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PINN-based forward and inverse bending analysis of nanobeams on a three-parameter nonlinear elastic foundation including hardening and softening effect using nonlocal elasticity theory

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Abstract

This paper introduces the application of Physics-Informed Neural Network (PINN), a novel class of scientific machine learning techniques, for analyzing the static bending response of nanobeams as essential structural elements in micro/nanoelectromechanical systems, including nanoprobes, atomic force microscope sensors, nanoswitches, nanoactuators, and nanoscale biosensors on a three-parameter nonlinear elastic foundation. The study combines Euler–Bernoulli beam theory and Eringen’s nonlocal continuum theory to derive the governing differential equation using the minimum total potential energy principle. PINN is utilized for approximating the differential equation solution and identifying the nanobeam’s nonlocal parameter through an inverse problem with measurement data. The loss function incorporates terms representing the initial and boundary conditions, along with the differential equation residual at specific points in the domain and boundary. The research demonstrates PINN’s efficacy in analyzing nanobeam behavior on nonlinear elastic foundations, providing valuable insights into responses under different loading and boundary conditions. The proposed approach's accuracy and efficiency are validated through comparisons with existing literature. Additionally, the study investigates the effects of activation functions, collocation points’ number and distribution, nonlocal parameter, foundation stiffness coefficients, loading types, and various boundary conditions on nanobeam bending behavior.

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Data availability

The data that support the findings of this study are available from the corresponding author, Saeid Sarrami (sarrami@iut.ac.ir), upon reasonable request.

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Acknowledgements

We would like to express our sincere gratitude to Danial Amini (Grad. student, at MIT) for his invaluable assistance in providing a basic introduction to the PINN framework.

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Authors and Affiliations

  1. Department of Civil Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Omid Kianian, Saeid Sarrami, Bashir Movahedian & Mojtaba Azhari

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  1. Omid Kianian
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  2. Saeid Sarrami
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Contributions

O. Kianian made the analysis, prepared the results, and wrote the manuscript draft. S. Sarrami wrote and revised the final manuscript text. B. Movahedian proposed the idea of the research. M. Azhari reviewed the manuscript.

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Correspondence to Saeid Sarrami.

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Kianian, O., Sarrami, S., Movahedian, B. et al. PINN-based forward and inverse bending analysis of nanobeams on a three-parameter nonlinear elastic foundation including hardening and softening effect using nonlocal elasticity theory. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-01985-1

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