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有限段法是一种有限单元半分析法。其基本想法是:沿梁的纵轴线将梁体横向切割成若干节段,节段数目由计算精度控制。梁段单元在横截面上的变形规律用某一已知形函数表述;梁段单元沿纵轴线的变形规律由节段间变形的连续条件控制。将箱形梁扭转的空间问题简化为一维问题。根据最小位能原理,求出每段梁体的单元刚度矩阵。再根据边界条件组成全梁总刚度矩阵。最后,把问题归结为求解一组以位移参数为未知数的线性方程组。
The finite segment method is a finite element half analysis. The basic idea is to cut the beam laterally into segments along the longitudinal axis of the beam, and the number of segments is controlled by the calculation accuracy. The deformation law of the beam element on the cross section is expressed by a known shape function; the deformation law of the beam element along the longitudinal axis is controlled by the continuous conditions of the deformation between the segments. The space problem of torsion of box beams is reduced to a one-dimensional problem. According to the principle of minimum potential energy, the element stiffness matrix for each segment of the beam is obtained. According to the boundary conditions, the total stiffness matrix of the whole beam is formed. Finally, the problem is attributed to solving a set of linear equations with unknown displacement parameters.