Abstract
In this paper, an element-based deep learning approach named DeepFEM for solving nonlinear partial differential equations (PDEs) in solid mechanics is developed to reduce the number of sampling points required for training the deep neural network. Shape functions are introduced into deep learning to approximate the displacement field within the element. A general scheme for training the deep neural network based on derivatives computed from the shape functions is proposed. For the sake of demonstrations, the nonlinear vibration, nonlinear bending, and cohesive fracture problems are solved, and the results are compared with those from the existing methods to evaluate the performance of the present method. The results demonstrate that DeepFEM can effectively approximate the solution of the nonlinear mechanics problems with high accuracy, while the shape functions can significantly improve the computational efficiency. Moreover, with the trained DeepFEM model, the solutions of nonlinear problems with different geometric or material properties can be obtained instantly without retraining. Finally, the proposed DeepFEM is employed in the identification of material parameters of composite plate. The results show that the longitudinal and transverse elastic moduli of the ply in the composite plates can be accurately predicted based on the nonlinear mechanical response of plates.
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Data Availability Statement
All models and computer codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is partially sponsored by the National Natural Science Foundation of China (Grant Nos. 11972224, 52109159, and 51775346).
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Published In
Journal of Engineering Mechanics
Volume 149 • Issue 2 • February 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 6, 2022
Accepted: Sep 3, 2022
Published online: Nov 17, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 17, 2023
ASCE Technical Topics:
- Artificial intelligence and machine learning
- Composite materials
- Computer programming
- Computing in civil engineering
- Continuum mechanics
- Differential equations
- Education
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- Equations (by type)
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Neural networks
- Nonlinear analysis
- Plates
- Practice and Profession
- Solid mechanics
- Structural analysis
- Structural engineering
- Structural members
- Structural systems
- Training
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