功能梯度材料稳态热传导问题的数值流形方法研究  

Numerical manifold study of steady heat conduction problems in functionally graded materials

作　　者：胡国栋[1] 张慧华[1] 谭育新[1] 

机构地区：[1]南昌航空大学土木建筑学院,南昌330063

出　　处：《应用力学学报》2017年第2期311-317,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11462014);江西省自然科学基金(20151BAB202003);江西省教育厅科技项目(GJJ14526)

摘　　要：数值流形方法(Numerical Manifold Method,简称NMM)中特有的两套覆盖系统(数学覆盖系统和物理覆盖系统)使得其在分析问题时可采用与物理域边界不一致的数学覆盖系统。发展了用于研究功能梯度材料(FGM)二维稳态热传导问题的NMM。给出了控制方程和边界条件,介绍了NMM的基本概念,导出了NMM的离散方程,探讨了相关矩阵的求积策略,选取了两个典型算例对方法的可行性和精确性进行了验证,结果表明该方法可以很好地模拟FGM稳态热传导问题。Due to the use of two cover systems,that is,the mathematical cover system and the physical cover system,the numerical manifold method(NMM)is capable of solving physical problems using mathematical cover system which can be independent of physical boundaries.In this paper,the NMM is extended to analyze two-dimensional steady heat conduction problems in functionally graded materials(FGMs).The governing equations and associated boundary conditions for concerned problems are presented.Basic concepts and approximations of the NMM are provided and then the NMM global equations are derived and the integration schemes are discussed.Finally,to verify the feasibility and accuracy of the proposed method,two typical examples are conducted.Our numerical results well demonstrate the power of the proposed method.

关 键 词：功能梯度材料 数值流形方法 稳态热传导 温度场 二维 

分 类 号：TK124[动力工程及工程热物理—工程热物理]