线弹性断裂力学问题的扩展自然单元法

为了更加有效地求解线弹性断裂问题，提出了扩展自然单元法。该方法基于单位分解的思想，在自然单元法的位移模式中加入扩展项表征不连续位移场和裂纹尖端奇异场。通过水平集方法确定裂纹面和裂纹尖端区域，并基于虚位移原理推导了平衡方程的离散线性方程。由于自然单元法的形函数满足Kronecker delta函数性质，本质边界条件易于施加。混合模式裂纹的应力强度因子由相互作用能量积分方法计算。数值算例结果表明扩展自然单元法可以方便地求解线弹性断裂力学问题。

AN EXTENDED NATURAL ELEMENT METHOD FOR LINEAR ELASTIC FRACTURE PROBLEMS

In order to solve linear elastic fracture problems more effectively, an extended natural element method is proposed in this paper. Based on the ideas of partition of unity, enriched functions are added to the displacement mode of the natural element method in order to characterize the discontinuous displacement field along crack face and stress singularity around the crack tip. The level set method is employed to determine the crack surface and the crack tip region. The discrete linear equation of the equilibrium equation is derived by the virtual displacement principle. The shape function of the natural element method satisfies the Kronecker delta property and thus it is very convenient to impose the essential boundary conditions. The interaction integral method is then utilized to calculate the mixed-mode stress intensity factors. Several numerical examples are presented to demonstrate that the proposed method can deal with linear elastic fracture problems conveniently.