Machine-learning-assisted multiscale topology optimization of functionally graded superimposed lattice structures

2026-08-28

AI Summary

本文提出了一种机器学习辅助的多尺度优化框架，通过训练神经网络代理模型来预测晶格结构的有效刚度和相对密度，以减少计算同质化的成本。

Abstract

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.

Problem

• multiscale topology optimization
• functionally graded lattice structures
• computational homogenization

Innovation

• machine learning
• multiscale topology optimization
• functionally graded lattice structures
• neural network surrogates
• homogenization