桥梁徐变效应的有限元算法研究及程序验证

Research on Finite Element Algorithm of Bridge Creep Effect and Program Verification

徐变是控制混凝土桥梁设计的重要因素,但因徐变计算一般封装于商业软件中,设计人员无法掌握计算原理。为研制自主有限元软件,摸索出桥梁徐变计算过程,从徐变系数开始研究,并对Midas帮助文件和基于Tröst-Bazant的工程实用分析算法进行基于公式推导的对比分析;基于分析结果进一步给出递推形式的徐变累加计算模型,并通过连续梁实例测试验证。研究结果表明:(1)Midas帮助文件给出的徐变算法和基于Tröst-Bazant基本方程的徐变算法本质上是一致的,当满足ρ(t,τ_(0))=1/2时,两者之间的方程是等价的;(2)通过加权最小二乘法将徐变系数写成通用格式,可将基于空间梁单元的徐变算法改造成递推形式,加快运算速度;(3)基于递推形式编制的卧龙程序,在同等边界条件下,其徐变位移的计算精度满足工程设计要求,竖向最大相对误差3%左右,且绝对误差较小,水平向相对误差在1%以内。

Creep is an important factor to control the design of concrete bridge.However,designers could hardly master the calculation principle because creep calculation is usually encapsulated in commercial software.In order to develop independent finite element software and find out creep calculation process of the bridge,creep coefficients are studied from the beginning,the Midas help file and the engineering practical algorithm based on Tröst-Bazant are compared and analyzed by means of formula derivation.Based on the analysis results,a recursive form of creep accumulation calculation model is established and verified by a continuous beam test.The research results show that:(1)The creep algorithm given in the Midas help document is essentially consistent with the creep algorithmbased on the Tröst-Bazant fundamental equation.Whenρ(t,τ_(0))=1/2,the equations between them are equivalent;(2)The creep coefficient is written in a general format by the weighted least square method,and the creep algorithm based on spatial beam element could be transformed into a recursive form to accelerate the operation speed;(3)Under the same boundary conditions,the creep displacement calculation accuracy of Wolong program based on the recursive form meets the requirements of engineering design.The maximum vertical relative error is about 3%,the absolute error is small,and the horizontal relative error is less than 1%.