Analytical Approach and Shooting Method for the Solution of a Nonlocal Eringen Elasticity Problem of Nanorods

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Authors

  • Aleksandra Manecka-Padaż Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland ORCID ID 0000-0001-5714-4927
  • Ewa Eliza Rożko Institute of Fundamental Technological Research, Polish Academy of Sciences; Institute of Outcomes Research, Maria Sklodowska-Curie Medical Academy, Poland ORCID ID 0000-0001-7020-7080
  • Zdzisław Nowak Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland ORCID ID 0000-0003-4441-5112
  • Piotr Chudzinski Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland ORCID ID 0000-0003-2362-9963

Abstract

The aim of this paper is to study the post-buckling behavior of nanorods, taking into account small scale effects. In this paper, the buckling of a nanorod column subjected to a tip load is investigated. The nanorod is on a clamped support at one end, while the other end is simply supported and subjected to axial compression. At this end, the nanorod is movable only in the horizontal direction. The governing differential equation describing the behavior of the nanorod is derived from the moment–curvature relationship, in analogy with the classical Euler–Bernoulli beam theory, together with the equilibrium equations, including the effects of nonlocal elasticity, as well as the corresponding boundary conditions. A numerical shooting method is derived and employed to solve the differential equations in this problem. The results, including nonlocal elasticity, reveal that nanorods have decreased structural stiffness and show a significant effect of geometrical parameters on the stability of buckled nanorods, emphasizing the importance of accounting for their interaction in the design of nanostructural systems.

Keywords:

nonlocal elasticity theory, nanorods, small-scale effect, postbuckling behaviors

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