基于余能驻值原理的悬索切线刚度推导及分析

Derivation and Analysis of Tangent Stiffness for Suspended Cable Based on Principle of Complementary Energy

摘要:

索结构分析中，索段静力平衡法和虚功增量方程法是两种主要的有限元理论分析基础，但这两种方法在数学复杂性和通用性方面存在局限性。基于余能驻值原理和变分计算，提出了一种新型的索结构有限元分析理论。与传统方法相比，该方法避免了复杂的数学推导，并具有更好的杆系结构通用性。算例分析表明，该方法在计算精度和收敛效率方面与现有方法相近，有较好的准确性和可靠性，可为索结构以及其他杆系结构的非线性有限元分析提供一种更为简洁有效的新思路。

Abstract:

In the analysis of cable structures, the static equilibrium method of cable segments and the virtual work increment equation method are currently the main theoretical foundations of finite element analysis. However, the two methods have limitations in terms of mathematical complexity and universality. Based on the principle of complementary energy and variational calculation, a new finite element analysis method for cable structures is proposed. Compared with the traditional methods, the proposed method avoids the complex mathematical derivations and has better generality for the structures of bar system. The analysis of examples show that this method is comparable to the existing methods in terms of computational accuracy and convergence efficiency with good accuracy and reliability, providing a concise and effective analysis method for the nonlinear finite element analysis of cable structures and other structures of bar system.