In this paper, the bending and buckling analysis of microbeam with the uniform and non-uniform cylindrical cross-section was examined based on the classical beam theory and the modified couple stress theory to model the micro-structures effects. The nonlinear effect of the Von-Kármán theory is regarded to study the large-deflection effect on the buckling of microtubes. The conservation energy principle is used to derive the nonlinear equation of motion and the boundary conditions. The effect of several applicable cross-sections, including the linear, exponential, and convex function, on the static behavior of cylindrical beam is investigated, which is made by the porosity-dependent axially functionally graded material. The homotopy perturbation technique as a semi-analytical solution, coupled with the generalized differential quadrature method, is employed to obtain the nonlinear results. Eventually, the influence of various parameters such as the porosity, volume fraction index, bending load, nonlinear deflection, length-scale effect on the bending deflection, and buckling of microbeam with both clamped and pinned supported are analyzed in details.

在本文中，基于经典梁理论和修正的耦合应力理论，研究了具有均匀和非均匀圆柱截面的微梁的弯曲和屈曲分析，以模拟微结构效应。Von-Kármán 理论的非线性效应被认为是研究微管屈曲的大挠度效应。能量守恒原理用于推导非线性运动方程和边界条件。研究了几种适用的横截面，包括线性函数、指数函数和凸函数，对圆柱梁静态行为的影响，圆柱梁由孔隙率相关的轴向功能梯度材料制成。同伦微扰技术作为半解析解，结合广义微分求积法，用于获得非线性结果。最后，详细分析了微梁的孔隙率、体积分数指数、弯曲载荷、非线性挠度、长度尺度效应对弯曲挠度和屈曲等各种参数的影响。