集中荷载作用下扭转支撑悬臂梁弯扭屈曲分析

Flexural-torsional buckling analysis for cantilever beam with torsional bracing under concentrated load

采用能量变分法,建立集中荷载作用下扭转支撑悬臂钢梁弯扭屈曲的总势能方程,选取6项三角级数表达的位移函数和转角函数,引入无量纲参数,计算扭转支撑悬臂钢梁弯扭屈曲的无量纲临界弯矩解析解;采用1stOpt数学优化分析软件,拟合扭转支撑悬臂钢梁无量纲临界弯矩计算公式;采用ANSYS有限元分析软件进行验证,研究荷载作用位置对悬臂钢梁弯扭屈曲强度的影响。结果表明,扭转支撑悬臂钢梁无量纲临界弯矩计算公式具有较高的精确性,为悬臂梁设计和稳定性研究提供参考。

The total potential energy equation is established for elastic flexural-torsional buckling of cantilever beam with torsional bracing under concentrated load by the energy variational method.The modal trial functions of the lateral displacement and torsional angle are expressed by the first six terms of the trigonometric function.By introducing dimensionless parameters,the dimensionless critical moment analytical solutions of the flexural-torsional bucking of cantilever beam with torsional bracing are obtained.With the help of 1stOpt which is mathematical optimization analysis software,the simple dimensionless calculating formula of the critical moment is obtained.Then,the accuracy of the dimensionless critical moment formula is verified by ANSYS finite element program,and a parametric study for the effect of the loading position on the flexural-torsional buckling strength is investigated.The results show that the given dimensionless critical moment formula is of high accuracy.Hence,the proposed equation can provide a reference for cantilevers design and stability research.