Limit load analysis and imperfection sensitivity of porous FG micro-tubes surrounded by a nonlinear softening elastic medium

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.