张力索网结构零应力态与预应力态计算方法（英文）

Computational methods for the zero-stress state and the pre-stress state of tensile cable-net structures

研究目的:减小张力索网结构所求实际预应力与预期预应力之间的差异,并更完善地描述结构力学行为。创新要点:提出张力索网结构全过程分析概念,并用10个状态描述了其物理或分析的状态,以及15个过程揭示了状态间内在的逻辑关系和力学分析理论;在应力释放分析中,采用逆分析法提出了一种用于求解合理零应力状态的迭代计算方法;在预应力成形分析中,为获取预应力状态建立了另一种迭代计算方法。研究方法:应力释放分析主要包括四个步骤:构件无应力长度及伸长量计算,最小范数最小二乘法,数值迭代方法,和执行程序(图4);预应力成形分析在能量方程的基础上提出了控制方程的显式表达式,并为避免初始刚度矩阵的奇异问题而采用了合理自应力模态(图5)。重要结论:比较本文提出的计算方法与动力松弛法得到的零应力态,发现结果吻合良好,证明计算过程收敛性良好且结果准确。在预应力成形分析中,采用本文迭代方法可以有效消除所求实际预应力与预期预应力之间的差异。此外,提出的所有计算方法都符合模块化流程,具有广泛适用性。

This paper proposes an extended design concept and mechanical description for cable-net structures, including 10 states and 15 procedures which are defined according to their physical nature and analytical capabilities. In the pre-stress release analysis, an iterative computational method is developed for the inverse evaluation from the equilibrium state to the zero-stress state, which adopts the least norm least square approach（LNLS） to the compatibility equation because of the indeterminate property of a cable-net structure. In the pre-tensioning development analysis, another iterative computational method is developed for the positive problem from the zero-stress state to the actual pre-stress state by moving the boundary joints, in which the explicit governing equations are formulated based on the particular energy function and a feasible self-stress mode is adopted to avoid the singularity of the initial stiffness matrix. To implement these methods, Matlab algorithms are developed and two examples are investigated. By comparing the results of the iterative method with those of the dynamic relaxation method, this study determines that they are comparable with each other, which validates the efficiency and accuracy of these iterative methods.