Large Deflection and Post-Buckling Analysis of Cantilever Nanorods Including Effects of Couple and Surface Stresses by Intrinsic Coordinate Finite Elements

Abstract

This paper presents a novel approach to the analysis of large deflection and post-buckling behavior of cantilever nanorods under different load conditions. The proposed approach utilizes a variational method, incorporating the Gurtin–Murdoch surface elasticity theory and the consistent couple stress theory to account for size-dependency effects. By accounting for the strain energy contributions of the bulk material, surface layer, and load conditions, this approach expresses the behavior of the nanorods in terms of their intrinsic coordinates. A finite element method was used to solve this numerical problem, generating a system of non-linear equations that were iteratively solved using the Newton–Raphson method. The results obtained from the finite element method were confirmed by those from the shooting method. Also, it highlights the effectiveness of the variational model in predicting the large deflection and post-buckling behavior of cantilever nanorods while considering both surface stress and couple stress effects. Furthermore, the study investigated the influence of surface stress and couple stress on the response of the nanorods to point and uniform loads. The results showed that incorporating both effects enhanced the stiffness of the nanorods compared to scenarios in which these effects were neglected. In addition, the couple stress effect was found to have a greater influence on the stiffening of nanorods for the same value of unitless parameters compared to surface stress effects. These findings offer valuable insights into the large deflection and post-buckling behavior of cantilever nanorods and highlight the importance of surface stress and couple stress effects. The model proposed in this study has potential applications in advanced technological device designs by providing a comprehensive understanding of the mechanical response of nanorods, allowing for more accurate predictions and enhanced device performance.