This paper presents a novel methodology to assess the accuracy of shell finite elements via neural networks. The proposed framework exploits the synergies among three well-established methods, namely, the Carrera Unified Formulation (CUF), the Finite Element Method (FE), and neural networks (NN). CUF generates the governing equations for any-order shell theories based on polynomial expansions over the thickness. FE provides numerical results feeding the NN for training. Multilayer NN have the generalized displacement variables, and the thickness ratio as inputs, and the target is the maximum transverse displacement. This work investigates the minimum requirements for the NN concerning the number of neurons and hidden layers, and the size of the training set. The results look promising as the NN requires a fraction of FE analyses for training, can evaluate the accuracy of any-order model, and can incorporate physical features, e.g., the thickness ratio, that drive the complexity of the mathematical model. In other words, NN can trigger fast informed decision-making on the structural model to use and the influence of design parameters without the need of modifying, rebuild, or rerun an FE model.

中文翻译：

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关于使用神经网络评估复合材料壳模型的性能

本文提出了一种通过神经网络评估壳有限元的准确性的新方法。拟议的框架利用了三种公认的方法之间的协同作用，即Carrera统一公式（CUF），有限元方法（FE）和神经网络（NN）。CUF基于厚度上的多项式展开生成任何阶数壳理论的控制方程。有限元提供数值结果，供神经网络进行训练。多层NN具有广义的位移变量，并将厚度比作为输入，目标是最大横向位移。这项工作调查了有关神经元和隐藏层数量以及训练集大小的NN最低要求。由于NN需要一部分有限元分析来进行训练，因此结果看起来很有希望，可以评估任何阶次模型的准确性，并且可以合并物理特征（例如，厚度比），从而驱动数学模型的复杂性。换句话说，NN可以触发要使用的结构模型和设计参数的影响的快速决策，而无需修改，重建或重新运行FE模型。