Abstract

This article deals with the linear and nonlinear buckling behavior of porosity-dependent functionally graded (FG) non-uniform microtubes. The modified couple stress theory is determined to consider small-scale effects on the micro-size tube which is modeled, based on the Euler–Bernoulli beam theory in conjunction with the employment of the conservation energy principle to derive the nonlinear governing equations regarding the nonlinear Von-Kármán strains. The main contribution of this article is the impact of cross-sections on the static behavior of cylindrical beams with four applicable cross-sections, involving the exponential, linear, and convex in comparison of uniform section for the radial distribution of ceramic and metal material based on the power-law function. Also, the pinned, clamped, and combination of these boundary conditions are defined as the boundary supports, and the generalized quadrature method (GDQM) is utilized as the numerical solving technique along with the iteration method to solve the nonlinear equations. Finally, the obtained results extracted to investigate the impact of various parameters, involving the nonlinear amplitude, power FG index, porosity parameter, small-scale parameter, and different cross-sections on the buckling treatment of cylindrical beam.

摘要

本文讨论了孔隙率相关的功能梯度 (FG) 非均匀微管的线性和非线性屈曲行为。修正的力偶应力理论考虑了微尺寸管的小尺度效应，基于欧拉-伯努利梁理论并结合能量守恒原理推导了非线性控制方程冯卡门菌株。本文的主要贡献是截面对具有四种适用截面的圆柱梁静态行为的影响，涉及基于陶瓷和金属材料的径向分布的均匀截面的指数、线性和凸形比较关于幂律函数。此外，固定、夹紧、并将这些边界条件的组合定义为边界支撑，并利用广义求积法（GDQM）作为数值求解技术与迭代法一起求解非线性方程。最后提取所得结果，考察非线性振幅、功率FG指数、孔隙率参数、小尺度参数、不同截面等参数对圆柱梁屈曲处理的影响。