Two-Scale Concurrent Topology Optimization Method Based on Boundary Connection Layer Microstructure
Hongyu Xu1,*, Xiaofeng Liu1, Zhao Li1, Shuai Zhang2, Jintao Cui1, Zongshuai Zhou1, Longlong Chen1, Mengen Zhang1
1 School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang, China
2 College of Vehicle and Traffic Engineering, Henan University of Science and Technology, Luoyang, China
* Corresponding Author: Hongyu Xu. Email: 
Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.075413
Received 31 October 2025; Accepted 16 January 2026; Published online 04 February 2026
Abstract
In two-scale topology optimization, enhancing the connectivity between adjacent microstructures is crucial for achieving the collaborative optimization of micro-scale performance and macro-scale manufacturability. This paper proposes a two-scale concurrent topology optimization strategy aimed at improving the interface connection strength. This method employs a parametric approach to explicitly divide the micro-design domain into a “boundary connection region” and a “free design domain” at the initial stage of optimization. The boundary connection region is used to generate a connection layer that enhances the interface strength, while the free design domain is not constrained by this layer, thus fully exploiting the design potential of the material layout. During the optimization process, the solid isotropic material with penalization (SIMP) method is first used to optimize the material distribution in the free design domain, and filtering and projection techniques are employed to alleviate numerical instability and obtain a clear topological structure. Subsequently, the effective performance of the microstructure is calculated through homogenization and transferred to the macro-scale for global response analysis. Throughout the iterative process, the geometry of the connection layer remains unchanged, and only the free design domain is optimized, thereby achieving a balance between high performance and good manufacturability. The effectiveness of the proposed method is verified through numerical examples.
Keywords
Two-scale topology optimization; connectable microstructure; interface connectivity; boundary connection layer; SIMP method; homogenization theory
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