悬索桥主缆线形确定的常用精确解析算法比较及电算高效实现方法研究

Comparison on common precise numerical analytical algorithms to determine main cables' curve shape in suspension bridges and study on highly effective methods of computation

以悬索桥主缆线形确定的常用精确数值解析算法为研究对象,通过对它们的比较分析和公式推导发现:在主缆理想柔性、忽略泊松比效应的最基本假定下,主缆线形确定的精确数值解析法可归结为主缆自重集度按其有、无应力长度计算作为已知条件的两大类算法;并且证明了在每大类解析算法中的所有方法是完全等价的.研究还表明:第二类解析算法为"全精确解析算法",第一类为"准精确解析算法";在第一类算法中,主缆无应力长度公式的计算值偏小.仅就悬索桥主缆成桥态线形确定而言,主缆线形确定的两大类数值解析算法都具有很高的工程精度,但第二类算法的主缆自重集度的确定更为精确、更接近实际情况,实际计算时应优先使用它.另外,针对两类解析算法涉及到大量的超越方程求解和递推迭代计算的情况,提出了基于MATLAB软件的高精度电算实现方法.最后,给出一个超大跨径悬索桥的中跨主缆线形确定的验证算例.

The common precise numerical analytical algorithms to determine main cables＇ curve shape in suspension bridges were investigated.By means of comparison among these algorithms and formulae inference,it is found that these algorithms can be reduced to two big categories of analytical ones according to different known conditions that weight intensity loads of main cables are calculated in terms of their lengths with stress and without stress under the basic hypotheses that main cables are ideally flexible and the effect of Poisson ratio of their cross-sections is neglected.It is proved that all methods among big categories of analytical ones are equivalent to each other.Moreover,further studies show that the second big category of analytical algorithms is ＂thoroughly precise analytical ones＂ and the first is quasi-precise analytical ones,and the latter one under-evaluates the length of main cables.Both categories of analytical algorithms to determine main cables＇ curve shape have very high precision of engineering as far as the determination of curve shape finished state of suspension bridges is concerned,but the method to determine weight intensity loads of main cables in the 2nd categories of analytical ones are more precise and nearer to actual cases,so the 2nd one is preferred choice in actual computations of suspension bridges.In addition,highly effective methods of computers are presented to solve a lot of transcendental equations and recurrence operations involved in by the two big categories of analytical algorithms.Finally,an example to determine main cables＇ curve shape of the middle span in a super-long span suspension bridge is given to validate the analysis in this paper.