Purpose

In engineering practice many structures are assembled by several linear components through nonlinear joints. A novel hybrid modeling method based on finite element model reduction and deep learning techniques is proposed to meet the ever-increasing requirements of efficient and accurate modeling for nonlinear jointed structures.

Methods

The main idea of the hybrid modeling method for nonlinear jointed structures is summarized as follows: Firstly, finite element models of linear components are reduced to improve the computing efficiency using the free-interface mode synthesis method, as numerical integration of governing equations of nonlinear structures with large numbers of degrees-of-freedom is always time-consuming. Secondly, deep neural networks are used to equivalently represent the nonlinear joints which are difficult to describe by accurate and physically-motivated models, so as to avoid the errors caused by traditional mechanism modeling or system identification. Nonlinear joints are finally replaced with their equivalent neural networks and connected with the substructure models of linear components through the compatibility of displacements and equilibrium of forces at the interfaces.

Results and Conclusions

The performance of the proposed hybrid modeling method is tested and assessed via a case study focused on a cantilever plate with nonlinear joints. Comparative results demonstrate the capability of the proposed method for efficient and accurate modeling of nonlinear jointed structures and predicting their intrinsic nonlinear behavior.

中文翻译：

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非线性连接结构的有限元模型简化和深度学习技术的混合建模

目的

在工程实践中，许多结构是通过非线性关节由几个线性组件组装而成的。提出了一种基于有限元模型约简和深度学习技术的混合建模方法，以满足对非线性节理结构进行高效，准确建模的不断增长的需求。

方法

非线性节理结构混合建模方法的主要思想概括如下：首先，通过自由界面模式综合方法，对非线性构件的控制方程进行数值积分，简化线性构件的有限元模型以提高计算效率。具有大量自由度总是很耗时。其次，用深度神经网络等效地表示非线性关节，这些非线性关节很难用精确的物理模型来描述，从而避免了传统机制建模或系统识别所引起的误差。

结果与结论

通过以带有非线性接头的悬臂板为重点的案例研究来测试和评估所提出的混合建模方法的性能。比较结果证明了所提方法对非线性节理结构进行高效，准确建模并预测其固有非线性行为的能力。