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This work proposed a novel Runge-Kutta Physics-Informed Neural Network (R-KPINN) framework for Computational Structural Dynamics (CSD). In the proposed framework, artificial neural networks (ANNs) are applied to predict the field variables in terms of velocity and displacement, while both the implicit and explicit Runge-Kutta (RK) methods are used to deal with temporal integration. Additionally, the R-KPINN is trained to approximate accurate results of the vibration problems by equilibrium equations and the corresponding initial/boundary conditions[1]. The proposed framework offers an alternative to traditional numerical methods, including mesh-based and meshfree methods. The R-KPINN's meshless nature effectively prevents the issues such as mesh distortion and re-meshing in CSD problems[2]. Besides, The R-KPINN globally calculates the differential terms of the partial differential equations (PDEs) rather than relying on the surrounding nodes or particles. Therefore, the proposed framework can address the accuracy problem caused by uneven sample points and boundary truncation issues in conventional meshfree methods. Finally, the R-KPINN based CSD framework's feasibility and stability are evaluated through several CSD benchmark problems, including one-dimensional Euler-Bernoulli beam, Timoshenko beam and two-dimensional plate vibration problems[3], showcasing its potential to revolutionize the way to solve CSD problems.

Keywords: Computational structural dynamics, Physics informed neural network, Deep learning, Runge-Kuta method

 

References

[1]      M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” J Comput Phys, vol. 378, pp. 686–707, Feb. 2019, doi: 10.1016/j.jcp.2018.10.045.

[2]      D. Baye, “The Lagrange-mesh method,” Physics Reports, vol. 565. 2015. doi: 10.1016/j.physrep.2014.11.006.

[3]      S. C. Lin and K. M. Hsiao, “Vibration analysis of a rotating Timoshenko beam,” J Sound Vib, vol. 240, no. 2, 2001, doi: 10.1006/jsvi.2000.3234.

Computational structural dynamics, Physics informed neural network, Deep learning, Runge-Kuta method