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A multi-material level set method using logical functions for phase controlling with the reaction–diffusion level set technique
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DOI：10.1007/s00158-026-04381-z.png)
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Abstract
En 中文
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.
Keywords:
Logical operation
Multi-material
Reaction–diffusion equation
Level set method
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4.8K
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