中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (4): 1-6.

• 研究论文 •    下一篇

功能梯度材料稳态热传导方程的分层精细指数法

蓝林华,富明慧,高文乐

  

  1. (中山大学应用力学与工程系, 广东 广州 510275)
  • 收稿日期:2010-07-19 修回日期:1900-01-01 出版日期:2011-07-25 发布日期:2011-07-25
  • 通讯作者: 富明慧

Layered Precise Exponential Method of Steady Heat Conduction Equationfor Functionally Graded Materials

LAN Linhua,FU Minghui, GAO Wenle   

  1. (Department of applied mechanics and engineering, Sun Yatsen University, Guangzhou 510275, China)
  • Received:2010-07-19 Revised:1900-01-01 Online:2011-07-25 Published:2011-07-25

摘要: 提出了功能梯度材料稳态热传导方程的分层精细指数化法(Layered Exponential Precise Method, LPEM)。首先将稳态热传导方程单向离散,转化为沿厚度解析的常微分边值问题。然后将厚度M等分,利用相邻结点间状态参量的精细积分关系式,将常微分边值问题转化为一个几乎无离散误差的代数方程组,并给出合并消元的递推公式。对于热传导系数沿厚度指数或者分段指数规律变化的情况,该方法具有极高的精度与效率;对于更一般的情况,提出了将热传导系数沿厚度分段指数化的求解方法。算例的结果证明了该文方法的有效性。

Abstract: An efficient algorithm (Layered Precise Exponential Method, LPEM)of steady heat conduction equation is presented for Functionally Graded Materials (FGMs) Firstly the steady-state heat conduction equation is discretized equidistantly along the thickness direction with the discrete number M and then is changed into analytic Ordinary Differential Boundary Value Problem (ODBVP) Secondly algebraic equations which have almost no discretization error are established from the ODBVP by using of the precise integral relations of the state parameter between adjacent points, and then the recursion formula for elimination is given from upper algebraic equations The results of Layered Precise Exponential Method have both good accuracy and good efficiency when the function of thermal conductivity is constanttype or exponential, and when the function of thermal conductivity is other forms of continuous and smooth function. The method also applies as long as the layered exponential approximation model is adopted.The numerical examples are presented to demonstrate the effectiveness and reliability of the proposed method.

Key words: Functionally Graded Materials (FGMs), steady heat conduction equation, Layered Precise Exponential Method (LPEM), twopoint boundary value problems, the recursion formula for elimination

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