Developing of neural network computing methods for solving inverse elasticity problems

Authors

DOI:

https://doi.org/10.15587/1729-4061.2024.313795

Keywords:

physics-informed neural networks, inverse problems, geometric nonlinearity

Abstract

This paper examines the use of neural network methods to solve inverse problems in the mechanics of elastic materials.

The aim is to design physics-informed neural networks that can predict the parameters of structural components, and the physical properties of materials based on a specified displacement distribution.

A key feature of the specified neural networks is the integration of differential equations and boundary conditions into the loss function calculation. This approach ensures that the error in approximating unknown functions has a direct impact on optimizing the network's weights. As a result, the resulting neural network approximations of unknown functions comply with the differential equations and boundary conditions.

To test the capabilities of the designed neural networks, inverse problems involving the bending of plates and beams have been solved, focusing on determining one or two unknown parameters. Comparison of predicted and exact values demonstrates high accuracy of the constructed neural network models, with a relative prediction error of less than 3 % across all cases.

Unlike analytical methods for solving inverse problems, the primary advantage of physics-informed neural networks is their flexibility when addressing both linear and nonlinear problems. For instance, the same network architecture can be employed to solve various boundary-value problems without modification. Compared to classical numerical methods, the parallelization capability of neural networks is inherently supported by modern software libraries.

Therefore, the application of physics-informed neural networks for solving inverse elasticity problems of plates and beams is effective, as evidenced by the achieved relative errors and the computational robustness of the method. In practice, the proposed solution can be used for relevant calculations during the design of structural elements. The developed software code can also be integrated into automated design systems or computer algebra systems

Author Biographies

Anastasiia Kaliuzhniak, Zaporizhzhia National University

PhD

Department of Computer Science

Oleksii Kudin, Zaporizhzhia National University

PhD, Associate Professor

Department of Software Engineering

Yuriy Belokon, Zaporizhzhia National University

Doctorof Technical Sciences, Professor

Department of Metallurgical Technologies, Ecology and Technological Safety

Dmytro Kruglyak, Zaporizhzhia National University

PhD, Associate Professor

Department of Metallurgical Technologies, Ecology and Technological Safety

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Developing of neural network computing methods for solving inverse elasticity problems

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Published

2024-12-20

How to Cite

Kaliuzhniak, A., Kudin, O., Belokon, Y., & Kruglyak, D. (2024). Developing of neural network computing methods for solving inverse elasticity problems. Eastern-European Journal of Enterprise Technologies, 6(7 (132), 45–52. https://doi.org/10.15587/1729-4061.2024.313795

Issue

Vol. 6 No. 7 (132) (2024): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2024 Anastasiia Kaliuzhniak, Oleksii Kudi, Yuriy Belokon, Dmytro Kruglyak

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