正交各向异性功能梯度层合板稳态热传导问题的精确解  

Exact Solution of Steady-state Heat Conduction for Axisymmetric Functionally Graded Layered Circular Plate

作　　者：汪文帅[1] 时朋朋[1,2] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021 [2]西安电子科技大学机电工程学院,陕西西安710071

出　　处：《数学的实践与认识》2014年第7期286-292,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(41204041;11261041;11261045);高等学校博士学科点专项科研基金资助课题(博导类;20116401110002)

摘　　要：对轴对称正交各向异性功能梯度层合圆板稳态热传导问题进行精确分析.假设材料热传导率沿板厚方向按指数函数形式梯度分布,从正交各向异性功能梯度圆板稳态热传导的基本方程出发,利用分离变量法,获得了在上、下表面作用任意热分布情况下的精确解.通过数值算例的分析,指出材料性质的梯度变化、板厚边界条件等分析了对温度场分布的影响.所获得的精确结果,可以作为评价其它近似方法的标准解答.An exact analysis of steady-state heat conduction was presented for the axisym- metric functionally graded layered circular plate. Based on the assumption that the heat conductivity has the exponential dependence on the plate- thickness direction, an exact solu- tion was obtained for the axisymmetric orthotropic functionally graded circular plate subjected to arbitrary thermal loads on its upper and lower surfaces by the variable separation method which is used to solve the basic equation of heat conduction. The influences of variation of material graded distributions and plate-thickness and variation of boundary condition on the temperature field distributions of the circular plate were studied through some numeri- cal examples. The obtained exact solution can serve as a benchmark result to assess other approximate methodologies.

关 键 词：功能梯度圆板 稳态热传导 分离变量法 精确解 

分 类 号：O175[理学—数学] O551.3[理学—基础数学]