AI 中文总结
针对大规模异构结构分析与设计，提出PIML-OFEM方法，利用与问题无关的机器学习加速重叠有限元技术。通过构建过采样数值基函数、混合局部基及U-Net映射等，降低计算成本、提高精度，为结构分析和拓扑优化提供高效物理-数据方法。
AI 中文摘要
大规模异构结构的高分辨率分析和设计需要精确的降阶模型和高效的在线计算。现有多尺度方法须为不同材料分布反复构建局部基函数，基于子结构的与问题无关的机器学习（PIML）方法受规定边界位移插值限制。本文提出PIML-OFEM，一种由与问题无关的机器学习加速的重叠有限元方法。各子结构仅保留角节点自由度，通过在扩展域上求解局部弹性问题并将解限制到目标子结构来构建过采样数值基函数，消除其边界上的规定位移插值。通过单位分解重叠公式混合独立构建的局部基以获得全局连续位移场。用U-Net学习从局部杨氏模量分布到数值基函数的映射，取代重复的在线局部求解并允许模型在不同载荷工况和全局边界条件下复用。数值算例表明，其位移和单元应变能与精细尺度有限元结果吻合良好。与直接有限元分析相比，PIML-OFEM降低了在线计算成本，比基于线性边界插值的PIML子结构模型提高了精度。在拓扑优化中，该方法支持小滤波半径下的稳定高分辨率迭代并保留精细尺度特征。该框架为大规模异构结构分析和高分辨率拓扑优化提供了一种高效的物理-数据方法。
英文摘要
High-resolution analysis and design of large-scale heterogeneous structures require accurate reduced-order models and efficient online computation. Existing multiscale methods must repeatedly construct local basis functions for different material distributions, whereas substructure-based problem-independent machine learning (PIML) methods can be limited by prescribed boundary displacement interpolation. We propose PIML-OFEM, an overlapping finite element method accelerated by problem-independent machine learning. Each substructure retains only its corner-node degrees of freedom. Oversampled numerical basis functions are constructed by solving local elasticity problems on extended domains and restricting the solutions to the target substructure, eliminating prescribed displacement interpolation on its boundary. Independently constructed local bases are blended through a partition-of-unity overlapping formulation to obtain a globally continuous displacement field. A U-Net learns the mapping from local Young's modulus distributions to numerical basis functions, replacing repeated online local solves and allowing the model to be reused across load cases and global boundary conditions. Numerical examples show close agreement with fine-scale finite element results in displacement and elemental strain energy. PIML-OFEM reduces online computational cost relative to direct finite element analysis and improves accuracy over PIML substructure models based on linear boundary interpolation. In topology optimization, the method supports stable high-resolution iterations with small filter radii and preserves fine-scale features, including local patterns resembling rank-2 microstructures. The framework provides an efficient physics-data approach for large-scale heterogeneous structural analysis and high-resolution topology optimization.
CommentsSubmitted to Acta Mechanica Sinica
