京师范大学珠海分校应用数学学院,广东珠海 519087

基金项目: 国家自然科学基金重点资助项目(10932003；11272075)；国家重点基础研究发展计划资助项目(973计划，2010CB832700)；国家工信部04重大专项项目基金资助项目（2011ZX04001-021）

详细信息

作者简介:
祝雪峰(1979—),男,河北人,师资博士后,博士(Tel:+86-411-84706475;E-mail:xuefeng@dlut.edu.cn);胡平(1956—),男,吉林人,教授,博士,博士生导师(通讯作者.Tel:+86-411-84702573;E-mail:pinghu@dlut.edu.cn).

中图分类号: O302
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出版历程
- 收稿日期: 2012-09-24
- 修回日期: 2013-07-01
- 刊出日期: 2013-08-15

Nonconforming Isogeometric Analysis With FETI Method

¹State Key Laboratory of Structural Analysis for Industrial Equipment, School of Automotive Engineering, Dalian University of Technology,Dalian, Liaoning 116024, P.R.China;²Department of Mechanical Engineering, Michigan University, Ann Arbor, Michigan 48105, USA;³College of Applied Mathematics, Beijing Normal University, Zhuhai, Guangdong 519087, P.R.China

摘要

摘要: 基于非均匀有理B样条的等几何分析方法是一种无需网格划分的新的计算方法，旨在实现直接利用CAD模型进行分析，有望取代目前传统有限元技术．等几何分析已被成功应用在固体力学，流固耦合及拓扑优化等诸多领域．等几何分析方法要求CAD曲面或者实体高阶连续，而绝大多数CAD模型内多个曲面不但无法保持高阶连续，而且在公共界面处是几何非协调的．这一缺陷严重制约了等几何分析技术的进一步发展和应用．另外，由于采用高阶单元，等几何分析计算量较等自由度传统有限元要耗时．为解决这些难题，笔者在先前工作基础之上，提出了基于FETI方法的非协调等几何分析．新方法较以往的零空间解法更加快捷，适用于大规模数据的并行计算．数值算例表明本方法无需修改CAD模型，实施简单，精度满足要求，可处理复杂CAD模型．
- 非协调等几何分析 /
- FETI算法 /
- NURBS有限元 /
- 高性能计算 /
- 并行计算
Abstract: Nonconforming isogeometric analysis (NIGA) with FETI method was proposed. The major purpose was to enable applying the isogeometric analysis directly to the NURBS models with trimmed patches for more general and practical engineering applications. The basic idea was to use the NURBS version of FETI to replace the zero space algorithm. The present method can deal with large scale engineering problem rapidly and is suitable for parallel computing. Numerical examples for patch tests and a car body analysis are presented to verify the efficiency of this method.
- nonconforming isogeometric analysis /
- FETI method /
- NURBS-based finite element method /
- parallel computing /

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参考文献(13)

[1]	Hughes T J R, Cottrell J A, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement[J].Computer Methods in Applied Mechanics and Engineering,2005, 194(39/41): 4135-4195.
[2]	Cottrell J A, Hughes T J R, Reali A. Studies of refinement and continuity in isogeometric structural analysis[J]. Computer Methods in Applied Mechanics and Engineering,2007, 196(41/44): 4160-4183.
[3]	Bazilevs Y, Hsu M C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar T E. 3D simulation of wind turbine rotors at full scale—part I: geometry modeling and aerodynamics[J].International Journal for Numerical Methods in Fluids,2011, 65(1/3): 207-235.
[4]	Bazilevs Y, Calo V M, Zhang Y, Hughes T J R. Isogeometric fluidstructure interaction analysis with applications to arterial blood flow[J].Computational Mechanics,2006, 38(4/5): 310-322.
[5]	Wall W A, Frenzel M A, Cyron C. Isogeometric structural shape optimization[J].Computer Methods in Applied Mechanics and Engineering,2008, 197(33/40): 2976-2988.
[6]	王东东, 轩军厂, 张灿辉. 几何精确 NURBS 有限元中边界条件施加方式对精度影响的三维计算分析[J]. 计算力学学报, 2012, 29(1):31-37.(WANG Dong-dong, XUAN Jun-chang, ZHANG Can-hui. A three dimensional computational investigation on the influence of essential boundary condition imposition in NURBS isogeometric finite element analysis[J].Chinese Journal of Computational Mechanics,2012, 29(1): 31-37.(in Chinese))
[7]	张勇, 林皋, 胡志强, 钟红. 基于等几何分析的比例边界有限元方法[J]. 计算力学学报, 2012, 29(3): 433-438. (ZHANG Yong, LIN Gao, HU Zhi-qiang, ZHONG Hong. Scaled boundary finite element method based on isogeometric analysis[J].Chinese Journal of Computational Mechanics,2012, 29(3): 433-438.(in Chinese))
[8]	祝雪峰, 马正东, 胡平. 几何精确的非协调等几何分析[J]. 固体力学学报, 2012, 33(5): 487492.(ZHU Xue-feng, MA Zheng-Dong, HU Ping. Nonconforming isogeometric analysis with exact geometry[J].Chinese Journal of Solid Mechanics,2012, 33(5):487-492. (in Chinese))
[9]	Cottrell J A, Hughes T J R, Bazilevs Y.Isogeometric Analysis: Toward Integration of CAD and FEA [M]. Wiley, 2009.
[10]	Piegl L A, Tiller W.The NURBS Book [M]. 2nd ed. Monographs in Visual Communication. Springer Verlag, 1997.
[11]	Farhat C, Roux F X. A method of finite element tearing and interconnecting and its parallel solution algorithm[J].International Journal for Numerical Methods in Engineering,1991, 32(6): 1205-1227.
[12]	Farhat C, Roux F. Implicit parallel processing in structural mechanics[J].Computational Mechanics Advances,1994, 2(1): 1-124.
[13]	Farhat C, Lesoinne M, Le Tallec P, Pierson K, Rixen D. FETIDP: a dual-primal unified FETI method?—part I: a faster alternative to the twolevel FETI method[J].International Journal for Numerical Methods in Engineering,2001, 50(7): 1523-1544.