Thermally induced nonlinear stability and imperfection sensitivity of temperature- and size-dependent FG porous micro-tubes

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.