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.

本文介绍了在高温区域中功能梯度多孔（FGP）拱结构的分析过程。FGP弓由石墨烯血小板（GPL）增强。解析表达式用于说明孔和GPL在交叉轮廓中的分布。通过在胎冠部分引入较小的点载荷来考虑较小的胎冠凹痕。非线性薄壁壳理论被用来表达变形拱的势能函数。然后，通过假设余弦函数来描述变形拱的径向位移，明确表示该能量函数。通过微分能量函数获得了两个非线性的平衡公式，从而导致临界温度变化的隐式形式，当凹痕可忽略时，它可以简化为显式形式。此外，导出的分析溶液已通过具有均质性的铝环验证。最后，进行分析以估计各种几何和材料参数对临界温度变化和平衡图的影响。