Устойчивость неоднородных нано-микро элементов на основе нелокальной теории упругости

Abstract

In this article, the bending and stability analysis of nonhomogeneous nano and micro elements have been made by using the nonlocal elasticity theory. Beam has been chosen as the structural model type. Euler-Bernoulli beam theories have been used for beam theories. The motion equations of Euler-Bernoulli beam theories were expressed by using nonlocal elasticity theory ,which was proposed by Eringen. According to different boundary conditions, the bending and stability equations of micro-nano beam have been generated then, in order to observe the effect of non local behavior, analysis have been made over carbon nanotybe and microtubules and results have been compared with the classical theory. After solving the equations obtained Analytical formulas for determining critical load and held various analysis. Analysis numerical calculations shows that the heterogeneity of the material properties of the element can have a significant impact on the critical parameters of the element.