Details
| Original language | English |
|---|---|
| Article number | 104225 |
| Journal | European Journal of Mechanics, A/Solids |
| Volume | 87 |
| Early online date | 26 Jan 2021 |
| Publication status | Published - May 2021 |
Abstract
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.
Keywords
- Activation function, Autoencoder, Buckling, Deep learning, Energy method, Kirchhoff plate, Transfer learning, Vibration
ASJC Scopus subject areas
- Materials Science(all)
- General Materials Science
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: European Journal of Mechanics, A/Solids, Vol. 87, 104225, 05.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning
AU - Zhuang, Xiaoying
AU - Guo, Hongwei
AU - Alajlan, Naif
AU - Zhu, Hehua
AU - Rabczuk, Timon
N1 - Funding Information: The authors extend their appreciation to the Distinguished Scientist Fellowship Program (DSFP) at King Saud University for funding this work.
PY - 2021/5
Y1 - 2021/5
N2 - 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.
AB - 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.
KW - Activation function
KW - Autoencoder
KW - Buckling
KW - Deep learning
KW - Energy method
KW - Kirchhoff plate
KW - Transfer learning
KW - Vibration
UR - http://www.scopus.com/inward/record.url?scp=85100031045&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2010.05698
DO - 10.48550/arXiv.2010.05698
M3 - Article
AN - SCOPUS:85100031045
VL - 87
JO - European Journal of Mechanics, A/Solids
JF - European Journal of Mechanics, A/Solids
SN - 0997-7538
M1 - 104225
ER -