Analytical buckling scheme of a functionally graded porous liner reinforced by nanocomposites encased in an egg-shaped pipe

This study uses the FGP-GPLs (functionally graded porous metal reinforced by graphene platelets) to rehabilitate the egg-shaped liner-pipe system. The water penetrates the cracked pipe and surrounds the thin-walled liner, resulting in hydrostatic pressure that may contribute dominantly to the buckling of the thin-walled liner. The critical buckling pressure is derived analytically by combining the thin-walled shell theory, a refined displacement function, and the energy scheme. It is found the egg-shaped FGLs liner sustains higher buckling pressure than the circular FGP-GPLs one. Furthermore, a finite element model is developed to verify the theoretical solutions. The results indicate the numerical equilibrium paths agree well with the analytical ones. In addition, the present analytical predictions are compared successfully with other close-formed solutions. Finally, parametric analyses indicate that the addition of GPLs may significantly improve the stability of the egg-shaped liner, while the increase of pores decreases the stability of the liner. The thickness of the GPLs has a slight effect on the stability of the liner when the volume of GPLs is constant. Thus, thick GPLs may be recommended in engineering practices to reduce the manufacturing cost.