Stability analysis of arbitrary restrained nanobeam embedded in an elastic medium via nonlocal strain gradient theory

A novel stability model is analytically reformulated for the nano-sized beam resting on a one-parameter elastic foundation. The stability solution is based on the nonlocal strain gradient elasticity theory. To corporate the small size effects, two small scale parameters are introduced. The six-order...

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Bibliographic Details
Published in:Journal of strain analysis for engineering design 2023-11, Vol.58 (8), p.672-683
Main Authors: Uzun, Büşra, Yaylı, Mustafa Özgür
Format: Article
Language:English
Subjects:
Boundary conditions
Buckling
Elastic deformation
Elastic foundations
Elastic media
Elastic properties
Formability
Fourier series
Lateral stability
Linear equations
Mathematical models
Parameters
Sine series
Size effects
Stability analysis
Strain
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Summary:A novel stability model is analytically reformulated for the nano-sized beam resting on a one-parameter elastic foundation. The stability solution is based on the nonlocal strain gradient elasticity theory. To corporate the small size effects, two small scale parameters are introduced. The six-order ordinary differential form of the buckling equation, together with two force boundary conditions, are utilized to examine the stability equation in terms of lateral deflection. The infinite terms of linear equations are discretized with the help of the Stokes’ transformation and Fourier sine series. The present work can investigate the effects of elastic spring parameters at the ends, nonlocal properties, elastic medium properties, strain gradient parameter, and buckling behavior of the nanobeam. The predictions of the proposed analytical model with deformable boundary conditions are in agreement with those available in the scientific literature for the nanobeam on elastic foundation based on a closed form of solution. The presence of the deformable conditions, elastic foundation, nonlocal, and strain gradient properties change the buckling loads and buckling mode shapes.
ISSN:0309-3247
2041-3130
DOI:10.1177/03093247231164261