An imperfection sensitivity analysis for the nonlinear post-buckling behavior of functionally graded (FG) porous micro-tubes is performed in this research. The case of geometrically imperfect micro-tubes surrounded by a nonlinear elastic medium under axial compressive load is analyzed. Properties of the micro-tube with uniform distributed porosity are FG across the radius of the cross-section. Two types of boundary conditions as simply-supported and clamped are considered. The high-order shear deformation theory of tubes is utilized to approximate the displacement field. Differential equations governing the equilibrium position of the micro-tube are extracted using the virtual displacement principle. These nonlinear equations are analytically solved by means of the two-step perturbation technique and Galerkin procedure. It is shown that when the imperfect micro-tube is in contact with a sufficiently soft foundation, the post-buckling path of the structure is unstable, and therefore the structure is imperfection sensitive. Since the imperfection sensitivity of micro-tubes is not reported in literature, results of this study are compared with buckling responses of perfect FGM tubes. The effects of porosity coefficient, power law index, length scale parameter, and geometrical parameters upon the limit buckling load of imperfect micro-tubes are investigated.

中文翻译：

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非线性软化弹性介质包围的多孔 FG 微管的极限载荷分析和缺陷敏感性

本研究对功能梯度 (FG) 多孔微管的非线性屈曲后行为进行了缺陷敏感性分析。分析了在轴向压缩载荷下被非线性弹性介质包围的几何缺陷微管的情况。具有均匀分布孔隙率的微管的特性是横截面半径上的 FG。考虑了简支和夹紧两种类型的边界条件。利用管的高阶剪切变形理论来近似位移场。使用虚拟位移原理提取控制微管平衡位置的微分方程。这些非线性方程通过两步微扰技术和伽辽金程序进行解析求解。结果表明，当缺陷微管与足够软的基础接触时，结构的后屈曲路径不稳定，因此结构对缺陷敏感。由于文献中没有报道微管的缺陷敏感性，因此将本研究的结果与完美 FGM 管的屈曲响应进行了比较。研究了孔隙率系数、幂律指数、长度尺度参数和几何参数对不完美微管极限屈曲载荷的影响。本研究的结果与完美 FGM 管的屈曲响应进行了比较。研究了孔隙率系数、幂律指数、长度尺度参数和几何参数对不完美微管极限屈曲载荷的影响。本研究的结果与完美 FGM 管的屈曲响应进行了比较。研究了孔隙率系数、幂律指数、长度尺度参数和几何参数对不完美微管极限屈曲载荷的影响。