大曲率薄壁曲线梁几何非线性问题的力学模型

Mechanics model for geometrical nonlinear problem of large curvature thin-walled curved girder

假设翼板横截面上的悬臂板、顶板和底板的剪力滞翘曲位移函数,得到了结构的总势能泛函;利用能量变分原理,推导了考虑曲率半径沿梁宽变化影响的大曲率薄壁曲线梁的几何非线性控制微分方程,然后采用样条最小二乘配点法求其近似解,得出了荷载作用下结构的内力和位移,分析了曲率半径对结构的影响.通过算例将计算结果与试验值对比可以看出,两者基本吻合,特别是曲线箱梁截面的重要受力位置两者非常接近,说明了计算理论的正确性.结果表明:当宽径比小于0.1时,可以不考虑曲率半径沿梁宽变化对剪力滞系数影响;随着曲率半径的逐渐增大,各截面的剪力滞系数逐渐趋向于对称,扭转角和挠度均逐渐减小,且两者与荷载的关系中线弹性范围都逐渐增加.

The shear lag warping displacement function of the cantilever, top and bottom plate of flange section were assumed. The total potential energy function of the structure was obtained by the assumption. Based on potential various principles, the geometrical nonlinear governing equation of the large curvature thin-walled curved girder was deduced with regarding of the influence of curvature radius change along beam width. The approximate solution was obtained by spline least squares collocation method to deduce the internal force and displacement of the structures under loads. Effect of curvature radius on the structure was also analyzed. The comparison of calculating value with test results illuminates that the proposed method is reliable, and especially that the important force locations of curved box girder cross-sec tion are very close. The results show that the influence of curvature radius change along the beam width on shear lag could be ignored when the ratio of width and diameter is less than 0.1. The shear lag coefficient in each section tends to symmetry gradually with the increasing of the curvature radius, while the torsional angle and the deflection decrease with the increase of their linear elastic scopes in the relationship of torsional angle-load and deflection-load.