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<p>Topology optimization for multi-material is a powerful tool for lightweight or complex structures that require more than one material with different properties. This paper presents a new approach, called Logical Operation-based Multi-Material Level Set (LO-MMLS), that extends the multi-material level set method by using Boolean functions, specifically the AND operation, to control material generation at level set intersections with reaction–diffusion equation. Each material phase is a separate definition from the level set functions, derived by combining logic functions, which clearly and precisely define materials and avoid duplication during material regeneration in optimization. This paper also incorporates a new hyperbolic tangent (tanh) function to control intermediate density values and improve design flexibility. Numerous computational examples demonstrate the new LO-MMLS method’s ability to optimize multi-material structures with clearly distributed material regions, improving stiffness performance by up to 9.37% compared to previous methods. At the same time, the proposed method also demonstrates high computational efficiency, with fast computation time and low resource usage.</p>

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A multi-material level set method using logical functions for phase controlling with the reaction–diffusion level set technique

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Loc Tan Le,
  • Tatacipta Dirgantara,
  • Lavi Rizki Zuhal,
  • Annisa Jusuf

摘要

Topology optimization for multi-material is a powerful tool for lightweight or complex structures that require more than one material with different properties. This paper presents a new approach, called Logical Operation-based Multi-Material Level Set (LO-MMLS), that extends the multi-material level set method by using Boolean functions, specifically the AND operation, to control material generation at level set intersections with reaction–diffusion equation. Each material phase is a separate definition from the level set functions, derived by combining logic functions, which clearly and precisely define materials and avoid duplication during material regeneration in optimization. This paper also incorporates a new hyperbolic tangent (tanh) function to control intermediate density values and improve design flexibility. Numerous computational examples demonstrate the new LO-MMLS method’s ability to optimize multi-material structures with clearly distributed material regions, improving stiffness performance by up to 9.37% compared to previous methods. At the same time, the proposed method also demonstrates high computational efficiency, with fast computation time and low resource usage.