This paper presents a steady-state and transient heat conduction analysis framework using the polygonal scaled boundary finite element method (PSBFEM) with polygon/quadtree meshes. The PSBFEM is implemented with commercial finite element code Abaqus by the User Element Sub-routine (UEL) feature. The detailed implementation of the framework, defining the UEL element, and solving the stiffness/mass matrix by the eigenvalue decomposition are presented. Several benchmark problems from heat conduction are solved to validate the proposed implementation. Results show that the PSBFEM is reliable and accurate for solving heat conduction problems. Not only can the proposed implementation help engineering practitioners analyze the heat conduction problem using polygonal mesh in Abaqus, but it also provides a reference for developing the UEL to solve other problems using the scaled boundary finite element method.

翻译：本文介绍了使用多边边形边距限制要素法(PSBFEM)与多边形/夸德树间带的多边形边界限制要素法(PSBFEM)的稳定状态和短暂热导分析框架。PSBFEM由用户元素次常规(UEL)特性使用商业限制要素代码Abaqus实施。框架的详细实施、UEL元素的定义和二元值分解解决坚硬度/质量矩阵。热导出的若干基准问题得以解决,以验证拟议的实施。结果显示PSBFEM在解决热导问题方面是可靠和准确的。拟议的实施不仅有助于工程从业人员利用Abaqus的多边形网格分析热导问题,而且还为开发UL提供了参考,以使用缩放的边框要素方法解决其他问题。