Bending Vertically and Horizontally of Compressive Nano-rods Subjected to Nonlinearly Distributed Loads Using a Continuum Theoretical Approach

Abstract

In nano-electro-mechanical systems, a component named a compressive nano-rod sometimes bears lateral and axial loads at the same time, resulting in a vertical and horizontal bending deformation. Motivated by it, this paper presents the bending vertically and horizontally of a compressive nano-rod, and the nano-rod is subjected to lateral nonlinearly distributed loads and axial compressive stresses initially. Different from the previous studies most of which were concerned on a simply supported compressive rod with linear loads, a statically indeterminate fixed–fixed compressive nano-rod is investigated. Based on the strain gradient type of nonlocal continuum theory, we derive the theoretical formulations analytically. To this end, the nonlocal differential constitutions for stress and bending moment provide the bases of theoretical modeling. The effects of an internal characteristic scale and other external parameters on bending vertically and horizontally including the limit compressive stress, bending deflection and bending moment are examined, respectively, via the explicit results obtained in the theoretical model. It shows that the limit compressive stress decreases due to the existence of the nonlocal scale effect, but it increases with increasing the material stiffness of nano-rods. Hence, the critical value of material stiffness is predicted. If the material stiffness is higher than its critical value, the bending vertically and horizontally of compressive nano-rods with nonlinear loads is stale, while it turns to be instable if the material stiffness is lower than its critical value. Moreover, the nonlocal scale and material stiffness are coupled in bending vertically and horizontally. The work can offer a reference for designing, regulating and controlling the compressive nano-rods with nonlinearly distributed loads.