The field of optimal design of linear elastic structures has seen many exciting successes that resulted in new architected materials and structural designs. With the availability of cloud computing, including high-performance computing, machine learning, and simulation, searching for optimal nonlinear structures is now within reach. In this study, we develop convolutional neural network models to predict optimized designs for a given set of boundary conditions, loads, and optimization constraints. We have considered the case of materials with a linear elastic response with and without stress constraint. Also, we have considered the case of materials with a hyperelastic response, where material and geometric nonlinearities are involved. For the nonlinear elastic case, the neo-Hookean model is utilized. For this purpose, we generate datasets composed of the optimized designs paired with the corresponding boundary conditions, loads, and constraints, using a topology optimization framework to train and validate the neural network models. The developed models are capable of accurately predicting the optimized designs without requiring an iterative scheme and with negligible inference computational time. The suggested pipeline can be generalized to other nonlinear mechanics scenarios and design domains.

中文翻译：

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使用深度学习对具有非线性的二维结构进行拓扑优化

线弹性结构的优化设计领域已经取得了许多令人兴奋的成功，这些成功导致了新的建筑材料和结构设计。随着云计算的出现，包括高性能计算、机器学习和模拟，搜索最优非线性结构现在已经触手可及。在这项研究中，我们开发了卷积神经网络模型来预测一组给定的边界条件、载荷和优化约束的优化设计。我们已经考虑了具有和不具有应力约束的线性弹性响应材料的情况。此外，我们还考虑了具有超弹性响应的材料的情况，其中涉及材料和几何非线性。对于非线性弹性情况，使用了新胡克模型。以此目的，我们生成由优化设计与相应边界条件、载荷和约束配对组成的数据集，使用拓扑优化框架来训练和验证神经网络模型。开发的模型能够准确预测优化设计，无需迭代方案，推理计算时间可忽略不计。建议的管道可以推广到其他非线性力学场景和设计领域。