Abstract
Motivated by the need to have a fully nonlinear beam model usable at the nanoscale, in this paper the equilibrium problem of inflexed nanobeams in the context of nonlocal finite elasticity is investigated. Considering both deformations and displacements large, a three-dimensional kinematic model has been proposed. Extending the linear nonlocal Eringen theory, a constitutive law in integral form for the nonlocal Cauchy stress tensor has been defined. Finally, by imposing the equilibrium conditions, the governing equations are obtained. These take the form of a coupled system of three equations in integral form, which is solved numerically. Explicit formulae for displacements, stretches and stresses in every point of the nanobeam are derived. By way of example, a simply supported nanobeam, which is inflexed under nonlinear conditions, has been considered. The nonlocal effects on the deformation and internal actions are shown through some graphs and discussed in detail.
Highlights
Nanobeams are fundamental mechanical components in different areas of modern nanotechnology
Both strains and displacements are considered large and the anticlastic deformation of the cross sections has been taken into account
The bending theory for nanobeams in the fully nonlinear framework of finite elasticity is presented in this paper
Summary
Nanobeams are fundamental mechanical components in different areas of modern nanotechnology. Buchanan and McNitt [9] were the first to apply nonlocal continuum mechanics to capture the size effects on bending of cantilever nanobeams. Recent contributions on this subject can be found in [10], [11], [12], [13] and [14]. Despite the numerous applications in emerging scientific fields, where the nonlinear effects related to large deformations and large displacements are evident, to date a modeling of nanobeams in the framework of fully nonlinear continuum mechanics is still not available. The results obtained using the nonlocal theory have been compared and discussed with those provided by the classical local theory
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