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<p>This article presents a novel univariate mapping-based material interpolation method for density-based multi-material topology optimization. The proposed multi-material interpolation model maps the single-variable design field to the multi-variable physical field based on a smoothed Heaviside projection. Multi-material topology optimization problems can be efficiently addressed, and definitive binary results (0 or 1) can be obtained for each candidate material through a parameter continuation scheme. The proposed interpolation function and its first derivative demonstrate continuity, enabling their application in gradient-based optimization algorithms. The issues associated with false material coexistence and material envelope in single-variable interpolation schemes for multiple materials are examined, and a new filtering technique is developed to mitigate these problems. An educational MATLAB code is presented for 2D and 3D multi-material topology optimization problems utilizing the proposed univariate mapping-based interpolation scheme. This document presents a solution for the topology optimization of multiple materials aimed at minimum compliance while adhering to a total mass constraint. It includes details on the multi-material interpolation model, specialized filtering techniques, optimization iterations, and post-processing procedures. Benchmark numerical examples involving multiphase materials illustrate the effectiveness and efficiency of the code, highlighting the impact of parameters on the optimization results. The outcomes obtained by the proposed approach are compared with those of other state-of-the-art methods documented in the literature. The appendix section of this article includes the educational MATLAB code, which is also accessible on the website (<a href="https://github.com/TopJay/SVMMTO">https://github.com/TopJay/SVMMTO</a>) for further learning.</p>

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An easy-to-use univariate mapping-based method for multi-material topology optimization with implementation in MATLAB

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Wenjie Ding

摘要

This article presents a novel univariate mapping-based material interpolation method for density-based multi-material topology optimization. The proposed multi-material interpolation model maps the single-variable design field to the multi-variable physical field based on a smoothed Heaviside projection. Multi-material topology optimization problems can be efficiently addressed, and definitive binary results (0 or 1) can be obtained for each candidate material through a parameter continuation scheme. The proposed interpolation function and its first derivative demonstrate continuity, enabling their application in gradient-based optimization algorithms. The issues associated with false material coexistence and material envelope in single-variable interpolation schemes for multiple materials are examined, and a new filtering technique is developed to mitigate these problems. An educational MATLAB code is presented for 2D and 3D multi-material topology optimization problems utilizing the proposed univariate mapping-based interpolation scheme. This document presents a solution for the topology optimization of multiple materials aimed at minimum compliance while adhering to a total mass constraint. It includes details on the multi-material interpolation model, specialized filtering techniques, optimization iterations, and post-processing procedures. Benchmark numerical examples involving multiphase materials illustrate the effectiveness and efficiency of the code, highlighting the impact of parameters on the optimization results. The outcomes obtained by the proposed approach are compared with those of other state-of-the-art methods documented in the literature. The appendix section of this article includes the educational MATLAB code, which is also accessible on the website (https://github.com/TopJay/SVMMTO) for further learning.