Thermal-elastic buckling of the arch-shaped structures with FGP aluminum reinforced by composite graphene platelets

Abstract

This paper presents the analytical process of the functionally graded porous (FGP) arch structure in an elevated thermal field. The FGP arch is reinforced by graphene platelets (GPLs). Analytical expressions are used to illustrate the distribution of the pores and GPLs in the cross profile. A small crown dent is considered by introducing a small point load on the crown portion. The nonlinear thin-walled shell theory is used to formulate the potential energy function of the deformed arch. Then, this energy function is expressed explicitly by assuming a cosine function to describe the radial displacement of the deformed arch. Two nonlinear formulae of equilibrium are obtained by differentiating the energy function, resulting in an implicit form of the critical temperature change, which reduces to an explicit form when the dent is negligible. Moreover, the derived analytical solutions are verified by an aluminum ring with homogeneity. Finally, an analysis is developed to estimate the effect of various geometric and material parameters on the critical temperature changes and the equilibrium plots.