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A nonlocal finite element model for buckling and vibration of functionally graded nanobeams

A.I. Aria, M.I. Friswell, Michael Friswell

Composites Part B: Engineering, Volume: 166, Pages: 233 - 246

Swansea University Author: Michael Friswell

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DOI (Published version): 10.1016/j.compositesb.2018.11.071

Abstract

In this paper, a nonlocal (strain-driven) finite element model is presented to examine the free vibration and buckling behaviour of functionally graded (FG) nanobeams on the basis of first-order shear deformation theory (FSDBT). The proposed beam element has five nodes and ten degrees of freedom. Th...

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Published in: Composites Part B: Engineering
ISSN: 13598368
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa46044
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Abstract: In this paper, a nonlocal (strain-driven) finite element model is presented to examine the free vibration and buckling behaviour of functionally graded (FG) nanobeams on the basis of first-order shear deformation theory (FSDBT). The proposed beam element has five nodes and ten degrees of freedom. The material properties of the FG nanobeam are assumed to vary in the thickness direction according to the power-law form. The stretching-bending coupling effect is eliminated by employing the neutral axis concept. Governing equations are deduced with the aid of Hamilton's principle. Buckling loads and natural frequencies are calculated for different nonlocal coefficients, boundary conditions (BCs), power-law indices, and span-to-depth ratios. The accuracy of the proposed element is verified by comparing with available benchmark results in the literature.
Keywords: Functionally graded materials, Nonlocal elasticity theory, Finite element method, Free vibration, Buckling, First-order shear deformation theory
College: Faculty of Science and Engineering
Start Page: 233
End Page: 246

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