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DHEM: a deep heat energy method for steady-state heat conduction problems

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Abstract

Based on the deep energy method recently brought forward to handle linear-elastic or hyper-elastic finite deformation problems in solid mechanics, in this paper, we propose a deep heat energy method (DHEM) which is specially tailored to deal with structural steady-state heat conduction problems with the help of deep learning techniques. In our work, the deep neural networks are utilized to construct the admissible temperature fields; secondly, the potential energy functional in the heat conduction process which works as the loss function of the deep neural networks is calculated by numerical integration techniques; finally, the parameters of the network including weights and bias, are optimized by the quasi-Newton method to yield the minimal of the potential energy functional which indicates the heat conduction has entered a steady state. Numerical examples with a diversity of materials, including the isotropic and homogeneous material, the orthotropic material, the non-homogeneous materials and temperature dependent materials, are carried out to illustrate the validity and capacity of DHEM in both linear uncoupled and thermal-material coupling heat conduction problems.

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Abbreviations

κ :

Thermal conductivity coefficient

T :

Structural temperature

T e :

Medium temperature

q :

Heat source intensity

\({\bar h_c}\) :

Heat transfer coefficient

w :

Network weights

b :

Network bias

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Acknowledgments

The authors acknowledge the financial support from the Fundamental Research Funds for the Central Universities under JLU (93K172020K28), we would like to express our sincere thanks to the Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University.

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130022, P.R. China

    Huanhuan Gao, Wenjie Zuo, Zengming Feng & Jinxing Yang

  2. Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130022, P.R. China

    Huanhuan Gao & Tingting Li

  3. College of Naval Architecture and Ocean Engineering, Naval University of Engineering, Wuhan, 430033, P.R. China

    Ping Hu

Authors
  1. Huanhuan Gao
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  2. Wenjie Zuo
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  3. Zengming Feng
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  4. Jinxing Yang
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  5. Tingting Li
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  6. Ping Hu
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Corresponding author

Correspondence to Zengming Feng.

Additional information

Zengming Feng is a Professor of the School of Mechanical and Aerospace Engineering, Jilin University, China. His research fields include mechanical transmission and dynamic control, multi-body dynamic modeling and simulation, friction and wear.

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Gao, H., Zuo, W., Feng, Z. et al. DHEM: a deep heat energy method for steady-state heat conduction problems. J Mech Sci Technol 36, 5777–5791 (2022). https://doi.org/10.1007/s12206-022-1039-0

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  • DOI: https://doi.org/10.1007/s12206-022-1039-0

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