Abstract

This article studies the large deflection stability of axially functionally graded (AFG) cantilever column for analyzing post-buckling behavior. Consideration is given to a nonlinearly tapered column with a regular polygon cross section, whose volume is constant. The governing differential equations of the problem are derived based on the large deflection beam theory. To calculate the elastica and buckling load of the AFG column, the differential equations are solved with the direct integration method together with the nonlinear solution method. The computed results are compared with those reported in literature and obtained from finite element method. Numerical examples are provided to ascertain the effects of the geometric and material parameters on the elastica and buckling load. The elastica shape is shown to depend on applied load and column properties, and the optimal shape such that the AFG column with fixed volume enables to bear the maximum buckling load is discussed.

摘要

本文研究了轴向功能梯度 (AFG) 悬臂柱的大挠度稳定性，用于分析后屈曲行为。考虑具有正多边形截面且体积恒定的非线性锥形柱。基于大偏转梁理论推导了该问题的控制微分方程。为了计算AFG柱的弹性和屈曲载荷，微分方程采用直接积分法和非线性求解法求解。将计算结果与文献中报道的和通过有限元方法获得的结果进行了比较。提供了数值示例以确定几何和材料参数对弹性和屈曲载荷的影响。