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| 基于带通过滤的等体积拓扑优化方法 |
| Volume-equalizing Optimization Method Based on Band-pass Filter |
| 投稿时间：2023-09-26 修订日期：2023-11-20 |
| DOI： |
| 中文关键词: 拓扑优化 尺寸控制 过滤方法 |
| 英文关键词:topology optimization size control filtering method |
| 基金项目: |
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| 中文摘要: |
| 带通过滤是拓扑优化中一种基于过滤技术的新型尺寸控制方法。带通过滤会出现负数密度变量，需要采用Heaviside密度映射方法对物理密度进行映射，这会使得优化过程中体积振荡控制难度加大。为此，本文提出了一种等体积拓扑优化格式，该方法通过调整非线性映射函数中的参数，以保证体积约束在优化过程中事先满足，可减少非线性映射所导致的收敛振荡。文中给出了该方法的优化列式，并推导了目标函数的敏度。采用不同过滤参数和非线性映射参数下的优化算例，比较了该方法和原带通过滤方法的优化结果、收敛过程和计算时间。结果表明，该方法相比于原带通过滤方法收敛更加稳定，并且优化效率大幅提高。 |
| 英文摘要: |
| Band-pass filter is a novel method for size controlling technology in topology optimization. It will cause negative variables after filtering, so that the Heaviside projection method is necessary, which may leads the volume oscillation is hard to control during the optimization procedure. A Volume-equalizing optimization method is proposed in this paper. This new method can alleviate the oscillating problem during optimization iteration due to the presence of nonlinear projection function, which is achieved by adjust the parameter of the nonlinear projection function to a value at which volume constraint can be meet in advance. Formulation of the new method and derivation of objective function’s sensitivity are presented. Numerical examples in which parameters from both band-pass filter and nonlinear projection function varies are analyzed by the new method and the original method. Optimization results, iteration history and computational time are compared between these two methods. Comparison results show that the present method can promote optimization efficiency and ensure the stability of iteration history. |
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