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Volume 16
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10.3390/nano16140852
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Coupled Thermal and Nonlocal Effects in Advanced Composite Nanobeams: An Efficient Higher-Order Modeling Approach

by
Rabab A. Alghanmi
1 and
Mohammed Sid Ahmed Houari
2,*
1
Department of Mathematics, College of Sciences and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia
2
Laboratoire d’Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, Mascara 29000, Algeria
*
Author to whom correspondence should be addressed.
Nanomaterials 2026, 16(14), 852; https://doi.org/10.3390/nano16140852
Submission received: 7 June 2026 / Revised: 3 July 2026 / Accepted: 8 July 2026 / Published: 10 July 2026
(This article belongs to the Section Theory and Simulation of Nanostructures)
Versions Notes

Abstract

The present research proposes a mathematical method to examine the combined impacts of thermal loading and nonlocal elasticity on the dynamic behavior of functionally graded (FG) nanobeams. A refined higher-order shear deformation theory is introduced, featuring an enhanced displacement field with integral unknowns and a hyperbolic thickness-dependent function to accurately capture transverse shear strains without shear correction constants. Temperature affects the material characteristics, which follow a power-law pattern as they rise through thickness. Using Hamilton’s principle, the study establishes and solves the governing equations analytically. The study discusses how thermal environment, material gradation, and nonlocality alter the dynamic response of FG nanobeams, providing important insights into their nanoscale thermomechanical behavior.
Keywords: FG nanobeams; nonlocal elasticity; thermo-mechanical behavior; dynamic analysis; size-dependent effects FG nanobeams; nonlocal elasticity; thermo-mechanical behavior; dynamic analysis; size-dependent effects

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MDPI and ACS Style

Alghanmi, R.A.; Houari, M.S.A. Coupled Thermal and Nonlocal Effects in Advanced Composite Nanobeams: An Efficient Higher-Order Modeling Approach. Nanomaterials 2026, 16, 852. https://doi.org/10.3390/nano16140852

AMA Style

Alghanmi RA, Houari MSA. Coupled Thermal and Nonlocal Effects in Advanced Composite Nanobeams: An Efficient Higher-Order Modeling Approach. Nanomaterials. 2026; 16(14):852. https://doi.org/10.3390/nano16140852

Chicago/Turabian Style

Alghanmi, Rabab A., and Mohammed Sid Ahmed Houari. 2026. "Coupled Thermal and Nonlocal Effects in Advanced Composite Nanobeams: An Efficient Higher-Order Modeling Approach" Nanomaterials 16, no. 14: 852. https://doi.org/10.3390/nano16140852

APA Style

Alghanmi, R. A., & Houari, M. S. A. (2026). Coupled Thermal and Nonlocal Effects in Advanced Composite Nanobeams: An Efficient Higher-Order Modeling Approach. Nanomaterials, 16(14), 852. https://doi.org/10.3390/nano16140852

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