槽形梁动力反应分析的能量变分法
|
摘要
以分析箱形梁剪滞效应提出的方法为基础,考虑了剪滞翘曲应力的自平衡条件,为了准确反应槽形梁翼板的动位移变化,三个广义动位移η(x,y,z,t)、w(x,t)和θ(x,t)被引入。利用能量变分原理建立了槽形梁动力反应w(x,t)、u(x,t)和θ(x,t)的控制微分方程和自然边界条件,获得了相应广义位移的闭合解,据此对槽形梁的动力反应特性进行了研究,揭示了槽形梁桥动力反应的规律。算例中,该解析解与有限元数值解进行了比较,证明了该动力分析方法的有效性。
Based on the analysis methods of shear lag effect of box girders,a new warping displacement model of an U-shaped beam was chosen to meet the axial self-equilibrium conditions for the corresponding stresses.Three generalized displacement functions η(x,y,z,t),w(x,t),and θ(x,t) were introduced in analyzing dynamic response of the U-shaped beam in consideration of shear lag effect using the energy-variation principle.The differential equations and the corresponding natural boundary conditions of the U-shaped beam were derived based on the minimum potential principle.According to the fundamental differential equations and the corresponding natural boundary conditions,the dynamic characteristics of U-shaped beams were discussed.In calculation examples,the finite element solutions were compared with the analytical solutions,the results verified the validity of the proposed approach.
Based on the analysis methods of shear lag effect of box girders,a new warping displacement model of an U-shaped beam was chosen to meet the axial self-equilibrium conditions for the corresponding stresses.Three generalized displacement functions η(x,y,z,t),w(x,t),and θ(x,t) were introduced in analyzing dynamic response of the U-shaped beam in consideration of shear lag effect using the energy-variation principle.The differential equations and the corresponding natural boundary conditions of the U-shaped beam were derived based on the minimum potential principle.According to the fundamental differential equations and the corresponding natural boundary conditions,the dynamic characteristics of U-shaped beams were discussed.In calculation examples,the finite element solutions were compared with the analytical solutions,the results verified the validity of the proposed approach.
引文
[1]郭金琼.箱形梁设计理论[M].北京:人民交通出版社,1991.
[2]Vlasov VZ.Thin-walled elastic beams[M].Washington D C.National Science Foundation,1961.
[3]Chang S T.Prestress influence on shear lag effect in continu-ous box girder bridge[J].J Struct Engrg,ASCE,1992,118(11):3113-3121.
[4]周坚,涂令康.再论槽型梁的剪力滞[J].工程力学,1994,12(2):65-75.
[5]邵爱军,吴代华.基于能量法的槽型梁剪滞效应分析[J].武汉理工大学学报,2003,25(3):52-55.
[6]陆广闾.连续铁路槽形梁桥空间作用分析[J].铁道学报(增刊),2000,22:41-46.
[7]黄新艺,盛洪飞,陈彦江,等.薄壁箱梁桥动力特性分析的三梁式计算模型及试验研究[J].振动与冲击,2008,27(12):40-43.
[8]张冠华,葛耀君.砼连续箱梁人行天桥振动特性测试与分析[J].振动与冲击,2009,28(2):102-106.
[9]宋一凡,周勇军,贺拴海,等.连续梁桥横桥向地震动分析[J].振动与冲击,2006,25(2):147-151.
[10]甘亚南,周广春.薄壁箱梁纵向剪滞翘曲函数精度选择的研究[J].工程力学,2008,25(6):100-106.
[11]吴亚平,赖远明.考虑剪滞效应的薄壁曲梁有限单元法[J].工程力学,2002,19(4):85-89.
[12]R.克拉夫.结构动力学[M].王光远等译.北京:高等教育出版社,2006.11.
[2]Vlasov VZ.Thin-walled elastic beams[M].Washington D C.National Science Foundation,1961.
[3]Chang S T.Prestress influence on shear lag effect in continu-ous box girder bridge[J].J Struct Engrg,ASCE,1992,118(11):3113-3121.
[4]周坚,涂令康.再论槽型梁的剪力滞[J].工程力学,1994,12(2):65-75.
[5]邵爱军,吴代华.基于能量法的槽型梁剪滞效应分析[J].武汉理工大学学报,2003,25(3):52-55.
[6]陆广闾.连续铁路槽形梁桥空间作用分析[J].铁道学报(增刊),2000,22:41-46.
[7]黄新艺,盛洪飞,陈彦江,等.薄壁箱梁桥动力特性分析的三梁式计算模型及试验研究[J].振动与冲击,2008,27(12):40-43.
[8]张冠华,葛耀君.砼连续箱梁人行天桥振动特性测试与分析[J].振动与冲击,2009,28(2):102-106.
[9]宋一凡,周勇军,贺拴海,等.连续梁桥横桥向地震动分析[J].振动与冲击,2006,25(2):147-151.
[10]甘亚南,周广春.薄壁箱梁纵向剪滞翘曲函数精度选择的研究[J].工程力学,2008,25(6):100-106.
[11]吴亚平,赖远明.考虑剪滞效应的薄壁曲梁有限单元法[J].工程力学,2002,19(4):85-89.
[12]R.克拉夫.结构动力学[M].王光远等译.北京:高等教育出版社,2006.11.
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