四结点等参元XFEM程序设计及在裂纹问题中的应用

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。%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.