基于光滑扩展有限元的平板裂纹参数不确定性反求

张利轩; 卿宏军; 胡德安

doi:10.3879/j.issn.1000-0887.2016.01.005

基于光滑扩展有限元的平板裂纹参数不确定性反求

doi: 10.3879/j.issn.1000-0887.2016.01.005

湖南大学特种装备先进设计技术与仿真教育部重点实验室, 长沙 410082

基金项目: 国家自然科学基金（11272118）

详细信息

作者简介:
张利轩（1987—），男，博士生(E-mail: 410182zlx@163.com);卿宏军(1971—)，男，博士(通讯作者.E-mail: qinghongjun@hnu.edu.cn).

中图分类号: U462.3
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出版历程
- 收稿日期: 2015-09-21
- 修回日期: 2015-10-08
- 刊出日期: 2016-01-16

Uncertain Inversion of Crack Parameters for Plates Based on the SmXFEM

Key Laboratory of Advanced Design and Simulation Technology for Special Equipments, Ministry of Education, Hunan University, Changsha 410082, P.R.China

Funds: The National Natural Science Foundation of China(11272118)

摘要

摘要: 裂纹位置和尺寸等是工程监测需掌握的非常重要的信息.光滑扩展有限元是近年来发展起来的一种模拟裂纹的有效方法，即使采用极度不规则单元仍可获得精确的模拟结果，无需单元“质量”要求.因此在单元自动划分方面具有突出的优势，这一特点也使得该方法适用于裂纹反求过程的实时调用和含裂纹仿真模型的网格自动划分.研究基于光滑扩展有限元的不确定反求方法，用于识别平面弹性板中直裂纹位置和尺寸参数，即采用光滑扩展有限元法进行拉伸工况的正问题分析，通过测量平板边缘的节点位移建立优化模型，调用遗传算法实现裂纹参数的反求.反求过程中将材料的弹性模量和Poisson(泊松)比作为区间不确定变量，采用一阶Taylor（泰勒）公式实现了平板裂纹参数的不确定性反求.
- 不确定性反求 /
- 光滑扩展有限元 /
- 裂纹 /
- 遗传算法 /
- 优化模型
Abstract: The crack parameters of positions and sizes are very important information for engineering monitoring. The smoothed extended finite element method (SmXFEM) was an effective method developed for the simulation of crack problems in recent years. The SmXFEM works well without high demand on the element quality, and gives accurate simulation results even with extremely irregular elements. The great advantages of the SmXFEM make it very suitable for automatic mesh generation of crack models in the real time calculation of crack inversion. An approach of uncertain inversion based on the SmXFEM was proposed to indentify the positions and sizes of straight cracks in elastic plane plates. In this approach, the SmXFEM, used to solve the forward problem of the crack model under tension, was called repeatedly by the genetic algorithm. Then an optimization model was established through measurement of the displacements of selected key nodes at the edge of the plate. Finally, with the elastic modulus and Poisson’s ratio as uncertain interval variables, the 1storder Taylor formula was used for the identification of crack parameters in the plates. The results show the correctness and applicability of the present method.
- uncertain inversion /
- SmXFEM /
- crack /
- genetic algorithm /
- optimization model

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参考文献(22)

[1]	Rabinovich D, Givoli D, Vigdergauz S. XFEM-based crack detection scheme using a genetic algorithm[J]. International Journal for Numerical Methods in Engineering,2007,71(9): 1051-1080.
[2]	Rabinovich D, Givoli D, Vigdergauz S. Crack identification by ‘arrival time’ using XFEM and a genetic algorithm[J]. International Journal for Numerical Methods in Engineering,2009,77(3): 337-359.
[3]	Sukumar N, Huang Z Y, Prévost J H, Suo Z. Partition of unity enrichment for bimaterial interface cracks[J]. International Journal for Numerical Methods in Engineering,2004,59(8): 1075-1102.
[4]	Ashari S E, Mohammadi S M. Delamination analysis of composites by new orthotropic bimaterial extended finite element method[J]. International Journal for Numerical Methods in Engineering,2011,86(13): 1507-1543.
[5]	Mos N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing[J]. International Journal for Numerical Methods in Engineering,1999,46(1): 131-150.
[6]	Fries T P, Belytschko T. The extended/generalized finite element method: an overview of the method and its applications[J]. International Journal for Numerical Methods in Engineering,2010,84(3): 253-304.
[7]	Chessa J, Belytschko T. An enriched finite element method for axisymmetric two-phase flow with surface tension[J]. Journal of Computational Physics,2003,58(13): 2041-2064.
[8]	Chopp D, Sukumar N. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method[J]. International Journal of Engineering Science,2003,41(8): 845-869.
[9]	Duddu R, Bordas S, Moran B, Chopp D. A combined extended finite element and level set method for biofilm growth[J]. International Journal for Numerical Methods in Engineering,2008,74(5): 848-870.
[10]	Ji H, Chopp D, Dolbow J. A hybrid extended finite element/level set method for modeling phase transformations[J]. International Journal for Numerical Methods in Engineering,2002,54(8): 1209-1233.
[11]	Bordas S, Rabczuk T, Hung N X, Nguyen V P, Natarajan S. Strain smoothing in FEM and XFEM[J]. Computers & Structures,2010,88(23): 1419-1443.
[12]	Chen L, Rabczuk T, Bordas S P A, Liu G R, Zeng K Y, Kerfriden P. Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth[J]. Computer Methods in Applied Mechanics &Engineering,2012,209(324): 250-265.
[13]	ZHAO Xu-jun, Bordas S, QU Jian-min. A hybrid extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities[J]. Computational Mechanics,2013,52(6): 1417-1428.
[14]	Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing[J].International Journal for Numerical Methods in Engineering,1999,45(5): 602-620.
[15]	Yoo J W, Moran B, Chen J S. Stabilized conforming nodal integration in the natural-element method[J].International Journal for Numerical Methods in Engineering,2004,60: 861-890.
[16]	Liu G R. A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods[J].International Journal of Computational Methods,2008,5(2): 199-236.
[17]	Belytschko T, Mos N, Usui S, Parimi C. Arbitrary discontinuities in finite elements[J].International Journal for Numerical Methods in Engineering,2001,50(4): 993-1013.
[18]	Liu G R. A G space theory and weakened weak (W2) form for a unified formulation of compatible and incompatible methods: part I theory[J].International Journal for Numerical Methods in Engineering,2009,81(9): 1093-1126.
[19]	Freund L B.Dynamic Fracture Mechanics [M]. Cambridge: Cambridge University Press, 1990.
[20]	姜潮. 基于区间的不确定性优化理论与算法[D]. 博士学位论文. 长沙: 湖南大学机械与运载工程学院, 2008: 13-40.(JIANG Chao. Optimization theory and algorithm based on interval uncertainty[D]. PhD Thesis. Changsha: Hunan University, College of Mechanical and Vehicle Engineering, 2008: 13-40.(in Chinese))
[21]	JIANG Chao, HAN Xu, LIU Gui-ping. A nonlinear interval number programming method for uncertain optimization problems[J].European Journal of Operational Research,2008,188(1): 1-13.
[22]	JIANG Chao, HAN Xu, LIU Gui-ping. Uncertain optimization of composite laminated plates using a nonlinear interval number programming method[J]. Computers and Structures,2008,86(17): 1696-1703.