工程随机因素对索网结构初始形状确定的灵敏度分析

SENSITIVITY ANALYSIS OF THE INITIAL EQUILIBRIUM FORM OF CABLE NET

考虑了张拉结构找形过程中的不确定性,将这些不确定性用随机变量表示。在预拉力给定的索网结构形状确定的特殊拉索单元法的基础上,推导了等效外力向量、等效单元不平衡力向量和单元切线刚度矩阵的偏导计算式,建立了初始平衡状态几何向量的灵敏度计算迭代格式。根据平衡几何向量的灵敏度和索段长度的灵敏度,计算出索网零状态时,索段放样长度对随机变量的灵敏度,并进一步求出了放样长度均匀性的灵敏度。以此为依据,对设计参数进行修改,使索网放样长度更均匀,便于施工安装。此方法同样也可用在放样长度给定的索网找形分析中,使得其初始平衡状态的预应力更均匀,提高索网的受力性能。

The uncertainties in form finding of tension structures were considered. Factors in form finding models can be treated as random variables reflecting inherent uncertainties. The special cable element method for form finding of specified prestressed cable net was used. The partial derivatives were derived for the equivalent external force vector, equivalent internal resisting force vector and tangent stiffness matrix. The sensitivity iterative formulas of initial balance shape coordinates were presented. With the sensitivities of shape coordinates and the sensitivities of cable length in balance state, the sensitivities of unprestressed cable length were calculated, and the sensitivity of the unprestressed cable length homogeneity was calculated. According to these sensitivity information, the design parameters of the cable network were modified, so that the unprestressed cable length is more homogeneous and the construction is more convenient. The process can also be applied to form finding of specified unprestressed-cable-length net to homogenize the prestress distribution in order to improve the network capability under stress.