【摘要】 系统地给出了直接计算应力强度因子的扩展有限元法。该方法以常规有限元法为基础,利用单位分解法思想,通过在近似位移表达式中增加能够反映裂纹面的不连续函数及反映裂尖局部特性的裂尖渐进位移场函数,间接体现裂纹面的存在,从而无需使裂纹面与有限元网格一致,无需在裂尖布置高密度网格,也不需要后处理就可以直接计算出应力强度因子,并且大大简化了前后处理工作。最后通过两个简单算例验证了该方法的精度,分析了影响计算结果的因素,并与采用J积分计算的应力强度因子作了对比,得出了两种方法计算精度相当的结论。更多还原

【Abstract】 A method named as extended finite element method(XFEM) for directly evaluating stress intensity factors(SIFs) is presented.XFEM is based on the classical FEM and partition of unit method(PUM).Near a crack,the standard displacement approximation is enriched with discontinuous fields and the near tip asymptotic fields which present discontinuous displacement of crack surface and local property of the crack tip respectively.Thus,the crack surface can be presented indirectly and the SIFs can be calculated directly without the demand of making the crack surface associated to the mesh,without dense mesh near the crack tip and without post-processing.So,the pre-processes and postprocesses can be simplified greatly.The basic theory of XFEM for directly calculating SIFs is presented and the integral method for elements containing crack surfaces is improved.Finally,the accuracy of the method and influencing factors to results are analyzed by two typical examples.It is concluded that the results obtained by direct method are as good as by interaction integral.更多还原