Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6749314 | International Journal of Solids and Structures | 2013 | 13 Pages |
Abstract
This work presents several higher-order atomistic-refined models for the static, free vibration and stability analysis of three-dimensional nano-beams. Stemming from a one-dimensional approach and thanks to a compact notation for the a priori kinematic field approximation over the beam cross-section, the model derivation is made general regardless the approximation order. This latter is a free parameter of the formulation. Several higher-order beam theories can be obtained straightforwardly. Classical beam models, such as Euler-Bernoulli's and Timoshenko's, are obtained as particular cases. The assumed constitutive equations for orthotropic materials account for the surface free energy effect as well as the third-order elastic constants. The resulting stiffness coefficients depend upon the cross-section side length. The governing equations and boundary conditions are variationally obtained through the Principle of Virtual Displacements. A Navier-type, strong form solution is adopted. Simply supported beams are, therefore, investigated. Static, free vibration and buckling analyses are carried out in order to investigate the effect of the cross-section side as well as the crystallographic plane orientation on the mechanical response. Beams with different values of the length-to-thickness ratio are considered. Results are validated in terms of accuracy and computational costs towards three-dimensional FEM solutions. Numerical investigations show the advantages of refined beam models over the classical ones demonstrating that accurate results can be obtained with reduced computational costs.
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Authors
Gaetano Giunta, Yao Koutsawa, Salim Belouettar, Heng Hu,