基于Steffensen迭代法的拉索等效预张力确定方法研究  

Study on determination method of cable equivalent pre-tension based on Steffensen iteration method

作　　者：赵文雁 潘文智 查晓雄 ZHAO Wenyan;PAN Wenzhi;ZHA Xiaoxiong(School of Civil and Environmental Engineering,Harbin Institute of Technology,Shenzhen,Shenzhen 518055,China;Zhejiang Jinggong Steel Building Group Co.Ltd.,Shaoxing 312030,China)

机构地区：[1]哈尔滨工业大学(深圳)土木与环境工程学院,广东深圳518055 [2]浙江精工钢结构集团有限公司,浙江绍兴312030

出　　处：《中南大学学报(自然科学版)》2024年第12期4570-4582,共13页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(52178129)。

摘　　要：针对现有拉索等效预张力确定方法存在的局限性大、稳定性差和计算效率低等问题,基于数学推导和表达,将预应力结构的拉索等效预张力确定转化为求解多个相对独立的非线性隐式方程,并结合数值分析理论,提出基于Steffensen迭代法的拉索等效预张力确定方法,以提高找力分析的计算效率、稳定性及适用性,通过常规及异形弦支穹顶结构算例分析验证该方法的可行性。研究结果表明:该方法具有突出的计算稳定性,相比于常规方法,在相同求解精度下具有二阶以上的收敛效率;该方法对不同迭代初值均具有较好的适应性,并且对多变量耦合的高精度求解问题依然具有较高的计算效率。因此,该方法可适用于各类复杂预应力空间结构,为预应力分级分批张拉所需的拉索等效预张力确定提供了一种高效、可靠的方法。Considering the limitations,poor stability,and low computational efficiency of the existing methods for determining cable equivalent pre-tension,its determination was transformed into solving several relatively independent nonlinear implicit equations based on mathematical deduction and representation.To enhance computation efficiency,stability,and applicability,a determination method for cable equivalent pre-tension based on Steffensen iteration method was proposed.The feasibility of the proposed method was verified by the examples of conventional and complex suspended dome structures.The results show that this method exhibits outstanding computational stability with at least second-order convergence speed compared to conventional methods while maintaining solution precision.Additionally,it demonstrates good adaptability for various initial iteration values and high computational efficiency in solving multivariate coupling problems with high precision requirements.In conclusion,an efficient and reliable approach for determining cable equivalent pre-tension in various complex prestressed spatial structures is provided by applying the Steffensen method.

关 键 词：预应力结构 预应力模拟 等效预张力 Steffensen迭代法 数值分析 

分 类 号：TU394[建筑科学—结构工程]