In the analysis of functionally graded materials （FGMs）, the uncoupled approach is used broadly, which is based on homogenized material property and ignores the effect Of local micro-structural interaction. The higher-order theory for FGMs （HOTFGM） is a coupled approach that explicitly takes the effect of micro-structural gradation and the local interaction of the spatially variable inclusion phase into account. Based on the HOTFGM, this article presents a quadrilateral element-based method for the calculation of multi-scale temperature field （QTF）. In this method, the discrete cells are quadrilateral including rectangular while the surface-averaged quantities are the primary variables which replace the coefficients employed in the temperature function. In contrast with the HOTFGM, this method improves the efficiency, eliminates the restriction of being rectangular cells and expands the solution scale. The presented results illustrate the efficiency of the QTF and its advantages in analyzing FGMs.
