基于扩展有限元法计算二维应力强度因子
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摘要
基于ABAQUS有限元分析平台和UEL用户自定义单元接口,采用Matlab编制了扩展有限元的分析程序,对单边裂纹有限板条试件进行了扩展有限元模拟,并用位移外推法计算了裂纹的应力强度因子,探讨了网格密度和积分区域尺寸以及积分点个数对计算应力强度因子精度的影响。数值结果表明:细化网格可以显著提高有限元的计算精度,但由于扩展有限元本身精度较高,细化网格对提高扩展有限元计算精度的效果不明显;合理确定富集单元积分区域范围以及增加积分点个数都可以提高计算精度。
An extended finite element analysis program(XFEM) is compiled by Matlab which based on finite element analysis platform ABAQUS and user-defined unit UEL. The extended finite element simulation of a striped specimen with single edge crack was carried out,and the stress intensity factor of crack on the specimen was calculated by displacement extrapolation method. The effects of mesh density,integral region size and the number of integral points on the stress intensity factor were discussed. Numerical results show that mesh refinement of classical finite element method can significantly improve the accuracy of the stress intensity factor. Due to high accuracy of extended finite element method,melioration of mesh refinement is not obvious for XFEM method. Determiningintegral region size and number of integration points reasonably can improve the calculation accuracy.
An extended finite element analysis program(XFEM) is compiled by Matlab which based on finite element analysis platform ABAQUS and user-defined unit UEL. The extended finite element simulation of a striped specimen with single edge crack was carried out,and the stress intensity factor of crack on the specimen was calculated by displacement extrapolation method. The effects of mesh density,integral region size and the number of integral points on the stress intensity factor were discussed. Numerical results show that mesh refinement of classical finite element method can significantly improve the accuracy of the stress intensity factor. Due to high accuracy of extended finite element method,melioration of mesh refinement is not obvious for XFEM method. Determiningintegral region size and number of integration points reasonably can improve the calculation accuracy.
引文
[1]朱锐,邓乾金.位移外推法在应力强度因子计算中的应用[J].机械工程与自动化,2013,112(2):190-191.
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[4]BELYTSCHKO T,GU L,LU Y Y.Fracture and crack growth by element free galerkin methods[J].Modelling and Simulation in Materials Science and Engineering,1994,2(3A):519-534.
[5]BOUCHARD P O,BAY F,CHASTEL Y.numerical modelling of crack propagation:automatic remeshing and comparison of different criteria[J].Computer Methods in Applied Mechanics and Engineering,2003,192(35):3887-3908.
[6]KHOEI A R,AZADI H,MOSLEMI H.Modeling of crack propagation via an automatic adaptive mesh refinement based on modi-fied superconvergent patch recovery technique[J].Engineering Fracture Mechanics,2008,75(10):2921-2945.
[7]BELYTSCHKO T,BLACKT.Elastic crack growth in finite elements with minimal remeshing[J].International Journal for Numerical Method in Engineering,1999,45:601-620.
[8]MOS N,DOLBOW J,BELYTSCHKO T.A finite element method for crack growth withoutremeshing[J].International Journal for Numerical Method in Engineering,1999,46:131-150.
[9]董玉文,余天堂,任青文.直接计算应力强度因子的扩展有限元法[J].计算力学学报,2008,25(1):72-77.
[10]程靳,赵树山.断裂力学[M].北京:科学出版社,2006.
[11]HUANG Y,SONG Q,WANG K,et al.Study on stress intensity factor of two dimensional unilateral crack based on finite element method[C]//2016 International Conference on Architectural Engineering and Civil Engineering.Paris,France:Atlantis Press,2016.
[12]中国航空研究院.应力强度因子手册[M].北京:科学出版社,1993.
[13]龙靖宇,王宏波.基于有限元法的二维裂纹应力强度因子研究[J].武汉科技大学学报,2005,28(3):244-246.
[14]余天堂.扩展有限元法的数值方面[J].岩土力学,2007,129(S1):305-310.
[2]茹忠亮,申崴.扩展有限元法求解应力强度因子[J].河南理工大学学报(自然科学版),2012,31(4):459-463.
[3]PORTELA A,ALIABADI M H,ROOKE D P.The dual boundary element method:Effective implementation forcrack problems[J].International Journal for Numerical Methods in Engineering,1992,33(6):1269-1287.
[4]BELYTSCHKO T,GU L,LU Y Y.Fracture and crack growth by element free galerkin methods[J].Modelling and Simulation in Materials Science and Engineering,1994,2(3A):519-534.
[5]BOUCHARD P O,BAY F,CHASTEL Y.numerical modelling of crack propagation:automatic remeshing and comparison of different criteria[J].Computer Methods in Applied Mechanics and Engineering,2003,192(35):3887-3908.
[6]KHOEI A R,AZADI H,MOSLEMI H.Modeling of crack propagation via an automatic adaptive mesh refinement based on modi-fied superconvergent patch recovery technique[J].Engineering Fracture Mechanics,2008,75(10):2921-2945.
[7]BELYTSCHKO T,BLACKT.Elastic crack growth in finite elements with minimal remeshing[J].International Journal for Numerical Method in Engineering,1999,45:601-620.
[8]MOS N,DOLBOW J,BELYTSCHKO T.A finite element method for crack growth withoutremeshing[J].International Journal for Numerical Method in Engineering,1999,46:131-150.
[9]董玉文,余天堂,任青文.直接计算应力强度因子的扩展有限元法[J].计算力学学报,2008,25(1):72-77.
[10]程靳,赵树山.断裂力学[M].北京:科学出版社,2006.
[11]HUANG Y,SONG Q,WANG K,et al.Study on stress intensity factor of two dimensional unilateral crack based on finite element method[C]//2016 International Conference on Architectural Engineering and Civil Engineering.Paris,France:Atlantis Press,2016.
[12]中国航空研究院.应力强度因子手册[M].北京:科学出版社,1993.
[13]龙靖宇,王宏波.基于有限元法的二维裂纹应力强度因子研究[J].武汉科技大学学报,2005,28(3):244-246.
[14]余天堂.扩展有限元法的数值方面[J].岩土力学,2007,129(S1):305-310.