| 基于矩阵特殊运算的高阶流形单元分析 |
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| 引用本文： | 林绍忠,祁勇峰,苏海东.基于矩阵特殊运算的高阶流形单元分析[J].长江科学院院报,2006,23(3):36-39. |
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| 作者姓名： | 林绍忠 祁勇峰 苏海东 |
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| 作者单位： | 长江科学院非连续变形分析实验室,武汉,430010;长江科学院水利部,岩土力学与工程重点实验室,武汉,430010;长江科学院材料与结构研究所,武汉,430010;长江科学院非连续变形分析实验室,武汉,430010;长江科学院材料与结构研究所,武汉,430010 |
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| 摘 要： | 在数值流形法的单元分析中广泛采用单纯形积分进行精确积分，然而在高阶数值流形法中采用单纯形积分并不容易，因为要求被积函数为显式多项式函数。采用Kronecker积、Hadamard积和拉直等矩阵特殊运算进行高阶流形单元分析，使得单元矩阵的推导过程简单且被积函数易表示为多项式形式。在此基础上，开发了三维弹性连续体静力分析的高阶数值流形法程序。通过实例验证了公式和程序的正确性。
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| 关 键 词： | 数值流形法 高阶覆盖函数 单元分析 矩阵特殊运算 单纯形积分 |
| 文章编号： | 1001-5485（2006）03-0036-04 |
| 收稿时间： | 2006-01-09 |
| 修稿时间： | 2006-01-09 |
Element Analysis of High-order Numerical Manifold Method based on Special Matrix Operations |
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| LIN Shao-zhong,QI Yong-feng,SU Hai-dong.Element Analysis of High-order Numerical Manifold Method based on Special Matrix Operations[J].Journal of Yangtze River Scientific Research Institute,2006,23(3):36-39. |
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| Authors: | LIN Shao-zhong QI Yong-feng SU Hai-dong |
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| Affiliation: | Yangtze River Scientific Research Institute, Wuhan 430010, China |
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| Abstract: | The simplex integration is commonly used in the numerical manifold method(NMM) for accurate integration.But a difficulty is encountered in adopting the simplex integration in high-order NMM since all integrands have to be explicitly expressed in polynomial functions.To determine the explicit form of integrands,the formulation of element matrices of high-order NMM is derived by using the special matrix operations including Kronecker product,Hadamard product and vectorization,resulting in a convenience of the derivation of the element matrices and the explicit expression of integrands.Based on the derived formulae,a program of 3-D NMM with high-order for elastic static anlysis of continuum is developed and verified by examples. |
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| Keywords: | numerical manifold method high-order cover function element anlysis special matrix operation simplex integration |
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