AI 中文总结
本研究提出机器学习辅助的多尺度拓扑优化框架，结合SIMP与MMA方法，替代重复计算均匀化，实现功能梯度叠加点阵结构的优化，在MBB梁基准上验证了其有效性。
AI 中文摘要
功能梯度点阵结构可实现轻量化设计，具备空间可调的刚度与密度，但在多尺度拓扑优化中的应用受限于重复计算均匀化的成本。本研究提出一种用于规则叠加点阵结构的机器学习辅助多尺度优化框架：单胞由体心立方、面心立方、简单立方点阵组件组合而成，各组件由独立几何参数控制；采用离线计算均匀化生成有效刚度数据，用于训练带乔列斯基约束的神经网络替代模型，该模型以物理可容许形式重构均匀化刚度张量；训练另一个神经网络，用于从基于蒙特卡洛的密度估计值预测相对密度。将替代模型整合到两阶段拓扑优化策略中：第一阶段采用固体各向同性材料惩罚（SIMP）方法获取宏观拓扑；所得固体区域用于微尺度点阵优化，采用移动渐近线法（MMA）更新局部点阵参数，训练后的刚度与密度替代模型替代该阶段的重复在线均匀化。以三维Messerschmitt-Bölkow-Blohm（MBB）梁基准验证该方法，得到与材料约束下柔度最小化一致的空间变化点阵参数及相对密度场。
英文摘要
Functionally graded lattice structures enable lightweight designs with spatially tunable stiffness and density, but their use in multiscale topology optimization is limited by the cost of repeated computational homogenization. This work presents a machine learning-assisted multiscale optimization framework for regular superimposed lattice structures. The unit cell is formed by combining body-centered cubic, face-centered cubic, and simple cubic lattice components, each controlled by an independent geometric parameter. Offline computational homogenization is used to generate effective stiffness data, which are then used to train a Cholesky-constrained neural network surrogate. This representation reconstructs the homogenized stiffness tensor in a physically admissible form. A separate neural network is trained to predict relative density from Monte Carlo-based density estimates. We incorporate our surrogates into a two-stage topology optimization strategy. First, a macroscale topology is obtained using the solid isotropic material with penalization (SIMP) method. The resulting solid region is then used for microscale lattice optimization, where the local lattice parameters are updated using the method of moving asymptotes (MMA). The trained stiffness and density surrogates replace repeated online homogenization during this stage. The method is demonstrated on a three-dimensional Messerschmitt-Bölkow-Blohm (MBB) beam benchmark, producing spatially varying lattice parameters and relative density fields consistent with compliance minimization under a material constraint.
