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A reaction–diffusion level set method for stress-constrained topology optimization with precise volume control
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DOI：10.1016/j.compstruc.2025.108073.png)
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Abstract
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This paper presents a reaction–diffusion equation (RDE) driven level set method (LSM) for topology optimization (TO) that enforces both stress and volume constraints simultaneously. The method introduces a locally activated stress penalty that operates only where the allowable limit is exceeded, eliminating the need for global aggregation and improving fidelity in hot-spot regions. A refined in-element triangulation strategy provides accurate volume fractions without remeshing, enabling precise volume tracking on fixed structured meshes. Structural evolution is governed by RDE, enabling hole nucleation during optimization and eliminating the need for level set reinitialization. Numerical experiments in 2D and 3D demonstrate that the proposed method yields designs that satisfy the prescribed local stress limits and target volume fractions while achieving stable, efficient convergence.
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