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

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. © 2024 Central South University. All rights reserved.