An attempt is made in the current research to analyse the nonlinear thermal stability and imperfection sensitivity of functionally graded (FG) porous micro-tubes. Temperature-dependent properties of the geometrically imperfect micro-tube are graded across the radius of cross-section. It is assumed that the micro-tube with different end conditions is in contact with a two-parameter elastic foundation. The nonlinear component of the elastic foundation can be of the hardening or softening type. The equilibrium equations are obtained within the framework of von Kármán nonlinear assumptions and high-order shear deformation tube theory. The governing equations are reformulated for the case of imperfect micro-tubes based on the modified couple stress theory. The system of nonlinear differential equations is solved using the two-step perturbation technique and Galerkin procedure. The analytical solutions are obtained for three different types of immovable boundary conditions which are clamped-rolling, simply-supported and clamped–clamped. The closed-form expressions are given to obtain the large deflection in the micro-tube as a function of the elevated temperature. Novel parametric studies are given to explore the thermal stability and imperfection sensitivity analysis of the perfect and imperfect micro-tubes, respectively. The effects of boundary conditions, couple stress components, porosity coefficient, elastic foundation, FG pattern, temperature dependence and geometrical parameters are studied.

当前的研究试图分析功能梯度（FG）多孔微管的非线性热稳定性和缺陷敏感性。几何不完美的微管的随温度变化的特性在整个横截面半径上都是渐变的。假定具有不同最终条件的微管与两参数弹性基础接触。弹性基础的非线性成分可以是硬化或软化类型。在vonKármán非线性假设和高阶剪切变形管理论的框架内获得了平衡方程。基于改进的耦合应力理论，针对不完善的微管情况，重新制定了控制方程。使用两步摄动技术和Galerkin程序求解非线性微分方程组。对于三种不同类型的不动边界条件，即夹紧滚动，简单支撑和夹紧夹紧，可以获得解析解。给出封闭形式的表达式以获得微管中随高温升高的大挠度。进行了新颖的参数研究，分别探索了完美和不完美微管的热稳定性和不完美灵敏度分析。研究了边界条件，耦合应力分量，孔隙率系数，弹性基础，FG图案，温度依赖性和几何参数的影响。对于三种不同类型的不动边界条件，即夹紧滚动，简单支撑和夹紧夹紧，可以获得解析解。给出封闭形式的表达式以获得微管中随高温升高的大挠度。进行了新颖的参数研究，分别探索了完美和不完美微管的热稳定性和不完美灵敏度分析。研究了边界条件，耦合应力分量，孔隙率系数，弹性基础，FG图案，温度依赖性和几何参数的影响。针对三种不同类型的不动边界条件获得了解析解，这些条件是夹紧滚动，简单支撑和夹紧夹紧。给出封闭形式的表达式以获得微管中随高温升高的大挠度。进行了新颖的参数研究，分别探索了完美和不完美微管的热稳定性和不完美灵敏度分析。研究了边界条件，耦合应力分量，孔隙率系数，弹性基础，FG图案，温度依赖性和几何参数的影响。进行了新颖的参数研究，分别探索了完美和不完美微管的热稳定性和不完美灵敏度分析。研究了边界条件，耦合应力分量，孔隙率系数，弹性基础，FG图案，温度依赖性和几何参数的影响。进行了新颖的参数研究，分别探索了完美和不完美微管的热稳定性和不完美灵敏度分析。研究了边界条件，耦合应力分量，孔隙率系数，弹性基础，FG图案，温度依赖性和几何参数的影响。