基于能量原理的张弦拱结构求解与受力特性研究

Structural Analysis and Mechanical Characteristics Study of Arch String Structure Based on Energy Principle

根据张弦拱结构的变形特点,设定结构位移函数,并结合荷载条件,建立结构势能表达式。根据结构上弦拱、下弦索水平位移,按支座变形协调条件导出协调约束要求;在此基础上,引入拉格朗日乘子法,由势能驻值原理,运用瑞利-里兹法,求解出结构竖向位移及索力表达式。根据结构应变-位移微分方程得出上弦拱与下弦索的水平位移函数及撑杆相对位移表达式;对求解结果进行分析与简化,得出表达简洁、物理意义明确的简化公式。最后,通过多个算例,把理论分析公式、简化公式及有限元分析结果相互印证,证明分析结果的正确性。

Displacement function is assumed by the characteristics of deformation of the arch string structure,then function of potential energy is established based on displacement functions and loading conditions. Compatible equation is derived according to the end compatibility condition on horizontal displacement of up arch and low cable chord,then cable force and structure vertical displacement are obtained by Rayleigh Ritz method on the basis of the principle of potential energy,in which Lagrange multiplier method is induced with the compatible equation. The expressions about horizontal displacement functions of chord and relative displacement of brace strut are obtained by the strain-displacement differential equation. Analysis and simplification are developed on the results and then the simplified formulas are obtained,which have the merits of concise form and clear physical meanings. In the end,the results by the formula of theoretical derivation,the simplified and finite element method are confirmed mutually for a number of examples,the validity of deduction is also proved.