数据驱动的曲面构件形状-拓扑协同优化方法

Data⁃driven shape⁃topology optimization method for curved shells

针对紧凑设计空间下曲面构件极致轻量化需求,提出一种数据驱动的曲面构件形状-拓扑协同优化方法,主要包括离线、在线和更新3个阶段。离线阶段中,首先通过拉丁超立方采样方法在设计空间内采样,并利用网格变形技术进行参数化建模,获得样本点对应的网格模型。然后对上述网格模型分别进行拓扑优化,获得优化后的应变能。基于上述步骤获得的样本数据,训练径向基函数代理模型,其中形状设计变量为输入,拓扑优化获得的应变能为输出。在线阶段中,将基于离线阶段获得的代理模型开展优化设计,采用协方差矩阵自适应进化策略来提高优化效率。更新阶段中,计算代理模型优化结果的真实响应,并将其加入样本数据集进行代理模型更新。最后,通过简支梁和航天器舱门算例开展算法验证。结果表明相比针对固定形状获得的拓扑优化结果,提出方法优化获得的应变能结果分别降低了20.08%和37.93%,表明提出方法具有更优的设计能力。

Due to the extreme lightweight requirements of surface components in compact design space,this paper proposed a data-driven shape-topology optimization method of curved shells,which consists of three stages,namely the offline stage,the online stage and the update stage.First,in the offline stage,the Latin hypercube sampling method is used to extract the sample points from the design space,and the mesh deformation technique is used for modeling to obtain the mesh model corresponding to the sample points.Then,topology optimization was carried out on the mesh models to obtain the optimized strain energy.Based on the sample data obtained in the above steps,the radial basis function surrogate model is trained,where the shape design variable is the input and the strain energy af⁃ter topology optimization is the output.In the online stage,optimization is carried out based on the surrogate model obtained in the offline stage,and the covariance matrix adaptive evolution strategy is adopted to improve the optimiza⁃tion efficiency.In the update stage,the real response of optimization results of the surrogate model is calculated and added to the sample dataset to update the surrogate model.Finally,the algorithm is verified by a simply supported beam and a spacecraft cabin door.The results show that compared with the topology optimization with the fixed shape,the strain energy obtained by the proposed method can be reduced by 20.08%and 37.93%,respectively,in⁃dicating that the proposed method has better design capability.