张弦梁结构形态分析方法的改进

Improvement of Form-Finding Methods for Beam-String Structures

作为一种半刚性大跨空间结构,张弦梁结构的找形分析非常重要.改进的逆迭代法是找形分析中的一种比较有效的方法,通过引入初应变,能够在不破坏结构完整性的前提下,得到张弦梁结构的零状态几何和初状态预应力分布.但改进的逆迭代法在迭代过程中,由于找形和找力分开进行,影响了迭代效率.为此,基于改进的逆迭代法存在的问题,对其迭代过程进行了修正.通过在每次迭代中,将节点几何坐标和单元内力的精度要求同时作为收敛判据,并调整节点坐标和单元初应变,即使得体系的找形和找力过程同时进行;在迭代过程中分别引入节点坐标调整系数和初应变调整系数,并深入研究了这两个调整系数的不同取值对收敛速度的影响.算例结果表明:修正后的改进逆迭代法可显著减少迭代次数,提高了计算效率;研究发现两个调整系数对收敛速度有一定的影响,其中初应变调整系数的影响较节点坐标调整系数的影响大.在分析中选择合适的调整系数,可使找形分析的收敛速度更快.

Form-finding procedure is very important for beam-string structure, which is one special kind of semi- rigid large-span spatial structure. Modified inverse iteration method is relatively effective among all the form-finding methods for beam-string structure. With this method the zero state geometry and initial pre-stress distribution of beam- string structure could be obtained by introducing the initial strain without breaking the integrity status of the structure. But in this method the form-finding procedure and the force-finding one are operated separately, so the efficiency of the modified iteration method is somewhat low. In this paper, an improved iteration method was presented based on the modified iteration method. With this new iteration method, the two procedures of updating nodal coordinates and element forces were carried out simultaneously in each iteration step until the requirement of the accuracy of geometry and force was satisfied. Meanwhile, two adjusting factors were introduced in the improved iteration method and the influence of different values of the two adjusting factors on the rate of convergence was also further studied. The result shows that the improved inverse iteration method has reduced the iteration steps greatly, and also improved the com- putational efficiency obviously. Some conclusions could also be made as follows： the two adjusting factors have cer- tain influence on the rate of convergence; and the adjusting factor of initial strain has larger influence than the adjust- ing factor of node coordinates. It is noted that if an appropriate adjusting factor is chosen accordingly, the form- finding iteration process will result in a faster rate of convergence.