Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning

In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yieldin...

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Vydáno v:European journal of mechanics, A, Solids Ročník 87; s. 104225
Hlavní autoři: Zhuang, Xiaoying, Guo, Hongwei, Alajlan, Naif, Zhu, Hehua, Rabczuk, Timon
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin Elsevier Masson SAS 01.05.2021
Elsevier BV
Témata:
Activation function
Artificial neural networks
Autoencoder
Bending
Boundary conditions
Buckling
Configuration management
Continuity (mathematics)
Deep learning
Energy method
Energy methods
Feature extraction
Hyperbolic functions
Kirchhoff plate
Machine learning
Plates
Potential energy
Resonant frequencies
Robustness (mathematics)
Transfer learning
Vibration
Vibration analysis
Deep learning
Energy method
Vibration
Autoencoder
Activation function
Transfer learning
Kirchhoff plate
Buckling
ISSN:0997-7538, 1873-7285
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Shrnutí:In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yielding an unsupervised feature learning method. The DAEM is a specific type of feedforward deep neural network (DNN) and can also serve as function approximator. With robust feature extraction capacity, the DAEM can more efficiently identify patterns behind the whole energy system, such as the field variables, natural frequency and critical buckling load factor studied in this paper. The objective function is to minimize the total potential energy. The DAEM performs unsupervised learning based on generated collocation points inside the physical domain so that the total potential energy is minimized at all points. For the vibration and buckling analysis, the loss function is constructed based on Rayleigh’s principle and the fundamental frequency and the critical buckling load is extracted. A scaled hyperbolic tangent activation function for the underlying mechanical model is presented which meets the continuity requirement and alleviates the gradient vanishing/explosive problems under bending. The DAEM is implemented using Pytorch and the LBFGS optimizer. To further improve the computational efficiency and enhance the generality of this machine learning method, we employ transfer learning. A comprehensive study of the DAEM configuration is performed for several numerical examples with various geometries, load conditions, and boundary conditions. •Deep autoencoder based energy method (DAEM) with tailored activation function.•Stable and accurate results without gradient vanishing/exploding problems.•Unsupervised DAEM applied to Kirchhoff plates.
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ISSN:0997-7538
1873-7285
DOI:10.1016/j.euromechsol.2021.104225