Browsing by Author "Esfahani, Saba Sadat Mirsadeghi"

Now showing 1 - 2 of 2

Citation - WoS: 4
Citation - Scopus: 4
Physics-Informed Neural Network for Bending Analysis of Twodimensional Functionally Graded Nano-Beams Based on Nonlocal Strain Gradient Theory
(Univ Tehran, Danishgah-i Tihran, 2025) Esfahani, Saba Sadat Mirsadeghi; Fallah, Ali; Aghdam, Mohammad Mohamadi; Automotive Engineering; 06. School Of Engineering; 01. Atılım University
This paper presents the bending analysis of two-dimensionally functionally graded (2D FG) nano-beams using a physics-informed neural network (PINN) approach. The material properties of the nanobeams vary along their length and thickness directions, governed by a power-law function. Hamilton's principle, combined with the nonlocal strain gradient theory (NSGT) and Euler-Bernoulli beam theory, is employed to derive the governing equation for the bending analysis of 2D FG nanobeams. Due to the incorporation of size dependency and the variation of material properties in two dimensions, the governing equation becomes a high-order variable- coefficient differential equation, which is challenging, if not impossible, to solve analytically. In this study, the applicability of PINN for solving such high-order complex differential equations is investigated, with potential applications in nanomechanical engineering. In the PINN approach, a deep feedforward neural network is utilized to predict the mechanical response of the beam. Spatial coordinates serve as inputs, and a loss function is formulated based on the governing equation and boundary conditions of the problem. This loss function is minimized through the training process of the neural network. The accuracy of the PINN results is validated by comparing them with available reference solutions. Additionally, the effects of material distribution, power-law index (in both length and thickness directions), nonlocal strain gradient parameters, and material length scale parameters are investigated. This study demonstrates the versatility of the PINN approach as a robust tool for solving high-order differential equations in structural mechanics.
Physics-Informed Neural Network for Nonlinear Bending Analysis of Nano-Beams: A Systematic Hyperparameter Optimization
(MDPI, 2025) Esfahani, Saba Sadat Mirsadeghi; Fallah, Ali; Aghdam, Mohammad Mohammadi; 01. Atılım University
This paper investigates the nonlinear bending analysis of nano-beams using the physics-informed neural network (PINN) method. The nonlinear governing equations for the bending of size-dependent nano-beams are derived from Hamilton's principle, incorporating nonlocal strain gradient theory, and based on Euler-Bernoulli beam theory. In the PINN method, the solution is approximated by a deep neural network, with network parameters determined by minimizing a loss function that consists of the governing equation and boundary conditions. Despite numerous reports demonstrating the applicability of the PINN method for solving various engineering problems, tuning the network hyperparameters remains challenging. In this study, a systematic approach is employed to fine-tune the hyperparameters using hyperparameter optimization (HPO) via Gaussian process-based Bayesian optimization. Comparison of the PINN results with available reference solutions shows that the PINN, with the optimized parameters, produces results with high accuracy. Finally, the impacts of boundary conditions, different loads, and the influence of nonlocal strain gradient parameters on the bending behavior of nano-beams are investigated.