基于Fourier-TOuNN的鲁棒性拓扑优化设计

为推广拓扑优化设计方法的工程应用，需要在设计过程中考虑结构鲁棒性以应对实际工程荷载的随机性。本文基于神经网络提出了鲁棒性结构拓扑优化设计的高效方法。该方法通过优化Fourier-TOuNN神经网络的权值更新描述结构拓扑的密度变量，并引入随机荷载下结构柔顺度平均值和标准差的加权总和作为目标函数，从而定义了随机荷载下的结构鲁棒性优化问题。利用神经网络的自动反向微分功能，实现了优化过程中灵敏度的直接求解。借助Fourier-TOuNN细部尺寸可控特性，可在结构中生成细小支撑以抵抗随机荷载。数值算例表明，采用本文提出的方法可以高效地获得鲁棒性稳健的优化设计结果。

Robust topology optimization of structures subjected to random loads using the Fourier-TOuNN

To promote the engineering application of topology optimization,it is imperative to consider the randomness of structural loads often encountered in practical scenarios.In this paper,an efficient framework for robust structural topology optimization based on the neural network is developed,which updates the density variable describing the structural topology by optimizing the weights of the Fourier-TOuNN neural network.In the developed framework,the weighted sum of the mean and standard deviation of the structural compliance under random loads is introduced as the objective function,thereby defining the structural robustness under random loads.Using the automatic reverse differentiation function of the neural network,the automatic derivation of the sensitivities in the optimization process can be realized.With the controllablility of local of the Fourier-TOuNN,small auxiliary components can be generated in the structure to withstand random loads.Numerical examples show that robust structural designs can be efficiently obtained by using the developed framework.