功能梯度材料热传输问题的基本解方法  

The Method of Fundamental Solutions for Heat Conduction in Functionally Graded Materials

作　　者：王辉[1] 李钜[2] 刘伟[2] 

机构地区：[1]河南工业大学,郑州450052 [2]中原工学院,郑州450007

出　　处：《中原工学院学报》2009年第2期48-50,共3页Journal of Zhongyuan University of Technology

摘　　要：基于热传导理论和基本解理论,利用基本解的线性组合构造出了功能梯度材料热传输问题的一般无网格求解方程,并根据给定的边界条件得到求解方程组.最小二乘技术和截断的奇异值分解方法被用来对方程组进行对称化处理和求解并确定所有未知插值系数,进而计算出域内任意位置的温度分布.计算结果显示了算法的计算精度和有效性,并分析了梯度参数变化对温度分布的影响.Based on the basic theory of heat conduction and corresponding fundamental solution, a general meshless algorithm is developed for solving heat conduction in functionally graded materials （FGM）. Satisfaction of specified boundary conditions can produce the final linear system of equations, which is solved by the simple least-squares technique and truncated singular value decomposition （TSVD） to determine all unknown interpolation coefficients, and then temperature field at arbitrary points can be obtained. Numerical results show the accuracy and efficiency of the proposed algorithm by investigating the effect of various graded parameter to temperature distribution.

关 键 词：功能梯度材料 基本解方法 无网格法 最小二乘技术 截断奇异值分解 

分 类 号：TB330.1[一般工业技术—材料科学与工程]