Physics-informed neural network for bending and free vibration analysis of three-dimensional functionally graded porous beam resting on elastic foundation

• Published in: Engineering with computers 2024-02, Vol.40 (1), p.437-454
• Main Authors: Fallah, Ali, Aghdam, Mohammad Mohammadi
• Format: Article
• Language: English
• Subjects: Artificial neural networks; Bending; Boundary conditions; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Differential equations; Elastic foundations; Equations of motion; Free vibration; Functionally gradient materials; Hamilton's principle; Inverse problems; Material properties; Math. Applications in Chemistry; Mathematical and Computational Engineering; Neural networks; Original Article; Parameters; Porosity; Porous materials; Resonant frequencies; Systems Theory; Taguchi methods; Three dimensional analysis; Vibration analysis
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-023-01799-7

This study investigates the application of physics-informed neural networks (PINN) for bending and free vibration analysis of three-dimensional functionally graded (TDFG) porous beams. The beam material properties are assumed to vary continuously in three dimensions according to an arbitrary function. The governing equations of motion are obtained using Hamilton's principle and solved by a PINN computational approach. The beam deflection is approximated with a deep feedforward neural network which its input is the spatial coordinate. The network parameters are trained by minimizing a loss function comprised of the governing differential equation and the boundary conditions. The beam natural frequency is considered as an unknown parameter in the governing equation; thus, it has to be obtained by solving an inverse problem. This procedure makes it possible to find higher modes’ natural frequencies, which is impossible according to the previous PINN methods. A systematic procedure for tuning the network's hyperparameters is done based on the Taguchi design of the experiment and the grey relational analysis. The PINN results are validated with analytical and numerical reference solutions. Effects of material distribution, elastic foundation and porosity factor, and porosity distribution type on the bending behavior and natural frequencies of TDFG beams are investigated.