Abstract
This paper presents a multiscale level set topology optimization method for the design of graded cellular structures. The micro-scale level set-based prototype microstructure is periodically repeated to constitute a basic structure, which is cut by the macro-scale level set surface to generate the progressively-changing cellular structure. In the proposed method, the level set functions evolve in both scales, and then the configuration-optimized cellular microstructures are distributed in a well-arranged graded pattern. Due to the high-order continuity of parameterized level set function, the adjacent cellular microstructures connect to each other smoothly. For bridging different scales, the effective properties of microstructures are calculated by the numerical homogenization method. By studying the relation of microstructural elasticity tensors to the level set functions of both scales, the mechanical property and sensitivity analysis for cellular microstructure at an arbitrary position can be estimated effectively. Numerical examples demonstrate that the proposed method can customize both the configurations and distributions for graded cellular structures with favourable continuity.
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This work was supported by the National Key R&D Program of China (2018YFB1700803, 2018YFB1700804, 2020YFB1708300), the National Natural Science Foundation of China (52005192) and the Fundamental Research Funds for the Central Universities (HUST: 500310 0089).
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This work is built on parameterized level set topology optimization and inverse homogenization method. The opening source codes are presented in the related references. Therefore, the results can be replicated by implementing the formulas in this study.
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Yu, C., Wang, Q., **a, Z. et al. Multiscale topology optimization for graded cellular structures based on level set surface cutting. Struct Multidisc Optim 65, 32 (2022). https://doi.org/10.1007/s00158-021-03097-6
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DOI: https://doi.org/10.1007/s00158-021-03097-6