The accuracy of stress calculation with a fixed mesh significantly affects the stress-based topology optimization, due to potential non-physical stress concentrations in voxel-based topology descriptions. This paper proposes a novel problem-independent machine learning enhanced high-precision stress calculation method (PIML-HPSCM) to address this challenge. As an immersed analysis method, PIML-HPSCM combines the high efficiency of fixed mesh with the accuracy of body-fitted mesh, without complex integration schemes of other immersed methods. PIML-HPSCM utilizes the extended multiscale finite element method to depict the material heterogeneity within high-resolution boundary elements. The accurate stress field can then be calculated conveniently by establishing stress evaluation matrices of high-resolution boundary elements. Moreover, the PIML is independent of problem settings and is applicable for various problems with the same governing equation type. Invoking the offline-trained neural network online can enhance stress calculation efficiency by 10–20 times. The stress-based discrete variable topology optimization, which naturally avoids singular stress phenomenon, is efficiently addressed by the sequential approximate integer programming method with PIML-HPSCM. Results from 2D and 3D examples demonstrate that the stresses calculated by PIML-HPSCM are consistent with those by body-fitted mesh, and optimized designs effectively eliminate stress concentrations of initial designs and have uniform stress distributions.

中文翻译：

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与应力相关的离散变量拓扑优化，处理非物理应力集中


由于基于体素的拓扑描述中可能存在非物理应力集中，因此使用固定网格进行应力计算的准确性会显著影响基于应力的拓扑优化。本文提出了一种新的问题无关机器学习增强高精度应力计算方法 （PIML-HPSCM） 来应对这一挑战。作为一种浸没式分析方法，PIML-HPSCM 结合了固定网的高效率和体拟合网的精度，无需其他浸入式方法的复杂集成方案。PIML-HPSCM 利用扩展的多尺度有限元方法来描述高分辨率边界元中的材料异质性。然后，通过建立高分辨率边界元的应力评估矩阵，可以方便地计算精确的应力场。此外，PIML 独立于问题设置，适用于具有相同控制方程类型的各种问题。在线调用离线训练的神经网络可以将应力计算效率提高 10-20 倍。PIML-HPSCM 的顺序近似整数规划方法有效地解决了基于应力的离散变量拓扑优化，它自然地避免了奇异应力现象。2D 和 3D 实例结果表明，PIML-HPSCM 计算的应力与体拟合网格计算的应力一致，优化后的设计有效地消除了初始设计的应力集中，应力分布均匀。