Based on the Erdogan fundamental solutions for infinite cracked plates, a new hybrid boundary node method for linear fracture problems is proposed in this paper. The origin singular intensity factor for the Erdogan fundamental solutions is developed to overcome the singular when the field points are coincided with the source points, and no virtual source points are needed, a new scheme for calculating the origin singular intensity factor for the Erdogan fundamental solutions is developed. Based on the Erdogan fundamental solutions, the zero traction boundary condition on crack surfaces is naturally and strictly satisfied in this method, and no nodes are arranged on the crack surface in the entire calculation process. Based on the Erdogan fundamental solution of stress intensity factor for the mixed mode crack, the stress intensity factor of the present method can be easily interpolated by the Erdogan fundamental solutions. As a result, no complex scheme for calculating stress intensity factor is needed. Based on those theories and methods, the proposed method is further applied to analyze some linear crack problems, and the computational accuracy, convergence rate and the versatility of the present method are demonstrated in details.

基于无限裂纹板的埃尔多安基本解，提出了一种新的线性边界问题的混合边界节点方法。开发了Erdogan基本解的原点奇异强度因子，以克服场点与源点重合且不需要虚拟源点时的奇异点，这是一种计算Erdogan基本解的原点奇异强度因子的新方案被开发。该方法基于埃尔多安基本解，自然而严格地满足了裂纹表面的零牵引边界条件，并且在整个计算过程中，裂纹表面上没有布置任何节点。基于混合模式裂纹应力强度因子的埃尔多安基本解，本方法的应力强度因子可以通过埃尔多安基本解轻松插值。结果，不需要用于计算应力强度因子的复杂方案。基于这些理论和方法，将所提出的方法进一步应用于分析一些线性裂纹问题，并详细说明了该方法的计算精度，收敛速度和通用性。