The polygonal scaled boundary finite element method (PSBFEM) is a novel method integrating the standard scaled boundary finite element method (SBFEM) and the polygonal mesh technique. This work discusses developing a PSBFEM framework within the commercial finite element software Abaqus. The PSBFEM is implemented by the User Element Subroutine (UEL) feature of the software. The details on the main procedures to interact with Abaqus, defining the UEL element, and solving the stiffness matrix by the eigenvalue decomposition are present. Moreover, we also develop the preprocessing module and the postprocessing module using the Python script to generate meshes automatically and visualize results. Several benchmark problems from two-dimensional linear elastostatics are solved to validate the proposed implementation. The results show that PSBFEM-UEL has significantly better than FEM convergence and accuracy rate with mesh refinement. The implementation of PSBFEM-UEL can conveniently use arbitrary polygon elements by the polygon/quadtree discretizations in the Abaqus. The developed UEL and the associated input files can be downloaded from https://github.com/hhupde/PSBFEM-Abaqus.

中文翻译：

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PSBFEM-Abaqus：在 Abaqus 中为多边形缩放边界有限元方法开发用户单元子程序 (UEL)

多边形尺度边界有限元法（PSBFEM）是一种融合标准尺度边界有限元法（SBFEM）和多边形网格技术的新方法。这项工作讨论了在商业有限元软件 Abaqus 中开发 PSBFEM 框架。PSBFEM 由软件的用户元素子程序 (UEL) 功能实现。介绍了与 Abaqus 交互、定义 UEL 元素和通过特征值分解求解刚度矩阵的主要程序的详细信息。此外，我们还使用 Python 脚本开发了预处理模块和后处理模块，以自动生成网格并可视化结果。解决了二维线性弹性静力学的几个基准问题以验证所提出的实施方案。结果表明，PSBFEM-UEL 在网格细化方面具有明显优于 FEM 的收敛性和准确率。PSBFEM-UEL 的实现可以通过 Abaqus 中的多边形/四叉树离散化方便地使用任意多边形元素。开发的 UEL 和相关的输入文件可以从 https://github.com/hhupde/PSBFEM-Abaqus 下载。