| Wilson非协调数值流形方法 |
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| 引用本文： | 魏高峰,冯伟.Wilson非协调数值流形方法[J].岩土力学,2006,27(2):189-192. |
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| 作者姓名： | 魏高峰 冯伟 |
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| 作者单位： | 1. 山东轻工业学院 机械工程学院，济南250100；2. 上海大学 上海市应用数学和力学研究所，上海 200072 |
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| 摘 要： | 三维数值流形方法中，当数学覆盖取六面体体单元时流形单元总体位移函数中所包含的多项式并不是完全的，非完全的高次项非但对改善精度不起作用，而且还可能起相反的作用。为此，基于Wilson非协调元理论，推导了附加非协调位移基本项的流形元通用公式，通过内参静力凝聚处理，导出了消除单元内参后的单元应变矩阵、单元刚度矩阵，建立了非协调数值流形方法。数值试验表明，在规则数学网格覆盖下它们能够保证收敛，有较高的精度，从而证明所建方法的可行性。
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| 关 键 词： | 非协调元 数值流形方法 分片试验 有限覆盖 附加位移基本项 |
| 文章编号： | 1000-7598-（2006）02-0189-04 |
| 收稿时间： | 2004-06-21 |
| 修稿时间： | 2004-06-212004-11-05 |
Wilson incompatible numerical manifold method |
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| WEI Gao-feng,FENG Wei.Wilson incompatible numerical manifold method[J].Rock and Soil Mechanics,2006,27(2):189-192. |
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| Authors: | WEI Gao-feng FENG Wei |
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| Institution: | 1. Institute of Mechanical Engineering, Shandong Institute of Light Industry, Jinan 250100, China; 2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China |
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| Abstract: | In three-dimensional numerical manifold method(NMM),the total element test functions in the polynomial space are not entire when hexahedral solid meshes are given in mathematical cover.Non-entire high order terms cannot improve computational precision,but may play the contrary role.For avoiding the disadvantages,an additional incompatible manifold element rank formula is established based on the theory of Wilson incompatible element;Wilson incompatible numerical manifold method is presented.The element strain matrix and the element stiffness matrix are derived by eliminating the internal parameters.The method has high computing efficiency and accuracy under adding no generalized degrees of freedom.Finally several numerical examples are analyzed to illustrate the stability and convergence of the method.The results are shown that the method is highly validity and accuracy. |
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| Keywords: | incompatible element numerical manifold method patch test finite covering technique additional displacement term |
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