一种剪滞翘曲位移函数的解析构造法

针对剪力滞问题,提出了一种解析的求解方法.通过对控制微分方程解的形式进行研究,构造出一种针对不同余弦剪力分布的剪滞翘曲函数;进而对任意给定的外荷载作用下的剪力分布进行级数展开,并单独求取各剪力分量对应的正应力;最终通过对正应力进行叠加并求取剪力滞分布.采用能量变分法推导了基于任意剪滞翘曲位移函数的求解公式,并编制了通用求解程序.分别以矩形简支箱梁(不带悬臂板)受集中荷载和带悬臂箱梁受均布荷载为例,进行了计算对比.研究表明:相比于已有方法,所提出的方法对不同荷载作用形式具有更好的适应性,且由于是采用级数展开的思想,适用于任意荷载作用情况下的剪力滞分析.

An analytical construction method of wraping displacement function of shear lag

An analytical solution method was proposed to solve the problem of shear lag. A new shear lag warping function for the shear distribution of different cosine was constructed based on the solution of the governing equations. The trigonometric series were used to expand the shear distribution function under any given external loads, and the normal stress corresponding to each shear component was obtained separately. Finally, the superposition of normal stress was obtained and the distributions of shear lag were calculated. The energy variation method was used to derive the solution formulas based on the arbitrary warping displacement functions of shear lag effect, and a general solution procedure was developed. A rectangular simply supported box beam without cantilever plate under concentrated load and a box beam with cantilever plate under distributed load were analyzed. The calculation results show that the solution method proposed in this study could adapt well with different types of loads compared with the existing methods, and it could be effectively used for shear lag analysis of box beams subjected to arbitrary loads.