基于扩展有限元的应力强度因子的位移外推法

针对平面裂纹问题,阐述了扩展有限元法的单元位移模式、推导了扩展有限元法的控制方程、介绍了特殊单元的数值积分技术.基于最小二乘法,建立了应力强度因子位移外推法的计算公式.利用MATLAB编写计算程序,对平面裂纹问题用扩展有限元法进行了计算.基于扩展有限元法的计算结果,分别利用位移外推法和相互作用积分法,对平面裂纹的应力强度因子进行了计算.计算结果表明,位移外推法比相互作用积分法能更方便和准确地计算平面裂纹的应力强度因子.

DISPLACEMENT EXTRAPOLATION METHOD FOR STRESS INTENSITY FACTOR BASED ON EXTENDED FINITE ELEMENT METHOD

The element displacement modes of the extended finite element method for plane crack problems are discussed in this paper. The governing equations for the extended finite element method are derived based on the principle of virtual work. The numerical integration technique is adopted for special elements. The displacement extrapolation method is formulated to calculate the stress intensity factor based on the least square method. The numerical computation programs are developed by using the MATLAB, and the numerical calculations are carried out by the extended finite element method for the problem of plane crack. Based on the results of the extended finite element method, the stress intensity factors of plane crack are calculated by the displacement extrapolation method and the interaction integral method, respectively. Numerical results show that with the displacement extrapolation method, the stress intensity factors can be obtained more easily and precisely than the interaction integral method.