基于动态高斯滤波的拓扑优化灵敏度过滤方法

Topology optimization method based on dynamic Gaussian sensitivity filtering

为解决拓扑优化中出现的边界模糊问题,提出一种结构拓扑优化灵敏度过滤的动态高斯滤波方法。该方法的主要思想是:随着拓扑优化的进行,基于结构离散性能指标减小高斯函数标准差的值,即降低周围单元对中心单元的影响。结合固体各向同性惩罚微结构模型(SIMP),通过经典算例验证了该灵敏度过滤方法的可行性。数值实验结果表明:基于动态高斯滤波的灵敏度过滤方法,不仅可以消除棋盘格和网格依赖性等数值不稳定现象,还可以避免出现“边界扩散”现象,使拓扑优化结构具有清晰的边界;此外,该方法还可加快拓扑优化的收敛速度,提高拓扑优化的稳定性。

To solve the problem of boundary blurring in topology optimization,a dynamic Gaussian sensitivity filtering method for structural topology optimization was proposed.The main idea of the method was to reduce the value of the standard deviation of Gaussian function with the progress of topology optimization,which was to reduce the influence of surrounding elements on the central element based on the discrete performance index of structure.Combining with the Solid Isotropic Microstructures with Penalization model(SIMP),the classic examples were presented to demonstrate the feasibility of the proposed method.The numerical experiment results showed that the sensitivity filtering method could not only eliminate numerical instability phenomena such as checkerboard patterns and mesh dependence,but also avoid the phenomenon of"boundary diffusion",which made the topology optimization structure had a clear boundary.In addition,the method could also accelerate the convergence speed and improve the stability of topology optimization.