Influence of cross-section on the linear and nonlinear buckling analysis of imperfect functionally graded micro-tubes

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.