阶梯形圆形水池分析的传递矩阵法  

TRANSFER MATRIX METHOD FOR ANALYSIS OF STEPPED CIRCULAR WATER TANK

作　　者：夏桂云[1,2] 俞茂宏[2] 李传习[1] 曾庆元[3] 

机构地区：[1]长沙理工大学土木与建筑学院,长沙410004 [2]西安交通大学航天航空学院,西安710049 [3]中南大学土木建筑学院,长沙410075

出　　处：《工程力学》2011年第2期24-29,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(50778024);中国博士后基金项目(20080441177);长沙理工大学桥梁与隧道工程创新项目(2010-01)

摘　　要：考虑剪切变形的影响,推导了圆形水池在轴对称荷载作用下的中厚壳有矩理论公式,其微分方程与Winkler地基上Timoshenko梁的微分方程一致,当圆形水池池壁剪切刚度取无穷大时,其可退化成相应薄壳理论公式。利用初参数法,推导了微分方程的解形式和建立了结构分析的传递矩阵法。分析了底部固结顶部自由、在分布荷载和径向荷载作用下阶梯形圆形水池横向挠度、转角、剪力、弯矩随池壁高度的变化,并与不考虑剪切变形影响的计算结果、Ansys结果进行了比较。计算结果表明:圆形水池考虑剪切变形影响的计算结果偏小、采用薄壳理论偏安全;剪切变形对弯矩、剪力影响比对环向力、径向位移影响大;所建立的圆形水池初参数解和转递矩阵法丰富了圆形水池和Winkler地基上Timoshenko梁的计算理论。Considering the shear deformation,a circular water tank was treated as a thick shell,and the differential equation was derived,which was the same as the interactive equation of a Timoshenko beam on a Winkler foundation.When the shear stiffness of tank wall tended to infinite,corresponding equations of thick shell theory can be degenerated into that of thin shell theory.Using the initial parameter method,the solutions to the circular water tank were resolved and the transfer matrix method was established.A two stepped circular water tank with clamped bottom and free top under a triangular distributing load and a radial load was analyzed to demonstrate the shear deformation effect;the transverse deformation,rotating angle,shear force and bending moment were presented to describe the changing with the tank height.Results of thin shell theory,thick shell theory and Ansys software were compared.Numerical analyses indicate that shear deformation leads to small results and thin shell theory used at present is safe.Shear deformation affects the bending moment and shear force more than the loop force and radial displacement.The initial parameter solutions and the transfer matrix method enrich the computing theories of a circular water tank and a Timoshenko beam on a Winkler foundation.

关 键 词：圆形水池 传递矩阵法 剪切变形 中厚壳 初参数 

分 类 号：TU991[建筑科学—市政工程]