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[1]董冠文,李宗义,赵彦军,等.压杆稳定临界力欧拉公式统一推导[J].武汉工程大学学报,2012,(12):71-74.[doi:103969/jissn16742869201212004]
　DONG Guan wen,LI Zong yi,ZHAO Yan jun,et al.Unified deduction of pressure lever stability critical force Euler formula[J].Journal of Wuhan Institute of Technology,2012,(12):71-74.[doi:103969/jissn16742869201212004]
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压杆稳定临界力欧拉公式统一推导(/HTML)
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《武汉工程大学学报》[ISSN:1674-2869/CN:42-1779/TQ]

卷:
期数:
2012年12期
页码:
71-74
栏目:
机电与信息工程
出版日期:
2013-01-11

文章信息/Info

Title:
Unified deduction of pressure lever stability critical force Euler formula
文章编号:
16742869(2012)12001304
作者:
董冠文; 李宗义; 赵彦军; 王泽荫; 杨龙; 张庆华 ; 杜建霞; 赵典凯
甘肃机电职业技术学院，甘肃 天水 741001
Author(s):
DONG Guanwen; LI Zongyi; ZHAO Yanjun; WANG Zeyin; YANG Long; ZHANG Qinghua; DU Jianxia; Zhao Diankai
Gansu Mechanical & Electrical Vocational college，Tianshui 741001，China
关键词:
细长压杆;  微小弯曲;  压杆稳定;  临界力;  Euler公式
Keywords:
slender compressive bar; small bending; pressure lever stability; critical force; Euler formula
分类号:
O34
DOI:
103969/jissn16742869201212004
文献标志码:
A
摘要:
针对以往用弯剪方程挠曲线微分方程对压杆稳定临界力欧拉公式做了统一推导，既考虑剪力又考虑弯矩，没有体现真正意义上的杆的整体变形效应的问题，提出了以一端固定另一端铰支的细长压杆微小弯曲挠曲线方程作为统一的挠曲线方程，分别代入压杆两端铰支失稳、压杆一端固定另一端自由失稳、压杆两端固失稳定、压杆一端固定另一端定向可移动夹紧失稳的临界力边界条件的方法.结果表明：压杆两端铰支失稳临界力Euler（欧拉）公式，长度因数μ=1；压杆一端固定另一端铰支失稳临界力Euler公式，长度因数μ=0.7；压杆一端固定另一端自由失稳临界力Euler公式，长度因数μ=2；压杆两端固失稳定失稳临界力Euler公式，长度因数μ=0.5；压杆一端固定另一端定向可移动夹紧失稳的临界力Euler公式，长度因数μ=1，结果与工程力学或材料力学现有教材完全一致，表明此方法正确可行.使用此方法对压杆稳定临界力欧拉公式做了统一推导，真正体现了杆的整体变形效应，揭示了压杆稳定与拉、压、弯、扭区别的本质.
Abstract:
Aimed at unified derivation of stability critical force Euler’s formula of compression bar using deflection line differential equation of curved scissors equation, which considers the shear and bending moment, not reflecting in the true sense of the rod deformation effect, the one end fixing the other end hinged branch of slender compressive bar small bending deflection line equation as a unified deflection line equation was put forward, which was substituted respectively into pressure rod ends hinge branch instability, pressure rod end fixed the other end free instability, pressure rod ends solid lost stability, compression bar end fixed the other end directional movable clamp buckling critical force boundary conditions of the method. The results show that two ends are fixed destabilizing hinge buckling critical force Euler formula, length factor μ=1; one end of the destabilizing critical Euler formula hinged, length factor μ=0.7; one end of the columns is fixed and the other end destabilizing freedom critical Euler formula, the length factor μ=2; both ends are fixed loss of solid stability destabilizing critical Euler formula, length factor μ=0.5; one end of the columns is fixed and the other end can be directed to Euler formula about clamping instability critical force, length factor μ=1. Using this method to deduct the Euler’s formula about the pressure lever critical stable force, and the result really reflects the whole deformation effect of the bar, reveals the essential difference between the rod pressure stability and pull, pressure, bending, twisting.

参考文献/References:

［1］傅宁，杜家熙. 用弯剪方程求细长压杆的临界力\[J\].河南职技师院学报,1999，27（1）：3940.
［2］李有兴，肖芳淳.用弯剪矩阵法确定压杆临界力的教学研究\[J\].力学与实践,1995，17（1）：6971.
［3］张晓春，关于弯剪矩阵法的思考\[J\].力学与实践,1997，19（2）：6869.
［4］李世荣.材料力学\[M\].北京：科学出版社，2010:200203.

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备注/Memo

备注/Memo:
收稿日期：20120923作者简介：董冠文（1984），男，甘肃天水人，助教.研究方向：模具结构中的力学.
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