The surface effect of peridynamics seriously affects the accuracy of numerical results near the boundary. The fictitious node method can modify the surface effect of peridynamics, but the previous method (Le and Bobaru, 2018) is only applicable to problems with only stress boundary conditions. This paper proposes an extended fictitious node method for deriving the fictitious node displacement constraint equations that apply to the displacement boundary conditions, based on the corresponding equivalence of stress components along with the boundary normal and tangential directions on the left and right sides of the boundary node. Consequently, the extended fictitious node method can handle problems with mixed boundary conditions of stress and displacement constraints. Then, this method is verified through numerical examples with mixed boundary conditions. The results after the surface correction show good agreements with those of the finite element method or with analytical solutions.

近场动力学的表面效应严重影响边界附近数值结果的准确性。虚拟节点法可以修正近场动力学的表面效应，但之前的方法（Le and Bobaru, 2018）只适用于只有应力边界条件的问题。提出了一种扩展的虚拟节点方法，用于推导适用于位移边界条件的虚拟节点位移约束方程，基于边界节点左右两侧的边界法线和切线方向上应力分量的对应等价性。 . 因此，扩展虚拟节点法可以处理应力和位移约束的混合边界条件问题。然后，该方法通过具有混合边界条件的数值实例进行了验证。表面校正后的结果与有限元法或解析解的结果吻合良好。