A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under variable loads. The proposed DeepONet uses a ResUNet in the trunk to encode complex input geometries, and a fully-connected branch network encodes the parametric loads. Additional information fusion is introduced via an element-wise multiplication of the encoded latent space to improve prediction accuracy further. The performance of the proposed DeepONet was compared to two baseline models, a standalone ResUNet and a DeepONet with fully connected networks as the branch and trunk. The results show that ResUNet and the proposed DeepONet share comparable accuracy; both can predict the stress field and accurately identify stress concentration points. However, the novel DeepONet is more memory efficient and allows greater flexibility with framework architecture modifications. The DeepONet with fully connected networks suffers from high prediction error due to its inability to effectively encode the complex, varying geometry. Once trained, all three networks can predict the full stress distribution orders of magnitude faster than finite element simulations. The proposed network can quickly guide preliminary optimization, designs, sensitivity analysis, uncertainty quantification, and many other nonlinear analyses that require extensive forward evaluations with variable geometries, loads, and other parameters. This work marks the first time a ResUNet is used as the trunk network in the DeepONet architecture and the first time that DeepONet solves problems with complex, varying input geometries under parametric loads and elasto-plastic material behavior.

翻译：本文设计了一种新型深度算子网络（DeepONet），采用残差U-Net（ResUNet）作为主干网络，用于预测变荷载作用下拓扑优化获得的复杂几何体的全场高度非线性弹塑性应力响应。所提出的DeepONet在主干网络中使用ResUNet编码复杂输入几何形状，而全连接分支网络则编码参数化荷载。通过编码潜空间的逐元素乘法引入额外信息融合，以进一步提高预测精度。将该DeepONet的性能与两个基线模型（独立ResUNet以及分支和主干均为全连接网络的DeepONet）进行了比较。结果表明，ResUNet与所提出的DeepONet在精度上相当；两者均可预测应力场并准确识别应力集中点。然而，新型DeepONet具有更高的内存效率，且允许更灵活的框架架构修改。采用全连接网络的DeepONet因无法有效编码复杂变化的几何形状而导致高预测误差。一旦完成训练，三个网络预测全应力分布的速度均比有限元模拟快数个数量级。所提出的网络可快速指导初步优化、设计、灵敏度分析、不确定性量化以及许多其他需要对可变几何形状、荷载等参数进行大量正向计算的非线性分析。本研究首次将ResUNet用作DeepONet架构中的主干网络，并首次将DeepONet应用于解决具有复杂可变输入几何形状、参数化荷载及弹塑性材料行为的问题。