薄壁箱梁剪滞效应一维有限元分析

根据最小势能原理,建立薄壁箱梁挠曲剪滞基本微分方程.以其解析式作为形函数,利用刚度系数的定义,推导了考虑剪滞影响的箱形梁单元刚度矩阵及等效结点力公式.用该梁单元对一箱梁模型进行计算,并与按SAP通用程序计算结果及试验结果进行比较,证实了本文方法简单而且有效.为了探讨各种剪滞翘曲位移模式的合理性,分别选取二次抛物线、三次抛物线、四次抛物线及余弦函数等翘曲位移模式进行计算;结果表明,这些翘曲位移模式在一定程度上均存在不足,目前还缺乏一种更加合理的位移模式.

One-dimensional Finite Element Analysis for Shear Lag Effect in Thin-walled Box Girders

The differential governing equations of thin-walled box girder with shear lag effect are established by the principle of minimum potential energy.The analytic expression for shear lag displacement is used as shape function.Stiffness matrix and equivalent nodal force formula,which take into account of the influence of shear lag,are derived subsequently on the basis of the definition of stiffness coefficient.To validate the present element,a model of box girder is calculated.Comparing the calculation results with those obtained from the model test and the finite element software SAP,the method proposed in this paper is proved to be both simple and valid.In order to discuss the rationality of various warping displacement modes,second-degree parabola,cubic parabola,fourth-degree parabola and cosine function are selected respectively.It has been demonstrated that these displacement modes have limitation to some extent,and a more reasonable mode needs to be developed.