Browsing by Author "Fallah, Ali"

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Large Deflection Analysis of Functionally Graded Reinforced Sandwich Beams With Auxetic Core Using Physics-Informed Neural Network
(Taylor & Francis inc, 2025) Nopour, Reza; Fallah, Ali; Aghdam, Mohammad Mohammadi
This paper aims to investigate the large deflection behavior of a sandwich beam reinforced with functionally graded (FG) graphene platelets (GPL) together with an auxetic core, rested on a nonlinear elastic foundation. The nonlinear governing equations of the problem are derived using Hamilton's principle based on the Euler-Bernoulli beam theory for large deflections. Five different distributions are considered to describe the dispersion of GPL in the top and bottom faces of the sandwich beam. The Physics-Informed Neural Network (PINN) method is employed to model the nonlinear deflection of the beam under various boundary conditions. This study highlights the effectiveness of PINN in handling the complexities of nonlinear structural analyses. The findings underscore the impact of the core auxeticity, GPL amount and distribution, and elastic foundation coefficient on the nonlinear deflection of the sandwich beam under different loading scenarios. For instance, using Type I configuration can reduce the deflection of the beam by nearly half compared to using Type IV. Furthermore, a nonlinear foundation with a unit coefficient results in a 48% reduction in deflection compared to the scenario without an elastic foundation.
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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
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.