Work

PolyHeat2D: A method for size-constrained topology optimization of steady-state heat conduction in arbitrary design domains

Year: 2026

Type: article

Abstract: In additive manufacturing, controlling both minimum and maximum feature sizes is critical to satisfy fabrication resolution and prevent excessively large solid regions. However, existing topology optimization methods for heat conduction problems relying on regular meshes lack efficient integration of simultaneous minimum and maximum length controls, particularly for complex geometries. This paper presents a method for the size-constrained topology optimization of steady-state heat conduction in arbitrary two-dimensional design domains by utilizing polygonal finite element meshes. The proposed framework integrates a Voronoi-based polygonal mesh generator with the counter smoothing via a moving average filter, enabling robust discretization of complex geometries. A void insertion scheme with an annular test region is incorporated to enforce the size constraint, while a power mean aggregation strategy gathers numerous local size constraints into a single global measure to reduce the computational time. In contrast to a standard circular test region, the annular test region avoids unnecessary hollow circles. The objective function in topology optimization aims to minimize the thermal compliance based on a three-field density method. The effectiveness of the proposed method is demonstrated through two-dimensional examples involving both regular and irregular geometric shapes. The resulting topological configurations and additive manufacturing prototypes confirm that the proposed method effectively prevents overly bulky features while preserving manufacturability. The power mean aggregation strategy reduces the constraint-handling time from 3.8 s to 0.2 s per iteration, decreasing its share of the per-iteration cost from 40% to 3%. Imposing length control increases thermal compliance by 15.5% to 32.8% across various geometries, which is a necessary trade-off for preventing oversized features. The influences of key parameters in the adopted aggregation strategy on both topological configuration and objective function are also investigated. Compared with existing studies, this work provides a powerful tool for designing efficient and size-constrained thermal components with complex geometries, and demonstrates the advantages of polygonal meshes over conventional structured quadrilateral meshes in terms of geometric flexibility, accuracy and numerical stability. • A novel framework enables robust topology optimization for irregular geometries. • A power mean aggregation with annular test regions reduces computational cost. • A systematic parameter analysis offers insights into size constraints. • Validation through optimized designs and additive manufacturing prototypes.

Source: Applied Thermal Engineering

DOI: 10.1016/j.applthermaleng.2026.131081

Authors: Jian Wang, Qiang Gao, Zhe Ding, Wei-Hsin Liao

Institutions: Chinese University of Hong Kong, Southeast University, Wuhan University of Science and Technology

Language: English

Topic: Topology Optimization in Engineering

Subfield: Civil and Structural Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,660

Funders: Research Grants Council, University Grants Committee, Chinese University of Hong Kong, National University's Basic Research Foundation of China, Fundamental Research Funds for the Central Universities