横向力作用下悬臂梁固定端应力分布研究

Stress distribution at the fixed end of a cantilever beam under lateral force

在弹性力学Hamilton体系中,利用解析法,考虑圣维南原理所覆盖的解,对横向力作用下悬臂梁固定端应力分布问题进行研究,并对计算结果进行分析。研究结果表明,辛体系解析法采用对偶的二类变量求解,能很好地处理各种复杂边界条件,并且对此类问题的分析具有优越性,计算精度较高。该方法对其他边界问题的研究也具有指导意义。

In the Hamilton system of plane elasticity,using analytic method and taking the solution that covered by the Saint Venant Principle into account,the problem of the stress distribution of a cantilever beam subjected to lateral force at its free end is studied and its solution is attained.The results prove that symplectic analytic method is effective,and by using this method,various complicated boundary conditions can be handled better.Therefore,compared with traditional semi-inverse method,the analytic method has unique advantages including higher computational accuracy.This symplectic analytic method also has guiding significance for the study of other boundary problems.