Non-local theory of buckling of tapered nano columns under self weight and an axial tip load using matrix based Chebyshev spectral collocation (MBCSC)

Abstract

In this paper, elastic buckling of tapered Euler Bernoulli nano columns for tip load and self weight using non-local theory of elasticity is studied using matrix based Chebyshev spectral collocation method (MBCSC). The size effect is taken into consideration using Eringen’s non-local elasticity theory. Detailed numerical analyses about the effects of boundary conditions and load types are conducted and the influence of non-local parameter on the static buckling response of tapered or uniform nano tubes and rods is discussed. It is hoped that the results in this paper may present a bench mark in the study of buckling of tapered nano rods and tubes.