| 任意梁截面特性值的有限元计算方法 |
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| 引用本文： | 陈常松,阳斌,颜东煌. 任意梁截面特性值的有限元计算方法[J]. 长沙理工大学学报(自然科学版), 2013, 0(1): 41-46 |
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| 作者姓名： | 陈常松 阳斌 颜东煌 |
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| 作者单位： | 长沙理工大学土木与建筑学院 |
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| 基金项目： | 国家自然科学基金资助项目(51178058,51178059) |
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| 摘 要： | 利用目前成熟的弹性梁理论,建立悬臂梁受到自由扭转、约束扭转、横向剪力下的弹性方程,推导出截面翘曲函数的调和方程.引入圆柱自由边界条件,采用Galerkin方法,解出离散截面节点处的函数值.截面的特性值推导成积分形式,通过高斯积分可求出.利用本研究公式,采用4节点等参元,通过编写程序验证了公式的正确性.本研究公式适应于任意截面,对梁截面的优化方案可提供指导.
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| 关 键 词： | 梁截面特性值 有限元 翘曲函数 扭转常量 翘曲常量 剪切变形系数 |
A finite element method for the calculation of arbitrary beam sectional properties |
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| CHEN Chang-song,YANG Bin,YAN Dong-huang. A finite element method for the calculation of arbitrary beam sectional properties[J]. Journal of Changsha University of Science and Technology(Natural Science), 2013, 0(1): 41-46 |
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| Authors: | CHEN Chang-song YANG Bin YAN Dong-huang |
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| Affiliation: | (School of Civil Engineering and Architecture,Changsha University of Science and Technology,Changsha 410004,China) |
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| Abstract: | Using the mature elastic beam theory,the elastic equation is established that the cantilever beam load from free torsion, constraint torsion,transverse shear,derive the sec- tion warping the harmonic equation. Under the introduction of cylindrical free boundary and the Galerkin method,the discrete solutions are given in section node function values,after deducing the properties of the cross section into integral form,by Gauss integral. Exploiting the formula introducted in this article, through the use of 4-node isoparameteric element, program and verify the correctness of the formula. The formula in this article adapting in arbitray cross-section, can provide guidance for the optimization of beam cross-section. |
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| Keywords: | the properties of beam section finite element method warping function tor- sional constant warping constant shear deformation coefficients |
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