| 引用本文: | 孟丽霞,陆念力,刘士明.惯性矩二次变化变截面梁柱几何非线性分析[J].哈尔滨工业大学学报,2014,46(3):20.DOI:10.11918/j.issn.0367-6234.2014.03.004 |
| MENG Lixia,LU Nianli,LIU Shiming.Geometric nonlinear analysis of tapered beam with inertia moment vary quadratic[J].Journal of Harbin Institute of Technology,2014,46(3):20.DOI:10.11918/j.issn.0367-6234.2014.03.004 |
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| 摘要: |
| 为研究考虑剪切变形的变截面梁杆结构几何非线性问题,应用Timoshenko梁理论,采用位移、转角独立插值的方法,获取考虑剪切影响的惯性矩二次变化变截面梁单元的形函数;从严格的虚功增量方程出发,建立同时考虑轴力、剪切、弯曲效应及其耦合项的平面变截面梁柱单元几何非线性增量平衡方程,得到惯性矩二次变化变截面梁单元大位移切线刚度阵;与经典算例进行对比,验证了本文方法的精确性与有效性． |
| 关键词: 有限单元法 变截面梁 虚功增量方程 大位移 几何非线性 |
| DOI：10.11918/j.issn.0367-6234.2014.03.004 |
| 分类号: |
| 基金项目:国家科技支撑计划资助项目(2011BAJ02B01-02). |
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| Geometric nonlinear analysis of tapered beam with inertia moment vary quadratic |
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MENG Lixia, LU Nianli, LIU Shiming
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(School of Mechatronics Engineering, Harbin Institute of Technology, 150001 Harbin, China)
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| Abstract: |
| To research the geometric nonlinear problem of tapered beam with shear deformation, based on Timoshenko theory, the displacement and rotation independent interpolation method was adopted to obtain the shape functions of tapered beam considering shear deformation, whose inertia moment varied quadratic. Then, started from the virtual work increment equation, the geometric nonlinear incremental equilibrium equation of the plane tapered beam element was established, including axial force, shear effect, bending effect and its coupling term, and the large displacement tangential stiffness matrix of the tapered beam was obtained. Finally, the classical examples are calculated, and the results show that the proposed method is accurate and effective. |
| Key words: Finite element method Tapered beam Virtual work increment equation Large displacement Geometric nonlinear |
