基于扩散张量偏微分方程的拓扑优化过滤方法

为了有效抑制拓扑优化结果中出现的数值不稳定现象,提出了基于扩散张量偏微分方程的初边值模型,考虑Neumann边界条件,实现边界扩展,并采用有限差分法求解。将有限差分模型与拓扑优化循环相融合,分别实现单元密度和目标函数灵敏度的过滤处理。算例验证了方法的有效性与灵活性,结果表明：目标函数灵敏度过滤方法能保持边界清晰度,但需要较多的过滤迭代次数;单元密度过滤方法的计算效率较高,但结果边界模糊。

Filters in Topology Optimization Based on Diffusion Tensor of Partial Differential Equations

In order to eliminate numerical instabilities efficiently in topology optimization, an initial-boundary value model of diffusion tensor of partial differential equations was established. Together with Neumann conditions to expand boundary, finite difference method was used to solve the model. The model integrated smoothly into topology optimization circle, and was aimed at element density and objective function sensitivity for filtering operations respectively. At last, the examples checked the effectiveness and flexibility of the two methods. Results illustrate that objective function sensitivity filtering can keep boundary clarity, but needs more filtering iteration number. However element density filtering owns high computational filtering efficiency, but has vague boundary.