滑移索结构分析的精确三维有限元法

针对现有滑移索结构分析方法适用范围有限、精度不高的缺点,提出了一种通用、高精度的三维滑移索单元法。基于悬链线理论和Euler-Eytelwein公式,同时考虑了温度效应和滑动摩擦,分别建立了已知单元无应力索长和已知张拉力的三维滑移索单元的基本方程组;利用矩阵微分从单元基本方程组导出了单元的切线刚度矩阵;建立了滑移索结构从张拉到后期加载的全过程精细化分析流程,可实现自动调用建立的各类索单元,准确分析各滑移点的摩擦;通过3个算例的计算及与现有理论解、数值解和试验结果的比较来验证该文所提出方法的可靠性和有效性。结果表明,该文提出的三维有限元法准确可靠,计算效率较高,适用于工程中各种滑移索结构的高精度非线性分析。

HIGH-PRECISION THREE-DIMENSIONAL FINITE ELEMENT METHOD FOR ANALYSIS OF SLIDING CABLE STRUCTURES

To overcome the shortcomings of limited application range and low precision in the existing analysis methods for sliding cable structures, a general and high-precision three-dimensional finite element method for sliding cables is proposed. Based on the catenary theory and Euler-Eytelwein equation, the governing equations of the three-dimensional sliding cable elements with known unstressed cable length and with known tensile forces are respectively developed, accounting for the thermal effect and sliding friction. The tangent stiffness matrix of the element is derived directly from the governing equations by using matrix differential. A refined analysis procedure of sliding cable structures for the whole process from tensioning to later loadings is proposed, with the capability of automatically using all types of cable elements and accurately analyzing the friction at each sliding point. The reliability and effectiveness of the proposed method are verified by three computational examples and, by the comparison with the pertinent existing theoretical solutions and, with the pertinent numerical results and experimental ones. The computational results show that the three-dimensional finite element method proposed is accurate and reliable with high computational efficiency and is very suitable for the high-precision nonlinear analysis of various sliding cable structures in engineering practice.