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本文基于连续化模型,将框筒视为边缘加筋的平面应力平板组合结构,巧妙地变换框筒顶部的自由端边界条件,通过求解双调和方程得到了方形简体结构的弹性力学精确解,其主要工作是采用力法思想将框筒变为单块板的平面应力问题,再求出其级数形式的解.文中给出的级数解收敛快,能正确反映剪力滞效应和角柱效应,通过比较表明,以往的能量变分和有限条解均与之基本吻合,且本文解给出了更明显的剪力滞效应.
In this paper, based on the continuous model, the frame is considered as an edge-reinforced planar stress plate composite structure, and the free-end boundary conditions at the top of the frame tube are subtly transformed. The exact solution for the simplified structure of the square is obtained by solving the biharmonic equation. The main task is to use the force method to transform the frame tube into a single plate plane stress problem, and then find the solution of its series form. The series solution given in the text converges quickly and can correctly reflect the shear lag effect and the corner column effect. The comparison shows that the previous energy variation and finite strip solution are basically consistent with each other, and the solution of this paper gives a more obvious shear lag effect.