In discrete dislocation dynamics frameworks for finite samples, the evaluation of surface tractions caused by dislocations requires special attention to capture the contributions of dislocations piercing through the surface. Here we focus on this aspect only, and the convergence of an empirically improved Gauss integration and the Duffy and Duffy distance integration schemes commonly used for 1/r singularities, is investigated for a finite element surface area. It is found, that traction from a dislocation, using singular segment stress fields, can be integrated with an error smaller than 1% with the distance Duffy integration using a total of 48 integration points only. This scheme was tested for a wide range of dislocation Burgers vectors and glide plane orientations with respect to the surface. Furthermore the FEM nodal forces behave smoothly during the motion of exit point of the dislocation (the singular point) to a neighbouring surface element in the mesh.

在有限样本的离散位错动力学框架中，由位错引起的表面牵引力的评估需要特别注意以捕获贯穿表面的位错的贡献。在这里，我们仅关注此方面，并且经验地改进了高斯积分以及通常用于1 / r的Duffy和Duffy距离积分方案的收敛研究了有限元表面积的奇异性。结果发现，使用距离奇数段应力场，可以使用距离Duffy积分（总共使用48个积分点）以小于1％的误差对位错产生的牵引力进行积分。测试了该方案的各种位错Burgers矢量和相对于表面的滑行平面方向。此外，FEM节点力在位错的出口点（奇异点）运动到网格中相邻表面元素的过程中表现出平稳的行为。