In this work, an edge-based smoothed finite element method (ES-FEM) is embedded into the commercial software ABAQUS by using user defined element subroutines (Implicit/UEL, Explicit/VUEL). Unstructured meshes (i.e. triangular and tetrahedral elements) are employed in the framework due to their good geometric adaptability and the advantages of being automatically generated in the software. In ES-FEM, smoothing domains are further constructed associated with edges of triangular or tetrahedral elements. Linear and no-linear material models are included for static, free vibration, and large deformation analysis. Several numerical examples for predicting displacements, eigenvalues, and forging forming process are implemented. Results illustrated that the ES-FEM by using UEL and VUEL presents preciser than traditional finite element method (FEM), temporally stable, and can overcome the difficulties such as mesh distortion when the FEM is solving large deformation problems such as forging. It is valuable to embed the excellent numerical models, for example ES-FEM, into the commercial software since engineers can use it conveniently without professional knowledge. In this work, the detailed procedures are provided for the implementation of ES-FEM in UEL and VUEL, including pre-processing, post-processing and subroutine writing processes.

在这项工作中，通过使用用户定义的元素子例程（Implicit / UEL，Explicit / VUEL），将基于边缘的平滑有限元方法（ES-FEM）嵌入到商业软件ABAQUS中。非结构网格（即三角形和四面体元素）由于其良好的几何适应性以及在软件中自动生成的优点而被用于框架中。在ES-FEM中，进一步构造了与三角形或四面体元素的边缘关联的平滑域。包括线性和非线性材料模型，用于静态，自由振动和大变形分析。实现了几个用于预测位移，特征值和锻造成形过程的数值示例。结果表明，使用UEL和VUEL的ES-FEM比传统的有限元方法（FEM）更为精确，在时间上稳定，并且可以克服FEM解决诸如锻造之类的大变形问题时的困难（例如网格变形）。将出色的数值模型（例如ES-FEM）嵌入到商业软件中非常有价值，因为工程师无需专业知识即可方便地使用它。在这项工作中，提供了在UEL和VUEL中实施ES-FEM的详细过程，包括预处理，后处理和子例程编写过程。