Buckling Analysis of Non-Local Timoshenko Beams by Using Fourier Series

Year 2017, Volume: 9 Issue: 4, 89 - 99, 27.12.2017

Hayrullah Kadıoğlu , Mustafa Özgür Yaylı

https://doi.org/10.24107/ijeas.362242

Cited By: 3

Abstract

In this study, buckling
analysis of a nano sized beam has been performed by using Timoshenko beam
theory and Eringen’s nonlocal elasticity theory. Timoshenko beam theory takes
into account not only bending moment but also shear force. Therefore, it gives
more accurate outcomes than Euler Bernoulli beam theory. Moreover, Eringen’s
nonlocal elasticity theory takes into account the small scale effect. Thus,
these two theories are utilized in this study. The vertical displacement function
is chosen as a Fourier sine series. 
Similarly, the rotation function is chosen as a Fourier cosine series.
These functions are enforced by Stokes’ transformation, and higher order
derivatives of them are obtained. These derivatives are written in the
governing equations for the buckling of nonlocal Timoshenko beams. Hence
Fourier coefficients are acquired.  Subsequently
boundary condition of established beam model is identified with Timoshenko beam
and Eringen’s nonlocal elasticity theories, and the linear equations are
obtained.  A coefficients matrix is
created by utilizing these linear systems of equations. When determinant of
this coefficient matrix is calculated, the critical buckling loads are
acquired. Finally, achieved outcomes are compared with other studies in the
literature.  Calculated results are also
presented in a series of figures and tables

Keywords

Timoshenko beam theory, Eringen’s nonlocal elasticity theory, elastic buckling analysis, Stokes’ transformation

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