论文标题

使用深度学习对具有非线性的2D结构的拓扑优化

Topology optimization of 2D structures with nonlinearities using deep learning

论文作者

Abueidda, Diab W., Koric, Seid, Sobh, Nahil A.

论文摘要

线性弹性结构的最佳设计领域看到了许多令人兴奋的成功,从而带来了新的构建材料和结构设计。随着云计算的可用性,包括高性能计算,机器学习和模拟,现在可以搜索最佳的非线性结构。在这项研究中,我们开发了卷积神经网络模型,以预测给定的边界条件,负载和优化约束的优化设计。我们已经考虑了具有有或没有应力限制的线性弹性响应的材料情况。同样,我们考虑了具有超弹性反应的材料情况,其中涉及材料和几何非线性。对于非线性弹性情况,使用了新霍克人模型。为此,我们使用拓扑优化框架来训练和验证神经网络模型,生成由优化设计与相应边界条件,负载和约束配对的数据集。开发的模型能够准确预测优化的设计,而无需迭代方案并具有可忽略的推理计算时间。建议的管道可以推广到其他非线性力学场景和设计域。

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.

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