Please use this identifier to cite or link to this item:
|Title:||Discrete systems behave as nonlocal structural elements: Bending, buckling and vibration analysis|
|Keywords:||Finite difference equation|
|Source:||Challamel, N., Wang, C.M., Elishakoff, I. (2014). Discrete systems behave as nonlocal structural elements: Bending, buckling and vibration analysis. European Journal of Mechanics, A/Solids 44 : 125-135. ScholarBank@NUS Repository. https://doi.org/10.1016/j.euromechsol.2013.10.007|
|Abstract:||It is shown herein that the bending, buckling and vibration problems of a microstructured beam can be modeled by Eringen's nonlocal elasticity model. The microstructured model is composed of rigid periodic elements elastically connected by rotational springs. It is shown that this discrete system is the finite difference formulation of a continuous problem, i.e. the Euler-Bernoulli beam problem. Starting from the discrete equations, a continualization method leads to the formulation of an Eringen's type nonlocal equivalent continuum. The sensitivity phenomenon of the apparent nonlocal length scale with respect to the bending, the vibrations and the buckling analyses is investigated in more detail. A unified length scale can be used for the microstructured-based model with both nonlocal constitutive law and nonlocal governing equations. The Finite Difference Method is used for studying the exact discrete problem and leads to tractable engineering formula. The bending behaviour of the microstructured cantilever beam does not reveal any scale effect in the presence of concentrated loads. This scale invariance is not a deficiency of Eringen's nonlocality because it is in fact supported by the exact discreteness of the microstructured beam. A comparison of the discrete and the continuous problems (for both static and dynamics analyses) show the efficiency of the nonlocal-based modelling for capturing scale effects. As it has already been shown for buckling or vibrations studies, small scale effects tend to soften the material in this case. © 2013 Published by Elsevier Masson SAS.|
|Source Title:||European Journal of Mechanics, A/Solids|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Feb 14, 2018
WEB OF SCIENCETM
checked on Feb 14, 2018
checked on Feb 20, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.