A refined beam model for anisotropic nanobeams based on Eringen's differential constitutive model

Abstract

Based on the Eringen's differential constitutive law and Reissner’s Mixed Variational Theorem (RMVT), a refined nonlocal model is developed to analyze the bending, free vibration and buckling behaviors of anisotropic nanobeams. To overcome the drawbacks of the previous composite nonlocal models in dealing with continuous interlaminar stresses at the interfaces, present nonlocal zigzag model satisfied the interlaminar continuity conditions and free surface conditions a priori by introducing a refined zigzag theory and RMVT. Subsequently, several local and nonlocal beam models are taken as illustrative examples, the problem of the bending, free vibration and buckling are analytically and numerically solved based on the Navier method and differential quadrature method (DQM). Illustrative examples indicate that the predicted results agree well with the previous three-dimensional elasticity solutions which demonstrate the correctness and accuracy of present formulation. Furthermore, the nonlocal parameter has a significant effect on the stiffness of the beam. The stiffness of the material is getting soft with the increasing nonlocal parameter in the fully simply supported, fully clamped and simply supported-clamped boundary conditions. Finally, it is show that the layout, nonlocal parameter and length-to-thickness play important roles on the % error between present nonlocal zigzag model and the previous models.