Static Analysis of Functionally Graded Nanobeams with Exponential Load under Non-Ideal Boundary Constraints Using Machine Learning Technique

Abstract

This work analyzes the bending response of nanobeams made of functionally graded materials with non-ideal simply-supported boundary conditions. The nanobeam is subjected to a varying exponential load, and the Young's modulus of the nanobeam is assumed to vary in the thickness direction according to a power-law function. The Euler-Bernoulli beam theory is utilized to model the nanobeam, and Eringen's nonlocal elasticity theory is used to analyze the nonlocal effects of the nanobeam. By accounting for small but realistic deviations from perfectly supported ends, this model provides a more accurate representation of practical nanobeam behavior. Here, the governing differential equation is solved using Physics Informed Functional Link Neural Network (PI-FLNN), and the numerical predictions are validated against analytical results. The objective of this research is to show the implementation of PI-FLNN to solve the bending problem of said nanobeams. This investigation presents parametric results for different power-law indices, load parameters and boundary-imperfection amplitudes, and demonstrates the effectiveness of PI-FLNN in capturing the bending response of FG nanobeams.