A novel fractional nonlocal model and its application in buckling analysis of Euler-Bernoulli nanobeam

Abstract

The present study aims to analyze the buckling behavior of Euler–Bernoulli nanobeam in conjunction with a novel fractional nonlocal model namely conformable fractional nonlocal model. Fractional models are getting more popular among the researchers because of its applicability and fixability to handle many complex physical phenomena which are not possible to model with integer operators. Also, the main advantage of fractional models over integer model is its applicability to handle both the integer and noninteger operators which makes it much more flexible in term of real-world application. In this regards, the nonlocal constitutive relation is developed in conjunction with conformable fractional derivatives and fractional strain energy to analyze the buckling behavior of Euler–Bernoulli Nanobeam. In this study, the Simply Supported-Simply Supported (SS), Clamped-Simply Supported, and Clamped-Clamped boundary conditions are taken into the investigation with the help of the Differential Quadrature Method (DQM). Critical buckling load parameters are computed for the SS, CS, and CC boundary conditions from generalized eigenvalue problem. Graphical, as well as tabular results, are calculated by using MATLAB programmes and effects of various parameters such as fractional parameter, nonlocal parameter, aspect ratio on critical buckling load parameters extensively studied.