A polyhedral scaled boundary finite element method solving three-dimensional heat conduction problems

TL;DR

This paper introduces a polyhedral scaled boundary finite element method for 3D heat conduction problems, improving accuracy and efficiency in complex geometries through innovative mesh techniques and implementation in ABAQUS.

Contribution

The study develops a novel polyhedral scaled boundary finite element formulation with polygonal discretization and octree meshes, enhancing accuracy and computational efficiency over traditional FEM.

Findings

Higher accuracy than FEM with mesh refinement

Reduced computational costs using octree mesh acceleration

Effective handling of complex geometries in heat conduction simulations

Abstract

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.