边界变温时梯度板稳态热传导及影响因素

Steady heat conduction in FGM plate under boundary variable temperatures and effect factor

为了研究边界变温时功能梯度板的二维稳态热传导及梯度参数γ的影响,基于该板的二维稳态热传导基本方程,假设热导率沿板高呈指数函数形式分布,用分离变量法和三角函数正交性,导出三边界恒温与上边界变温时该板的二维稳态温度场的解析解,与有限元解对比可知,2种方法结果一致。结果显示:上边界线性热载时,板内温度场分布无对称性;上边界正弦热载时,板内温度场分布对称于过形心的y轴;随着γ的增大,板内高温区不断向两侧和下侧扩展。因此,可选择适合的梯度参数和边界不同变温来满足设计、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。

To study the 2D steady temperature fields in the functionally gradient materials （FGM） plate under boundary variable temperatures and the effect of gradient parameter γ.This analyrical solution was based on the 2D steady heat the analytical solution of the 2D steady temperature fields in the plate under three boundary constant temperatures and upper boundary variable temperatures was derived by variable separation method and the orthogonality of trigonometric function.This analyrical solution was compared with finite element method （FEM）,the results of these two methods were consistent.The results run as follows.First,the distribution of the temperature field in the plate is not symmetrical under upper boundary linear thermal load,and the temperature field distribution in the plate is symmetrical to the axis y through the centroid under upper boundary sine thermal load.Second,with the increase of γ,the high temperature zone in the plate extends continuously to the two sides and the lower side of the plate.Thus,the suitable selection ofγ and boundary different variable temperatures 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.