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<p>This paper presents compact and educational Matlab implementations for integrated topology optimization of functionally graded cellular structures in 2D and 3D. The method combines a modified Solid Isotropic Material with Penalization (SIMP) scheme with computational homogenization and a multiple-variable cutting (M-VCUT) level set method to jointly optimize macroscopic topology and microscopic configurations. To avoid repeated homogenization, an offline database is constructed to store homogenized equivalent elastic tensors and queried during optimization. This ensures computational efficiency while enabling continuous microstructural grading. The framework extends the classic 88-line SIMP code to a multiscale setting. Our contributions are: (1) offline generation of homogenized parameters for representative microstructures, (2) a code architecture for integrated optimization for functionally graded cellular structures (top88_2D.m, top88_3D.m) and (3) explicit geometric reconstruction (shapestore_2D.m, shapestore_3D.m) to generate optimized cellular structure. Numerical examples demonstrate the effectiveness of the proposed framework for compliance minimization. The open-source Matlab codes provide a practical and accessible platform for research and education in graded cellular materials and multiscale topology optimization.</p>

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Matlab code for macro-micro integrated topology optimization of cellular structure with data-driven M-VCUT level set method

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Yu Guo,
  • Hui Liu

摘要

This paper presents compact and educational Matlab implementations for integrated topology optimization of functionally graded cellular structures in 2D and 3D. The method combines a modified Solid Isotropic Material with Penalization (SIMP) scheme with computational homogenization and a multiple-variable cutting (M-VCUT) level set method to jointly optimize macroscopic topology and microscopic configurations. To avoid repeated homogenization, an offline database is constructed to store homogenized equivalent elastic tensors and queried during optimization. This ensures computational efficiency while enabling continuous microstructural grading. The framework extends the classic 88-line SIMP code to a multiscale setting. Our contributions are: (1) offline generation of homogenized parameters for representative microstructures, (2) a code architecture for integrated optimization for functionally graded cellular structures (top88_2D.m, top88_3D.m) and (3) explicit geometric reconstruction (shapestore_2D.m, shapestore_3D.m) to generate optimized cellular structure. Numerical examples demonstrate the effectiveness of the proposed framework for compliance minimization. The open-source Matlab codes provide a practical and accessible platform for research and education in graded cellular materials and multiscale topology optimization.