| 计及二阶效应的一种变截面梁精确单元刚度阵 |
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| 引用本文： | 陆念力,张宏生.计及二阶效应的一种变截面梁精确单元刚度阵[J].工程力学,2008,25(12). |
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| 作者姓名： | 陆念力 张宏生 |
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| 作者单位： | 哈尔滨工业大学机电工程学院; |
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| 基金项目： | 国家科技支撑计划项目(2006BAJ12B03-2) |
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| 摘 要： | 推导一种精确的Bernoulli-Euler变截面梁单元,解决了传统变截面梁单元在结构稳定性分析中存在的计算精度较低的问题,以常见的外形沿轴向按线性变化的变截面梁为例,给出梁单元的精确刚度阵。放弃传统有限元通过插值理论构建变形场,并通过虚位移原理获取单元刚度阵的方法,直接从计入二阶效应的单元平衡微分方程中得到变截面梁的载荷位移关系,进而得到有限元格式的变截面梁精确刚度阵。借助于变截面梁单元刚度阵,可导致与精确的微分方程解析法同样的计算精度。通过与几个经典算例和ANSYS计算结果比较表明:该精确刚度阵可直接应用于结构稳定性分析,获得变截面梁结构精确的欧拉临界力。
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| 关 键 词： | 有限单元法 结构稳定性分析 变截面Bernoulli-Euler梁 二阶效应 精确单元刚度阵 |
EXACT ELEMENTAL STIFFNESS MATRIX OF A TAPERED BEAM CONSIDERING SECOND-ORDER EFFECTS |
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| LU Nian-li,ZHANG Hong-sheng.EXACT ELEMENTAL STIFFNESS MATRIX OF A TAPERED BEAM CONSIDERING SECOND-ORDER EFFECTS[J].Engineering Mechanics,2008,25(12). |
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| Authors: | LU Nian-li ZHANG Hong-sheng |
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| Affiliation: | School of Mechatronics Engineering;Harbin Institute of Technology;Harbin;Heilongjiang 150001;China |
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| Abstract: | The exact stiffness matrix of the tapered Bernoulli-Euler beam is proposed, whose profile is assumed to be varying linearly, and it can be incorporated into stability analysis with high accuracy. The Bernoulli-Euler theory of bending is used to describe the motion of the beam. Classical finite element method to obtain stiffness matrix is replaced by interpolation method and the principle of virtual work. Solving the governing differential equation of motion with second-order effects, the force- displacement... |
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| Keywords: | finite element method structural stability analysis tapered Bernoulli-Euler beam second-order effects exact elemental stiffness matrix |
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