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模拟索段的折线模型,假定索线重以集中力形式作用于内节点上,用多折线模拟初始平衡态下的索段,其建模的直接参数为折线数和初始几何(内节点坐标)。以索的基本平衡微分方程和平衡条件为基础,建立了满足既定计算精度的折线数估计公式,提出折线数与拉索线重以及水平跨度和索端直线距离的开方成正比,与初始水平分力以及允许误差的开方成反比;根据索力或无应力索长的已知条件,提出了确定初始平衡态下初始几何的数值迭代方法。算例验证了索段在低应力和大垂度条件下折线数估计公式的合理性,在经过较少次数迭代计算后,所得到的初始几何满足索力和索线重的平衡条件。
It is assumed that the cable weight acts on the internal nodes in the form of concentrated force, and the cable segments in the initial equilibrium state are simulated by multi-broken lines. The direct parameters of modeling are the number of broken lines and the initial geometry (the coordinates of the internal nodes) . Based on the basic equilibrium differential equations of cable and the equilibrium conditions, the formula for estimating the number of broken lines which satisfies the established calculation precision is established. The number of broken lines is proposed to be proportional to the line weight of the cable, the horizontal span and the straight line distance of the cable end, Component force and allowable error are inversely proportional to the square root. According to the known conditions of cable force or stress-free cable length, a numerical iteration method is proposed to determine the initial geometry in the initial equilibrium state. The example shows the rationality of the formula for estimating the number of broken lines under low stress and large sag. After a small number of iterations, the obtained initial geometry satisfies the equilibrium conditions of the cable force and the line weight.