Details
| Original language | English |
|---|---|
| Pages (from-to) | 433-456 |
| Number of pages | 24 |
| Journal | Computers, Materials and Continua |
| Volume | 59 |
| Issue number | 2 |
| Publication status | Published - 2019 |
Abstract
In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning. Besides, the proposed DCM is based on a feedforward deep neural network (DNN) and differs from most previous applications of deep learning for mechanical problems. First, batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries. A loss function is built with the aim that the governing partial differential equations (PDEs) of Kirchhoff plate bending problems, and the boundary/initial conditions are minimised at those collocation points. A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters. In Kirchhoff plate bending problems, the C1 continuity requirement poses significant difficulties in traditional mesh-based methods. This can be solved by the proposed DCM, which uses a deep neural network to approximate the continuous transversal deflection, and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.
Keywords
- Collocation method, Deep learning, Higher-order PDEs, Kirchhoff plate
ASJC Scopus subject areas
- Materials Science(all)
- Biomaterials
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Mechanics of Materials
- Computer Science(all)
- Computer Science Applications
- Engineering(all)
- Electrical and Electronic Engineering
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In: Computers, Materials and Continua, Vol. 59, No. 2, 2019, p. 433-456.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A deep collocation method for the bending analysis of Kirchhoff plate
AU - Guo, Hongwei
AU - Zhuang, Xiaoying
AU - Rabczuk, Timon
PY - 2019
Y1 - 2019
N2 - In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning. Besides, the proposed DCM is based on a feedforward deep neural network (DNN) and differs from most previous applications of deep learning for mechanical problems. First, batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries. A loss function is built with the aim that the governing partial differential equations (PDEs) of Kirchhoff plate bending problems, and the boundary/initial conditions are minimised at those collocation points. A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters. In Kirchhoff plate bending problems, the C1 continuity requirement poses significant difficulties in traditional mesh-based methods. This can be solved by the proposed DCM, which uses a deep neural network to approximate the continuous transversal deflection, and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.
AB - In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning. Besides, the proposed DCM is based on a feedforward deep neural network (DNN) and differs from most previous applications of deep learning for mechanical problems. First, batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries. A loss function is built with the aim that the governing partial differential equations (PDEs) of Kirchhoff plate bending problems, and the boundary/initial conditions are minimised at those collocation points. A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters. In Kirchhoff plate bending problems, the C1 continuity requirement poses significant difficulties in traditional mesh-based methods. This can be solved by the proposed DCM, which uses a deep neural network to approximate the continuous transversal deflection, and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.
KW - Collocation method
KW - Deep learning
KW - Higher-order PDEs
KW - Kirchhoff plate
UR - http://www.scopus.com/inward/record.url?scp=85069584241&partnerID=8YFLogxK
U2 - 10.32604/cmc.2019.06660
DO - 10.32604/cmc.2019.06660
M3 - Article
AN - SCOPUS:85069584241
VL - 59
SP - 433
EP - 456
JO - Computers, Materials and Continua
JF - Computers, Materials and Continua
SN - 1546-2218
IS - 2
ER -