摘要
为了更有效地求解三维轴对称功能梯度材料瞬态热传导问题,对无网格自然单元法应用于此类问题进行了研究,并发展了相应的计算方法。基于几何形状和边界条件的轴对称性,三维的轴对称问题可降为二维平面问题。为了简化本质边界条件的施加,轴对称面上的温度场采用自然邻近插值进行离散。功能梯度材料特性的变化由高斯点的材料参数进行模拟。时间域上,采用传统的两点差分法进行离散求解,进而得到瞬态温度场的响应。数值算例结果表明,提出的方法是行之有效的,理论及方法不仅拓展了自然单元法的应用范围,而且对三维轴对称瞬态热传导分析具有普遍意义。
In order to solve the transient heat conduction problems in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs） more effectively, a novel numerical method based on the meshless natural element method is proposed. Axial symmetry of geometry and boundary conditions helps to transform the 3D axisymmetric problem into a two-dimensional （2D） prolem. In order to simplify the imposition of the essential boundary conditions, the natural neighbour interpolation is adopted to discretize the temperature field within the cross section. The variations of functionally graded material properties are simulated by employing proper material parameters at Gauss points. The spatially discretized heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. The present method not only broadens the application scope of the natural element method, but also will be generally available to transient heat conduction analyses of 3D axisymmetric solids.
出处
《土木建筑与环境工程》
CSCD
北大核心
2016年第2期69-74,共6页
Journal of Civil,Architectural & Environment Engineering
基金
国家自然科学基金(21466012)
江西省教育厅项目(KJLD14041)~~
关键词
自然单元法
轴对称
功能梯度材料
瞬态热传导
natural element method
axisymmetric
functionally graded materials
transient heat conduction
