An analytical model is proposed to evaluate the nodal force induced by a segment of dislocation upon an arbitrary shaped triangular element. This calculation is required in hybrid methods that associate dislocation dynamics to boundary or finite element to solve simultaneously the evolution of large ensembles of dislocations with complex boundary conditions. Nodal forces are defined as the triple integration of the unbalanced traction field induced by a straight dislocation upon the surface of the element. Following our previous approach (Queyreau et al 2014 Modelling Simul. Mater. Sci. Eng. 22 035004) on a simpler geometry and in the case of linear isotropic elasticity, triple integrals are solved by sequences of integration by parts that exhibit recurrence relations. The traction field is defined and finite everywhere even at the core of dislocations, thanks to the use of the non-singular stress expression formulated by Cai et al (2006 J. Mech. P...

中文翻译：

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非奇异位错在任意形状的三角形二次元上引起的牵引力的解析积分

提出了一个分析模型来评估由任意形状的三角形单元上的一段位错引起的节点力。在将位错动力学与边界或有限元相关联的混合方法中，需要进行此计算，以同时解决具有复杂边界条件的大位错集合的演化。节点力定义为由元件表面上的直位错引起的不平衡牵引场的三重积分。按照我们先前的方法（Queyreau等，2014 Modeling Simul。Mater。Sci。Eng。22 035004），在更简单的几何形状上以及在线性各向同性弹性的情况下，三元积分通过表现递归关系的零件的积分序列求解。