Multiscale concurrent topology optimization for cellular structures with multiple microstructures subjected to dynamic load

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (12) : 53-64.

JIANG Xudong1，WU Hao1，TENG Xiaoyan2，XIONG Yeping3

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Abstract

Topology optimization is an effective tool to perform the structure-material integrated design of a lattice structure with multiple microstructures for improving its mechanical performances. This paper aims to propose the concurrent design method for the lattice structure at both macro- and micro-scales considering the connectivity between neighboring microstructures for the dynamic stiffness maximization problem. Firstly, the double Helmholtz smoothing and piecewise projection scheme is introduced to identify the spatial distribution of multiple microstructure blocks at macroscale. Then, we optimize the spatial distribution of various microstructures by ordered SIMP method following the effective mechanical properties obtained by homogenization method. Meanwhile, the different microstructural unit cells share the same topology description within their boundary regions to ensure the connectivity. Subsequently, we implement the sensitivity analysis by adjoint variable method based on the “discretize-then-differentiate” approach, such that the consistent sensitivities are obtained on the space-time discretized system. Finally, we formulate the dynamic compliance minimization problem under the constraint of material volume fractions, and present the multiscale concurrent topology optimization method for structures periodically filled with multiple microstructures. Numerical examples demonstrate that this approach has the potential to perform the concurrent microscopic design of multiple unit-cells and their macroscopic layout for improving the load-carrying capacity and ensuring the geometrical connectivity between neighboring unit-cells. This method offers a theoretical reference for design of highly loading porous structures.

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multi-scale concurrent topology optimization / multiple cellular structure / transient dynamics / connectable microstructures / numerical homogenization

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JIANG Xudong1, WU Hao1, TENG Xiaoyan2, XIONG Yeping3. Multiscale concurrent topology optimization for cellular structures with multiple microstructures subjected to dynamic load[J]. Journal of Vibration and Shock, 2024, 43(12): 53-64

References

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