求解两端简支曲线梁面内内力和位移的精细传递矩阵法
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摘要
该文应用精细传递矩阵法和曲线结构热胀变形规律,建立了在集中荷载和变温作用下两端简支曲线两面内内力及位移解的精细传递矩阵式。运用该文方法对一简支曲梁进行了计算,计算结果与曲线梁有限元结果吻合较好,从而验证了该文解答的正确性。将该文方法扩展运用与多跨曲线桥的求解,得出在变温和桥墩顶部摩擦力共同作用下多跨曲线梁的面内内力及位移的精细传递矩阵格式。建立实际曲线桥的有限元简化模型,通过结构有限元分析与精细传递矩阵法的计算结果比较,说明了该文理论具有很好的工程应用性,可作为曲线桥结构研究和设计的理论依据。
Based on the theory of precise transfer matrix method and the principle of thermal expansion, a precise transfer matrix format for in-plane internal forces and displacements of curved beams with pinned-pinned ends are derived explicitly. And it is applied to a simply supported curved beam. Compared with the results of FEM, the veracity of analytical solutions by the precise transfer matrix method is verified. A real multi-span curved bridge subjected to concentrated loads and thermal load is analyzed using the precise transfer matrix method as well as FEM, and good agreements are observed.
Based on the theory of precise transfer matrix method and the principle of thermal expansion, a precise transfer matrix format for in-plane internal forces and displacements of curved beams with pinned-pinned ends are derived explicitly. And it is applied to a simply supported curved beam. Compared with the results of FEM, the veracity of analytical solutions by the precise transfer matrix method is verified. A real multi-span curved bridge subjected to concentrated loads and thermal load is analyzed using the precise transfer matrix method as well as FEM, and good agreements are observed.
引文
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[2]李华,武兰河.单根曲线梁法计算连续曲线梁桥影响线[J].工程力学,2005,22(增刊):26―30.Li Hua,Wu Lanhe.Influence line construction of continuous curved beam bridge using singular curved beam method[J].Engineering Mechanics,2005,22(Supplement):26―30.(in Chinese)
[3]单德山,李乔.曲线弯梁桥振动分析方法[J].土木工程学报,2005,38(10):62―65.Shan Deshan,Li Qiao.An ahalytical method of vibration analysis for curved-girder bridges[J].China Civil Engineering Journal,2005,38(10):62―65.(in Chinese)
[4]Wu Jong-shyong,Chiang Lieh-kwang.Out-of-plane responses of a circular curved Timoshenko beam due to a moving load[J].International Journal of Solids and Structures,2003,40:7425―7448.
[5]Kang B,Riedel C H,Tan C A.Free vibration analysis of planar curved beams by wave propagation[J].Journal of Sound and Vibration,2003,260:19―44.
[6]Ribeiro Pedro,Manoach Emil.The effect of temperature on the large amplitude vibrations of curved beams[J].Journal of Sound and Vibration,2005,285:1093―1107.
[7]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 dynarnics[J].Journal of Dalian University of Technology,1994,34(2):131―136.(in Chinese)
[8]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 method used in structure analysis[M].Beijing:China Railway Press,1997.(in Chinese)
[9]王一凡.直接积分法与精细积分法结合求解结构动力方程[J].工业建筑,2006,36(增刊):554―566.Wang Yifan.Solving structural dynamic equation using combination of the precise integraton method and direct precise integraton method[J].Industrial Architecture,2006,36(Supplement):554―566.(in Chinese)
[10]Zhong W X,Williams F W.A precise time step integration method[J].Journal of Mechanical Engineering Science,1994,208(6):427―430.
[11]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 precise integraton method for structural seismic response analysis[J].Engineering Mechanics,2007,24(4):35―40.(in Chinese)
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