Steady-state and transient thermal stress analysis using a polygonal finite element method

TL;DR

This paper introduces a polygonal finite element method (PFEM) using Wachspress basis functions for efficient and accurate thermal stress analysis in complex two-dimensional geometries, with improved computational performance.

Contribution

The work develops a novel PFEM with Wachspress basis functions and a quadtree acceleration strategy, enhancing geometric flexibility and computational efficiency in thermal stress analysis.

Findings

PFEM achieves high accuracy and convergence in benchmark tests.

The method reduces computational cost significantly compared to traditional FEM.

PFEM effectively handles complex geometries and multi-scale problems.

Abstract

This work develops a polygonal finite element method (PFEM) for the analysis of steady-state and transient thermal stresses in two dimensional continua. The method employs Wachspress rational basis functions to construct conforming interpolations over arbitrary convex polygonal meshes, providing enhanced geometric flexibility and accuracy in capturing complex boundary conditions and heterogeneous material behavior. A quadtree-based acceleration strategy is introduced to significantly reduce computational cost through the reuse of precomputed stiffness and mass matrices. The PFEM is implemented in ABAQUS via a user-defined element (UEL) framework. Comprehensive benchmark problems, including multi-scale and non-matching mesh scenarios, are conducted to verify the accuracy, convergence properties, and computational efficiency of the method. Results indicate that the proposed PFEM offers notable advantages over conventional FEM in terms of mesh adaptability, solution quality, and runtime performance. The method shows strong potential for large-scale simulations involving thermal-mechanical coupling, complex geometries, and multi-resolution modeling.