Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method

Recently, it was shown that the length scales presented in nonlocal elasticity and strain gradient theory each describe a different physical and material properties of structures at small scales. Accordingly, in this article, by using the new accurate nonlocal strain gradient theory, buckling behavior of nonuniform small-scale beam is investigated. Nanobeam is assumed with variable cross section through the length by exponentially varying the width. According to the size effects, higher order strain deformations and nonlocal effects are modeled on the Euler-Bernoulli beam. Governing equation of motion is presented using Hamilton's principle for nonuniform nonlocal strain gradient beams and solved using generalized differential quadrature method for higher order differential equations. Accuracy of the current methodology is discussed by increasing the number of sampling points and merging to unique solutions. Moreover, in order comprehend the nonuniformity effects on nonlocal strain gradient beams, parametric study is done and presented for different variables. It is shown that nonuniformity could have a significant efficacy on critical buckling loads depending on the ratio between nonlocal and strain gradient parameters. This study is a step forward in better understanding the behavior of nonuniform small scale beams to be used in different nanoscale structures. Keywords: Buckling, Nonlocal strain gradient theory, Nonuniform nanobeam, Variable cross section, GDQ