一种求解三维热传导问题的多面体比例边界有限元方法
A polyhedral scaled boundary finite element method solving three-dimensional heat conduction problems
AI总结：
本文提出一种基于Wachspress形函数的多面体比例边界有限元方法（PSBFEM），结合多边形离散化与八叉树网格技术，在ABAQUS中实现稳态和瞬态热传导分析，较传统FEM具有更高精度和计算效率。
摘要：
在本研究中，我们推导了用于热传导问题的三维比例边界有限元公式。通过引入Wachspress形函数，提出了一种多面体比例边界有限元方法（PSBFEM），以解决复杂几何体中的热传导挑战。为应对传统方法的复杂性，本工作引入了多边形离散化技术，简化了多面体网格的拓扑结构，并有效整合了多面体网格与八叉树网格，从而减少了单元面的数量，提高了网格对复杂形状的适应性。所开发的公式支持稳态和瞬态热传导分析，并通过用户自定义单元（UEL）在ABAQUS中实现。通过一系列数值算例，验证了所提方法的精度和收敛性。结果表明，随着网格细化，PSBFEM始终比有限元法（FEM）获得更高的精度。多面体单元为复杂模拟提供了一种计算高效的解决方案，显著降低了计算成本。此外，通过利用八叉树网格父单元加速技术，PSBFEM的计算效率超过了FEM。
英文摘要：
In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to address heat conduction challenges in complex geometries. To address the complexity of traditional methods, this work introduced polygonal discretization techniques that simplified the topological structure of the polyhedral mesh and effectively integrated polyhedral and octree meshes, thereby reducing the number of element faces and enhancing mesh efficiency to accommodate intricate shapes. The developed formulation supported both steady-state and transient heat conduction analyses and was implemented in ABAQUS through a user-defined element (UEL). Through a series of numerical examples, the accuracy and convergence of the proposed method were validated. The results indicated that the PSBFEM consistently achieved higher accuracy than the FEM as the mesh was refined. The polyhedral elements offered a computationally efficient solution for complex simulations, significantly reducing computational costs.Additionally, by utilizing the octree mesh parent element acceleration technique, the computational efficiency of PSBFEM surpassed that of the FEM.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
