使用铣削约束进行拓扑优化

2023年 2月 1日

铣削约束

\theta_f/R_\mathrm{mil} &=& \hat{m}_\mathrm{mil}^i \cdot \nabla \theta_m^i, \quad \theta_m = \left[{\sum}_{i=1}^n ((\theta_m^i)^{-p_\mathrm{mil}})/n\right]^{-1/p_\mathrm{mil}} \\

\theta &=& \frac{\tanh(\beta(\theta_m-\theta_\beta))+\tanh(\beta\theta_\beta)}{\tanh(\beta(1-\theta_\beta))+\tanh(\beta\theta_\beta)}

\theta_p &=& \theta_\mathrm{min}+(1-\theta_\mathrm{min})\theta^{p_\mathrm{SIMP}}

M=\rho V=\rho\int_\Omega \theta d\Omega

示例 3：轮辋

• 使用 12 个载荷工况而不是 1 个
• 扇区对称仅适用于设计（而不是物理场）
• 对流方程使用了线性离散化

https://comsol.wistia.com/medias/6ju19l1ox2?embedType=async&videoFoam=true&videoWidth=640&wmode=transparent
https://comsol.wistia.com/medias/qb5hn8rs7g?embedType=async&videoFoam=true&videoWidth=640&wmode=transparent

参考文献

1. L.C. Høghøj and E.A. Träff, “An advection-diffusion based filter for machinable designs in topology optimization,” Computer Methods in Applied Mechanics and Engineering, vol. 391, p. 114488, 2022; https://www.sciencedirect.com/science/article/pii/S0045782521007003