断裂力学问题的杂交边界点方法

STUDY ON THE HYBRID BOUNDARY NODE METHOD IN FRACTURE MECHANICS

提出了一种求解断裂力学的新的边界类型无网格方法-杂交边界点法.以修正变分原理和移动最小二乘近似为基础,同时具有边界元法和无网格法的优良特性,求解时仅仅需要边界上离散点的信息.该文将杂交边界点方法应用到弹性断裂问题中,将移动最小二乘方法中的基函数扩充,能更好的模拟裂纹尖端应力场的奇异性,推导了求解断裂力学的杂交边界点法方程,与传统的无网格方法相比,文中方法具有后处理简单,计算精度高的优点.数值算例表明了该方法的稳定性和有效性.

A boundary-type meshless method, named hybrid boundary node method （Hybrid BNM）, is proposed for solving fracture mechanics problems in this paper, which is based on the modified variational principle and moving least square （MLS） approximation. This method possesses the advantages of both BEM and meshless methods. Only random distributed nodal points on the boundary of the domain under consideration are required. In this paper, the Hybrid BNM is applied in fracture mechanics. Expansion of the basis functions is conducted for simulating the singularity of stress fields at crack-tips and the corre- sponding Hybrid BNM formulations are presented. Comparison with the other meshless methods shows that the present one possesses many advantages such as simple post-process and higher accuracy. Numerical examples have shown high accuracy and high convergence rates of the presented scheme.