Comparative Study of Bending Analysis using Physics-Informed Neural Networks and Numerical Dynamic Deflection in Perforated nanobeam

TL;DR

This study compares physics-informed neural network methods and traditional numerical techniques to analyze the bending behavior of perforated nanobeams under sinusoidal loading, emphasizing efficiency and accuracy.

Contribution

It introduces a novel FL-TFC framework with domain mapping that embeds differential equations into neural networks, avoiding complex architectures while ensuring boundary condition satisfaction.

Findings

FL-TFC with domain mapping accurately predicts static and dynamic bending responses.

The proposed method outperforms standard PINN in efficiency and boundary condition enforcement.

Static and dynamic deflections of perforated nanobeams are systematically related.

Abstract

In this chapter, we investigate the bending behavior of a perforated nanobeam subjected to sinusoidal loading using an efficient and computationally robust Physics-Informed Functional Link Constrained Framework with Domain Mapping (DFL-TFC) method. Our aim is to determine the relationship between static bending response and dynamic deflection of a perforated nanobeam for various perforation cases. The static bending is obtained using the FL-TFC with Domain mapped method, whereas dynamic deflection is determined using the Galerkin method. The proposed approach employs the theory of functional connections (TFC) to systematically embed governing differential equation constraints into a constrained expression (CE), which exactly satisfies all prescribed initial and boundary conditions (ICs and BCs) and domain of differential equation is mapped to domain of orthogonal polynomials. Within this framework, the free function appearing in the constrained expression is expressed through a functional link neural network (FLNN). The cost is minimized by the mean square residual of DE, allowing training without requiring complex deep network architectures. Relationship between static and dynamic defection of simply-supported (S-S) perforated nanobeams has been investigated here. FL-TFC with Domain mapped method eliminates the need for deep and complex neural network architectures while ensuring accuracy, efficiency, and strict satisfaction of boundary conditions as compared to standard PINN.