压杆弹性屈曲分析的精细传递矩阵法
|
摘要
压杆是房屋和桥梁结构的重要受力构件。当压杆所承受的荷载达到一定的临界值时,整个结构就会失去稳定性。该文根据精细传递矩阵法原理和压杆微弯平衡状态下的微分平衡方程,建立了在轴向荷载作用下压杆稳定分析的精细传递矩阵式。并运用精细传递矩阵法对不同边界约束的压杆进行了临界荷载的计算,计算结果与压杆屈曲的理论解基本一致,从而验证了该文方法是正确、有效的。算例表明:轴心受压杆件的屈曲荷载的增幅逐阶递增。建议采取措施以避开压杆的低阶屈曲荷载,从而可以有效的提高压杆的承载能力,充分发挥材料的性能。
Compression bar is an important structural member in buildings or bridges.When the compression of the bar reaches its critical load,the whole structure will lost the stability.Based on the theory of precise transfer matrix method and the slightly bending differential equation of compression bar,a precise transfer matrix format for buckling analysis of compression bar under axial load was derived.By this method,the critical loads of compression bar with different boundary constraints were calculated,and the calculation result agreed well with the theoretical result,showing that the method was accurate and effective.Examples showed that the amplification of critical loads of center compression bar increases with modes,so the design of center compression bar should avoid the occurrence of low mode buckling.
Compression bar is an important structural member in buildings or bridges.When the compression of the bar reaches its critical load,the whole structure will lost the stability.Based on the theory of precise transfer matrix method and the slightly bending differential equation of compression bar,a precise transfer matrix format for buckling analysis of compression bar under axial load was derived.By this method,the critical loads of compression bar with different boundary constraints were calculated,and the calculation result agreed well with the theoretical result,showing that the method was accurate and effective.Examples showed that the amplification of critical loads of center compression bar increases with modes,so the design of center compression bar should avoid the occurrence of low mode buckling.
引文
[1]孙训方,方孝淑,关来泰.材料力学[M].北京:高等教育出版社,2002.Sun Xunfang,Fang Xiaoshu,Guan Laitai.Materialmechanics[M].Beijing:Higher Education Press,2002.(in Chinese)
[2]钟万勰.结构动力方程的精细时程积分[J].大连理工大学学报,1994,34(2):131―136.Zhong Wanxie.On precise time-intergration method forstructural dynamics[J].Journal of Dalian University ofTechnology,1994,34(2):131―136.(in Chinese)
[3]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报,2001,5(1):18―23.Li Qingning.The transfer matrix method of bar elementswith variable cross-section[J].Journal of Xi’anUniversity of Architecture&Technology,2001,5(1):18―23.(in Chinese)
[4]郭泽英,李青宁,张守军.结构地震反应分析的一种新精细积分法[J].工程力学,2007,24(4):35―40.Guo Zeying,Li Qingning,Zhang Shoujun.A new preciseintegration method for structural seismic responseanalysis[J].Engineering Mechanics,2007,24(4):35―40.(in Chinese)
[5]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1996.Li Guohao.Stability and vibration of bridge structures[M].Beijing:China Railway Publishing House,1996.(inChinese)
[6]张素英,邓子辰.非线性动力方程的增维精细积分法[J].计算力学学报,2003,20(4):423―426.Zhang Suying,Deng Zichen.Incremental-dimensionalprecise integration method for nonlinear dynamicequation[J].Chinese Journal of ComputationalMechanics,2003,20(4):423―426.(in Chinese)
[7]任传波,贺光宗,李忠芳.结构动力学精细积分的一种高精度通用计算格式[J].机械科学与技术,2005,12(12):1507―1509.Ren Chuanbo,He Guangzong,Li Zhongfang.A high-precision and General Computational Scheme in PreciseIntegration of Structural Dynamics[J].MechanicalScience and Technology,2005,12(12):1507―1509.(inChinese)
[8]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191―195.Wang Mengfu,Zhou Xiyuan.Renewal precise time stepintegration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191―195.(inChinese)
[9]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.Liu Qingtan,Ni Guorong.The transfer matrix methodused in structure analysis[M].Beijing:China RailwayPublishing House,1997.(in Chinese)
[10]He Jihuan.A modified Newton-Raphson method[J].Communications in Numerical Methods in Engineering2004,20(10):801―805.
[2]钟万勰.结构动力方程的精细时程积分[J].大连理工大学学报,1994,34(2):131―136.Zhong Wanxie.On precise time-intergration method forstructural dynamics[J].Journal of Dalian University ofTechnology,1994,34(2):131―136.(in Chinese)
[3]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报,2001,5(1):18―23.Li Qingning.The transfer matrix method of bar elementswith variable cross-section[J].Journal of Xi’anUniversity of Architecture&Technology,2001,5(1):18―23.(in Chinese)
[4]郭泽英,李青宁,张守军.结构地震反应分析的一种新精细积分法[J].工程力学,2007,24(4):35―40.Guo Zeying,Li Qingning,Zhang Shoujun.A new preciseintegration method for structural seismic responseanalysis[J].Engineering Mechanics,2007,24(4):35―40.(in Chinese)
[5]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1996.Li Guohao.Stability and vibration of bridge structures[M].Beijing:China Railway Publishing House,1996.(inChinese)
[6]张素英,邓子辰.非线性动力方程的增维精细积分法[J].计算力学学报,2003,20(4):423―426.Zhang Suying,Deng Zichen.Incremental-dimensionalprecise integration method for nonlinear dynamicequation[J].Chinese Journal of ComputationalMechanics,2003,20(4):423―426.(in Chinese)
[7]任传波,贺光宗,李忠芳.结构动力学精细积分的一种高精度通用计算格式[J].机械科学与技术,2005,12(12):1507―1509.Ren Chuanbo,He Guangzong,Li Zhongfang.A high-precision and General Computational Scheme in PreciseIntegration of Structural Dynamics[J].MechanicalScience and Technology,2005,12(12):1507―1509.(inChinese)
[8]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191―195.Wang Mengfu,Zhou Xiyuan.Renewal precise time stepintegration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191―195.(inChinese)
[9]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.Liu Qingtan,Ni Guorong.The transfer matrix methodused in structure analysis[M].Beijing:China RailwayPublishing House,1997.(in Chinese)
[10]He Jihuan.A modified Newton-Raphson method[J].Communications in Numerical Methods in Engineering2004,20(10):801―805.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心