一种n阶变截面压杆稳定性计算方法的研究

中国机械工程 ›› 2014, Vol. 25 ›› Issue (13): 1744-1747,1799.

一种n阶变截面压杆稳定性计算方法的研究

王欣1;易怀军1;赵日鑫2;肖华3

1.大连理工大学，大连，116023
2.大连益利亚工程机械有限公司，大连，116024
3.大连理工大学(徐州)工程机械研究中心，徐州，221007

出版日期:2014-07-10 发布日期:2014-07-16

Research on Stability Analysis Method of n-order Variable Cross-Section Compression Bars

Wang Xin1;Yi Huaijun1;Zhao Rixin2;Xiao Hua3

1.Dalian University of Technology,Dalian,Liaoning,116023
2.Dalian Yiliya Construction Machinery Co.,Ltd.,Dalian,Liaoning,116024
3.Construction Machinery Research Center of Dalian University of Technology,Xuzhou,Jiangsu,221007

Online:2014-07-10 Published:2014-07-16

摘要/Abstract

摘要：

针对n阶变截面压杆稳定性问题，基于一般的压杆稳定性挠曲线方程建立了n阶变截面压杆的微分方程组，结合相邻阶的边界条件，求解方程组获取递推关系式，即关于临界载荷的方程，应用Newton迭代法对方程进行迭代求解。以1200t全地面起重机伸缩臂为例，分别采用Newton迭代法、弦截法及有限元法计算了伸缩臂的临界载荷，对比分析结果证明了所推导出的临界载荷关系式的合理性及Newton迭代法的高效性。

关键词: n阶变截面压杆, 临界载荷；稳定性, Newton迭代法

Abstract:

For the stability of n-order variable cross-section compression bars, the differential equations concerning the flexible curve equation were established. Based on the boundary conditions of neighbored-order, a critical load coefficient equation was built by solving the differential equations. And Newton iteration method was applied to calculate the critical load. As a case of telescopic boom for 1200 ton all-terrain crane, comparison results of calculation were analyzed among Newton iteration method, secant method and stability of ANSYS, which indicate the rationality of the critical load coefficient equation and efficiency of Newton iteration method.

Key words: n-order variable cross-section compression bar, critical load, stability, Newton iteration method

中图分类号:

王欣, 易怀军, 赵日鑫, 肖华. 一种n阶变截面压杆稳定性计算方法的研究[J]. 中国机械工程, 2014, 25(13): 1744-1747,1799.

Wang Xin, Yi Huaijun, Zhao Rixin, Xiao Hua. Research on Stability Analysis Method of n-order Variable Cross-Section Compression Bars[J]. China Mechanical Engineering, 2014, 25(13): 1744-1747,1799.

参考文献

[1]洪振德. 变截面压杆稳定临界力能量计算方法[J]. 江苏建筑, 2011(3):28-30.
Hong Zhende. Energy Method for Calculating the Critical Bucking Load of the Column with Variable Section[J]. Journal of Jiangsu Architecture, 2011(3): 28-30.
[2]刘庆潭. 复杂细长压杆临界力计算的传递矩阵法[J]. 力学与实践, 1997,19(6):51-54.
Liu Qintan.The Transfer Matrix Method for Calculating Critical Load of a Complex Long and Thin Pressure Bars[J]. Journal of Mechanics in Engineering, 1997, 19(6): 51-54.
[3]卞敬玲,王小岗.变截面压杆稳定计算的有限单元法[J].武汉大学学报(工学版),2002,35(4):100-104.
Bian Jingling, Wang Xiaogang. FEM for Calculating Stability of Variable Cross-section Compression Bars[J]. Journal of Wuhan University(Engineering Science), 2002, 35(4): 100-104.
[4]楼梦麟, 李建元. 变截面压杆稳定问题半解析解[J]. 同济大学学报(自然科学版), 2004,7(7): 857-860.
Lou Menglin, Li Jianyuan.Semi-analytical Approach for Stability of Variable Cross-section Compression Bars[J]. Journal of Tongji University(Natural Science), 2004, 7(7): 857-860.
[5]侯祥林, 范炜, 贾连光. 变截面压杆临界载荷的迭代算法[J].哈尔滨工业大学学报, 2011,43(增刊1): 237-240.
Hou Xianglin, Fan Wei, Jia Lianguang. Iterative Algorithm of the Critical Load about Variable Cross-section Bar[J]. Journal of Harbin Institute of Technology, 2011, 43(Sup1): 237-240.
[6]Safa B C, Mehmet T A.Determination of Critical Buckling Load for Elastic Columns of Constant and Variable Cross-sections Using Variational Iteration Method[J]. Computers and Mathematics with Applications, 2009, 58(11): 2260-2266.
[7]Mehmet T A,Safa B C. Elastic Stability of Euler Columns with a Continuous Elastic Restraint Using Variational Iteration Method[J]. Computers and Mathematics with Applications, 2009, 58(11): 2528-2534.
[8]刘鸿文. 材料力学[M]. 4版. 北京：高等教育出版社, 2004.