Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates
Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates
复制标题
曲线坐标下周期复合材料热传导问题的二阶渐近算法
DOI：
10.1016/j.cam.2016.04.007
复制
发表时间：
2016-11
影响因子：
2.4
通讯作者：
Z.Q. Wang
中科院分区：
文献类型：
--
作者：
Q. Ma;J.Z. Cui;Z.H. Li;Z.Q. Wang
针对具有周期构形的复合材料的热传导问题，提出了一种新的二阶双尺度（SOTS）渐近分析方法。在一般曲线坐标系下，求解了具有准周期结构的变换正则域上的热传导问题。通过渐近展开，依次得到了单元问题、有效材料系数问题和均质热传导问题。该近似模型的主要特点是在微观细胞域上定义的每个细胞问题都与宏观坐标相关联。在一定的正则性假设的基础上建立了渐近分析方法的误差估计。讨论了一些常见的坐标变换，并给出了SOTS的简化解。特别是考虑到一般的一维问题，导出了SOTS解的显式表达式，并给出了更强的误差估计。最后给出了相应的有限元算法，并对数值结果进行了分析。数值误差与理论预测吻合较好，证明了二阶渐近分析方法的有效性。通过坐标变换，将渐近分析方法推广到具有周期性微观结构的更一般的领域。
A new second-order two-scale (SOTS) asymptotic analysis method is presented for the heat conduction problems concerning composite materials with periodic configuration under the coordinate transformation. The heat conduction problems are solved on the transformed regular domain with quasi-periodic structure in the general curvilinear coordinate system. By the asymptotic expansion, the cell problems, effective material coefficients and homogenized heat conduction problems are obtained successively. The main characteristic of the approximate model is that each cell problem defined on the microscopic cell domain is associated with the macroscopic coordinate. The error estimation of the asymptotic analysis method is established on some regularity hypothesis. Some common coordinate transformations are discussed and the reduced SOTS solutions are presented. Especially by considering the general one-dimensional problem, the explicit expressions of the SOTS solutions are derived and stronger error estimation is presented. Finally, the corresponding finite element algorithms are presented and numerical results are analyzed. The numerical errors presented agree well with the theoretical prediction, which demonstrate the effectiveness of the second-order asymptotic analysis method. By the coordinate transformation, the asymptotic analysis method can be extended to more general domain with periodic microscopic structures.
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影响因子：
1.7
作者：
Zihao Yang;Yunsai Chen;Zhi-Qiang Yang-;Q. Ma
通讯作者：
Zihao Yang;Yunsai Chen;Zhi-Qiang Yang-;Q. Ma
DOI：
10.1360/02ys9171
发表时间：
2002-12
期刊：
Science in China Series A: Mathematics
影响因子：
--
作者：
Cao Li-qun;Junzhi Cui;Dechao Zhu;Jianlan Luo
通讯作者：
Cao Li-qun;Junzhi Cui;Dechao Zhu;Jianlan Luo
DOI：
10.4028/www.scientific.net/amr.629.160
发表时间：
2012-12
期刊：
Advanced Materials Research
影响因子：
--
作者：
Q. Ma;J. Cui
通讯作者：
Q. Ma;J. Cui
DOI：
10.1007/978-3-642-84659-5
发表时间：
1994
期刊：
--
影响因子：
--
作者：
V. Zhikov;S. Kozlov;O. Oleinik
通讯作者：
V. Zhikov;S. Kozlov;O. Oleinik
DOI：
10.1016/0022-247x(79)90211-7
发表时间：
1979-10
影响因子：
1.3
作者：
D. Cioranescu;J. Paulin
通讯作者：
D. Cioranescu;J. Paulin