Analytical and numerical studies on the nonlinear stability of the encased FGP-GPLs oval linings under mechanical loadings

The functionally graded porous (FGP) linings reinforced by graphene platelets (GPLs) are applied to rehabilitate damaged pipes in practical engineering. The lining is susceptible to local buckling under a crown-concentrated loading. Insufficient expansion and deformations of the host pipe may induce ovalization of the lining during installation, which poses a significant threat to the long-term stability of the pipe-lining system. Therefore, this study explores the instability mechanism of encased FGP-GPLs oval linings under a crown concentrated load. The cross-sectional distributions of pores and GPLs in the lining are established by combining the Halpin-Tsai micromechanical rule and the Gaussian random field, respectively. A displacement expression is proposed to express the deflection of the oval lining. The load-displacement equilibrium paths and buckling loads are predicted by employing the principle of minimum potential energy and nonlinear thin-walled shell approaches. The theoretical solutions are systematically compared with alternative closed-form solutions and numerical results. Good consistency confirms the effectiveness of the theoretical method. Finally, the impacts of porosity coefficient, GPLs content, and ovality on the load-displacement equilibrium paths are evaluated. It is found that the critical buckling load increases 54.45% by mixing 1% GPLs, and decreases by 39.20% as the ovality increases from 0% to 10%, respectively.