Size-dependent bending, buckling, and vibration behavior of a nanobeam with periodically distributed holes via a PINN-based method
ENGINEERING WITH COMPUTERS, vol.42, no.5, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 42 Issue: 5
- Publication Date: 2026
- Doi Number: 10.1007/s00366-026-02405-2
- Journal Name: ENGINEERING WITH COMPUTERS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, INSPEC, zbMATH, Engineering Source (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Bursa Uludag University Affiliated: Yes
Abstract
This study presents a physics-informed neural network (PINN) framework for the bending, buckling, and free vibration analysis of perforated nanobeams (PT-NBs). The mechanical model is formulated within the Euler-Bernoulli beam theory (EBBT), while size-dependent effects are captured using Eringen's nonlocal elasticity theory. In the free vibration analysis, the PT-NB is assumed to be subjected to axial compressive loads applied at both ends. To address each problem type, tailored loss functions are constructed by embedding the governing differential equations and boundary conditions (BCs) directly into the training process. The influence of periodic perforations on the structural response is explicitly accounted for through equivalent stiffness and mass parameters. A comprehensive parametric study is conducted to examine the effects of the nonlocal parameter, filling ratio, number of holes, and beam length under various BCs. The accuracy of the proposed PINN model is validated through extensive comparisons with available analytical solutions, demonstrating excellent agreement.