XFEM Programming for Four Nodes Isoparametric Element and Its Application in Crack Problems
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摘要: 虽然扩展有限元法(XFEM)在处理裂纹等这种强不连续性问题时理论上是成功的,得到很快的发展和广泛的应用,但在实际应用中,尚存在许多技术问题如网格密度等值得研究。为了验证和提高XFEM在计算裂纹应力强度因子上的有效性,针对四结点等参元推导了XFEM的相应公式,编写了用于计算含裂纹板裂纹尖端应力强度因子的完整的Matlab程序。针对典型含裂纹平板,采用本文编写的程序计算了裂纹尖端应力强度因子,与采用传统有限元法的结果进行了对比分析,并进一步研究了网格参数,对XFEM结果的影响。结果表明,XFEM在计算裂纹尖端应力强度因子上有很好的计算精度,但其计算结果对网格密度较为敏感,在实际应用中应当引起重视。Abstract: It was successful that extended finite element method(XFEM) was theoretically applied to the strong discontinuity problems such as cracks so that the development and application of the method are being increased rapidly.However,in practical applications,there are still many technical issues such as the mesh density to be studied.In order to verify and improve the effectiveness of XFEM on the calculation of crack stress intensity factor,the corresponding formula of XFEM with four-node isoparametric element was derived and a complete Matlab code was also edited aiming at calculating the crack tip stress intensity factor of a plate with crack.Based upon the program,the crack tip stress intensity factors for a typical plate with crack were calculated and the results by XFEM were compared with those by the traditional finite element method(FEM).The effect of the mesh parameters on the XFEM results was further studied.The study shows that XFEM has a very good accuracy in the calculation of crack tip stress intensity factor,but the results by XFEM are sensitive to the density of the mesh,this should be paid more attention to practical applications.
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Key words:
- XFEM /
- crack tip /
- stress intensity factor /
- four nodes isoparametric element /
- mesh density
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[1] Moes N,Dolbow J,Belytschko T. A finite element method forcrack growth without remeshing[J].International Journal forNumerical Methods in Engineering,1999,46:131-150 [2] Liu X Y,Xiao Q Z,Karihaloo B L. XFEM for direct evaluationof mixed mode SIFs in homogeneous and bi-materials[J].International Journal for Numerical Methods in Engineering,2004,59:1103-1118 [3] Moes N,Belytschko T. Extended finite element method for cohe-sive crack growth[J].Engineering Fracture Mechanics,2002(69):813-833 [4] Daux C,Moes N,Dolbow J,Sukumar N Belytschko T. Arbi-trary branched and intersecting cracks with the extended finite el-ement method[J].International Journal for Numerical Meth-ods in Engineering,2000,48:1741-1760 [5] Sukumar N,Moes N,Moran B,Belytschko T. Extended finiteelement method for three-dimensional crack modeling[J].International Journal for Numerical Methods in Engineering,2000,48(11):1549-1570 [6] Moes N,Gravouil A,Belytschko T. Non-planar 3D crack growthby the extended finite element and level sets-part I:mechanicalmodel[J].International Journal for Numerical Methods inEngineering,2002,53(11):2549-2568 [7] Xiao Q Z,Karihaloo B L. Improving the accuracy of XFEM cracktip fields using higher order quadrature and statically admissiblestress recovery[J].International Journal for NumericalMethods in Engineering,2005,66(9):1378-1410 [8] Nshima T,Omoto Y,Tani S. Stress intensity factor analysisof interface cracks using X-FEM[J].International Journal forNumerical Methods in Engineering,2003,56:1151-1173 [9] 李录贤,王铁军. 扩展有限元及其应用[J].力学进展,2005,35(1):5-20 [10] Sukumar N,Pr6vost J H. Modeling quasi-static crack growth withthe extended finite element method.Part I:computer implemen-tation[J].International Journal of Solids and Structures,2003,40:7513-7537.
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