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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。
Two sets of covering systems (mathematical cover system and physical cover system) which are unique in Numerical Manifold Method (NMM) make it possible to adopt mathematical cover system which is inconsistent with boundary of physical domain when analyzing problems. NMMs for the study of two-dimensional steady-state heat transfer problems in functional graded materials (FGMs) have been developed. The governing equations and boundary conditions are given. The basic concepts of NMM are introduced. The NMM discrete equations are derived. The quadrature strategy of correlation matrix is discussed. Two typical examples are selected to verify the feasibility and accuracy of the proposed method. The results show that this method can well simulate the steady-state heat transfer problem of FGM.