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考虑自重时压杆的临界荷载近似解析解 |
An approximate analytical solution for the critical load of a long column when considering of the self-weight |
投稿时间:2019-10-16 修订日期:2019-10-16 |
DOI: |
中文关键词: 材料力学 压杆 稳定方程 自重 临界荷载 |
英文关键词: mechanics of materials long column stability equation self-weight critical load |
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中文摘要: |
当考虑压杆的自重时,不能求得其临界荷载的精确解析解.为获得较合适的近似解析解,建立了压杆屈曲时的势能函数,由势能驻值原理导出了稳定方程.受既有的三种压杆的三角级数型挠曲线的启发,尝试补充了另外六种压杆的既满足位移边界条件又满足内力边界条件的三角级数型挠曲线,求得了九种理想支座压杆的临界荷载近似解析解.结果发现:(1)临界荷载与自重成线性或准线性关系;(2)若在所得的解答中令自重为零,就得到欧拉公式,若令上端轴心压力为零,就得到仅考虑自重时的临界荷载;(3)当考虑自重时,对两端不同支座的压杆,若互换支座位置,其临界荷载曲线一般有特别显著的变化.通过有限的比较表明,本文解答与基于贝塞尔方程的精确数值解较吻合. |
英文摘要: |
When considering of the self-weight of a long column, the precise analytical solution of its critical load cannot be obtained. In order to obtain a more suitable approximate analytical solution of the critical load, the potential energy function when buckling is set up, and the stability equation is obtained based on principle of potential energy stationary value. Inspired by the existing trigonometric series deflection curve about the three kinds of long columns, to the other six kinds of long columns, trying to supplement all trigonometric series deflection curve, which meet the boundary conditions both displacement and internal force. To a long column under nine kinds of ideal supports, an approximate analytical solution of the critical load is solved. The results show as these: (1) the relationship betweenSthe critical load and self-weight areSlinear or nearly linear; (2) in the solution, if let the self-weight equals to zero, will obtain the Euler"s formula, if let the axial load at the center of upper end equals to zero, will obtain the critical load of self-weight; (3) when consideration of the self-weight, to a long column of different supports at both ends, if exchanging the position of supports, generally, the critical loadScurve will change significantly. By comparing limited, the conclusion is that, the results in this paper are more consistent with the exact numerical solutions based on the Bessel equation. |
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