Static Bending Analysis of Nanobeam-Substrate Medium Systems Incorporating Mixture Stress-Driven Nonlocality, Surface Energy, and Substrate-Structure Interactions

Limkatanyu, Suchart; Sae-Long, Worathep; Rungamornrat, Jaroon; Damrongwiriyanupap, Nattapong; Keawsawasvong, Suraparb; Sukontasukkul, Piti; Hansapinyo, Chayanon

doi:10.22055/jacm.2024.47226.4679

Static Bending Analysis of Nanobeam-Substrate Medium Systems Incorporating Mixture Stress-Driven Nonlocality, Surface Energy, and Substrate-Structure Interactions

Document Type : Research Paper

Authors

Suchart Limkatanyu ¹

Worathep Sae-Long ²

Jaroon Rungamornrat ³

Nattapong Damrongwiriyanupap ²

Suraparb Keawsawasvong ⁴

Piti Sukontasukkul ⁵

Chayanon Hansapinyo ⁶

¹ Department of Civil and Environmental Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla, 90110, Thailand

² Civil Engineering Program, School of Engineering, University of Phayao, Phayao, 56000, Thailand

³ Applied Mechanics and Structures Research Unit, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand

⁴ Research Unit in Sciences and Innovative Technologies for Civil Engineering Infrastructures, Department of Civil Engineering, Faculty of Engineering, Thammasat School of Engineering, Thammasat University, Pathumthani, 12120, Thailand

⁵ Construction and Building Materials Research Center, Department of Civil Engineering, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

⁶ Center of Excellence in Natural Disaster Management, Department of Civil Engineering, Chiang Mai University, Chiang Mai, 50200, Thailand

10.22055/jacm.2024.47226.4679

Abstract

This paper proposes a novel nonlocal beam-substrate model for the static bending analysis of a nanobeam system on a substrate medium. The proposed model incorporates the coupling interaction among nonlocality, surface energy, and substrate-structure interaction. The mixture stress-driven nonlocal model is used to capture the material’s small-scale effects inherent in micro- and nanoscale systems, resulting in well-posed micro- and nanostructure responses. The Gurtin-Murdoch continuum surface-energy model and the Winkler foundation model, which respectively represent size-dependent and substrate-structure interaction effects, are considered. The governing differential equation (GDE) and its relevant boundary conditions are derived based on the displacement-based principle. The analytical solutions are directly obtained from the GDE and employed to assess the bending responses. To demonstrate the impact of the mixture parameter, surface energy, and substrate-structure interaction on the static bending analysis of nanobeam systems, four numerical simulations are conducted. The first simulation validates the proposed nanobeam system by comparing it to experimental results, while the second simulation demonstrates the impact of surface energy and substrate-structure interaction on beam deflection. The third and fourth simulations analyze the impact of different system variables on the normalized transverse displacement and effective bulk Young's modulus (EBYM), respectively. The analysis results demonstrate that material nonlocality caused by the mixture parameter and length-scale parameter, as well as surface energy and substrate-structure interaction effects, impact the bending behaviors of the nanobeam systems.

Keywords

Mixture parameter

Eringen’s integral elasticity

Small-scale effect

Bending analysis

Surface-energy effect

Subjects

Computational Mechanics

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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