Buckling Analysis of Nonlocal Nanocolumns Using Finite Element Method

Abstract

This research introduces a finite element method, considering size-dependent effect via nonlocal elasticity to analyze the buckling load of columns subjected to concentrated, distributed, and combined load cases. Two types of columns are considered: columns with a constant moment of inertia and nonuniform cross-section. The end conditions of columns comprise the following: clamped-free, hinged–hinged, clamped–hinged, and clamped–clamped. This paper illustrates the computational results using the relationship between buckling load normalized via the classical eigenvalue buckling load. The current findings show that the buckling load dramatically decreases at the normalized material length scale between 1 and 10. The most and least considerable effects on buckling load reduction are clamped–clamped and clamped-free end conditions. For the case of combined loads, a buckling concentrated load decreased proportionally as applied uniformly distributed force increased. An increase in concavity (or convexity) of parabolic columns will influence the buckling of the concentrated and uniformly distributed buckling loads.