Pre-buckling responses of Timoshenko nanobeams based on the integral and differential models of nonlocal elasticity: an isogeometric approach

Differential form of Eringen’s nonlocal elasticity theory is widely employed to capture the small-scale effects on the behavior of nanostructures. However, paradoxical results are obtained via the differential nonlocal constitutive relations in some cases such as in the vibration and bending analysi...

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Bibliographic Details
Published in:Applied physics. A, Materials science & processing Materials science & processing, 2017-05, Vol.123 (5), p.1-11, Article 330
Main Authors: Norouzzadeh, A., Ansari, R., Rouhi, H.
Format: Article
Language:English
Subjects:
Applied physics
Beam theory (structures)
Buckling
Characterization and Evaluation of Materials
Condensed Matter Physics
Constitutive relationships
Finite element method
Integrals
Machines
Manufacturing
Materials science
Mathematical analysis
Matrix algebra
Matrix methods
Nanotechnology
Nonlocal elasticity
Optical and Electronic Materials
Physics
Physics and Astronomy
Processes
Splines
Surfaces and Interfaces
Thin Films
Timoshenko beams
Vibration analysis
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Summary:Differential form of Eringen’s nonlocal elasticity theory is widely employed to capture the small-scale effects on the behavior of nanostructures. However, paradoxical results are obtained via the differential nonlocal constitutive relations in some cases such as in the vibration and bending analysis of cantilevers, and recourse must be made to the integral (original) form of Eringen’s theory. Motivated by this consideration, a novel nonlocal formulation is developed herein based on the original formulation of Eringen’s theory to study the buckling behavior of nanobeams. The governing equations are derived according to the Timoshenko beam theory, and are represented in a suitable vector–matrix form which is applicable to the finite-element analysis. In addition, an isogeometric analysis (IGA) is conducted for the solution of buckling problem. Construction of exact geometry using non-uniform rational B-splines and easy implementation of geometry refinement tools are the main advantages of IGA. A comparison study is performed between the predictions of integral and differential nonlocal models for nanobeams under different kinds of end conditions.
ISSN:0947-8396
1432-0630
DOI:10.1007/s00339-017-0887-4