The heat conductivity in the FGM plate was expressed by exponential function along the height direction of the plate,based on the plane steady heat conduction basic equation of the plate,the series analytical solution of the plane steady temperature fields of in the plate subjected to the different constant temperature of boundary was derived by variable separation method.Compared with FEM,the maximum node temperature error of two methods was 0.86％.Through the numerical calculations,the plane steady temperature field distributions in the plate were obtained,and the effects of material gradient parameters and the geometric composition of the plate on the temperature fields were studied.The main results show as follows:(1) The temperature field distribution in the plate is symmetrical to the axis y through the centroid.(2) With the increase of gradient parameter value,the high temperature zone in the plate is extended to the two sides and lower side of plate.(3) With the decreasing of the plate height,central lower temperature distribution in the plate tends gently.Thus,the suitable selection of gradient parameter and geometric composition can meet the need of the design,application and analysis of the thermal stress,and the analytical solution obtained can be used as a reference standard for other approximate methods.%假设热导率沿功能梯度板高呈指数函数形式分布,基于该板的平面稳态热传导基本方程,用分离变量法,导出边界不同恒温时该板的平面稳态温度场的级数解析解,与有限元解对比,两种方法的最大节点温度误差0.86％.通过数值计算,获得了该板的平面稳态温度场分布,研究了板的梯度参数和几何组成对温度场的影响.主要结果表明:板内的温度场分布对称于过形心的y轴；随着梯度参数值的增加,板内的高温区向左右两边界和下边界逐步扩展；随着板高的递减,板内中下部的温度分布趋于平缓.因此,可选择适合的梯度参数和几何组成来满足设计、应用和热应力分析的需要,所获得的解析解可作为检验其他近似方法的参考标准.
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