We present a low rank approximation approach for topology optimization of parametrized linear elastic structures. The parametrization is considered on loading and stiffness of the structure. The low rank approximation is achieved by identifying a parametric connection among coarse finite element models of the structure (associated with different design iterates) and is used to inform the high fidelity finite element analysis. We build an Artificial Neural Network (ANN) map between low resolution design iterates and their corresponding interpolative coefficients (obtained from low rank approximations) and use this surrogate to perform high resolution parametric topology optimization. We demonstrate our approach on robust topology optimization with compliance constraints/objective functions and develop error bounds for the the parametric compliance computations. We verify these parametric computations with more challenging quantities of interest such as the p-norm of von Mises stress. To conclude, we use our approach on a 3D robust topology optimization and show significant reduction in computational cost via quantitative measures.

我们提出了一种用于参数化线性弹性结构拓扑优化的低秩近似方法。参数化考虑结构的载荷和刚度。低秩近似是通过识别结构的粗略有限元模型（与不同的设计迭代相关联）之间的参数连接来实现的，并用于为高保真有限元分析提供信息。我们在低分辨率设计迭代与其相应的插值系数（从低秩近似中获得）之间构建了人工神经网络 (ANN) 映射，并使用此代理来执行高分辨率参数拓扑优化。我们展示了我们使用合规约束/目标函数进行稳健拓扑优化的方法，并为参数合规计算开发了误差界限。我们使用更具挑战性的感兴趣量来验证这些参数计算，例如p - von Mises 应力的范数。总而言之，我们将我们的方法用于 3D 稳健拓扑优化，并通过定量测量显示计算成本显着降低。