| MATHEMATICA在推导梁柱单元刚度矩阵中的应用 |
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| 引用本文： | 赵红华,杨庆山.MATHEMATICA在推导梁柱单元刚度矩阵中的应用[J].太原理工大学学报,2007,38(1):5-7,11. |
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| 作者姓名： | 赵红华 杨庆山 |
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| 作者单位： | 1. 北京林业大学,水保学院,北京,100083
2. 北京交通大学,土建学院,北京,100044 |
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| 基金项目： | 国家自然科学基金;山西省青年科研项目 |
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| 摘 要： | 利用MATHEMATICA强大的运算能力，将考虑多种因素相互作用下的空间粱复杂的刚度矩阵的推导，化做简单的公式运算，避免了繁琐的编程调试和元素寻址，得到了能够考虑拉压、弯曲、剪切、扭转、翘曲耦合影响下的空间梁单元刚度矩阵。在推导过程中，根据影响因素的不同，运用分块技术，将刚度矩阵分解为若干块的正应力刚度矩阵、剪应力刚度矩阵，以及相互影响的相关矩阵，实现了对刚度矩阵的贡献分析。算例进一步验证了所得结果的正确性和优越性。
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| 关 键 词： | 空间梁 耦合影响 单元刚度矩阵 相关矩阵 |
| 文章编号： | 1007-9432（2007）01-0005-03 |
| 收稿时间： | 2006-05-10 |
| 修稿时间： | 2006-05-10 |
The Application Of The MATHEMATICA Software In Deducing Beam Element Stiffness Matrix |
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| ZHAO Hong-hua,YANG Qing-shan.The Application Of The MATHEMATICA Software In Deducing Beam Element Stiffness Matrix[J].Journal of Taiyuan University of Technology,2007,38(1):5-7,11. |
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| Authors: | ZHAO Hong-hua YANG Qing-shan |
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| Institution: | 1. School of Soil and Water Conservation, Beijing Forestry university, Beijing 100083 ; 2. School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing 100044 |
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| Abstract: | This paper makes use of the powerful operation ability of the Mathematica software,simplifies the complicated deducing process of the element stiffness matrix of the space beam of loading manifold factors into the formulation operation,avoids the troublesome program debugging and variable addressing,and gets an element stiffness matrix considering the coupling affects of pulling and pressing,bending,shearing,torsion and warping.The matrix deduced by using the parting technique consists of several parts: the normal stress stiffness matrix,the shearing stress stiffness matrix,and the correlated stiffness matrix.Every part of the stiffness matrix has definite meaning and can be used to analyze the coupling influence of every factor,the result can be more mature and exact,and very convenient to be proceeded for the theoretic analysis. |
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| Keywords: | MATHEMATICA |
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