带刚臂平面悬链线索单元的非线性分析  

Nonlinear analysis for plane catenary cable element with rigid arm

作　　者：邓继华[1,2] 谭平[1] 彭建新[2] 

机构地区：[1]广州大学工程抗震研究中心,广州510405 [2]长沙理工大学土木与建筑工程学院,长沙410076

出　　处：《应用力学学报》2014年第3期348-352,487,共5页Chinese Journal of Applied Mechanics

基　　金：国家重点基础研究发展计划(2011CB013606);国家自然科学基金(51008037)

摘　　要：针对索梁混合结构中存在的索单元锚固点刚性连接问题，将锚固点的刚性连接视为刚臂，进行了带刚臂的平面悬链线索单元研究。一方面在已有文献的基础上，根据平面刚臂的受力和变形特点，基于微分方法导出了两端带任意刚臂的平面悬链线索单元切线刚度矩阵显式表达式；另一方面，为考虑温度变化对索单元计算的影响，基于索单元变形的几何与物理意义进行了考虑温度变化的索单元节点力计算方法的研究。通过与已有文献的对比，表明了本文研制的程序及导出的考虑温度变化的索单元计算方法的正确性；考虑温度变化下由本文方法得到的索水平张力与已有文献解析解最大仅相差0.862%。同时本文考虑的刚臂非线性因素更加全面，具体体现在：在非线性计算能力上，已有文献方法在荷载大于2.52kN 时计算无法收敛，远小于本文方法能达到的35kN；在计算效率方面，在7个荷载增量步内已有文献方法所需的迭代步数为4-33，而本文方法的迭代步数保持在4不变。Aiming at rigid connection of anchorage region for cable element in cable-girder hybrid structures, a plane catenary cable element by taking rigid connection of anchorage region as rigid arm is developed in this paper. Based on the existed references, according to the characteristics of the motion and deformation of rigid arm, an explicit expression of nonlinear tangent stiffness matrix of plane catenary cable element with arbitrarily rigid arms in both ends is derived by differential method. Meanwhile, taking influences of temperature change on constructional calculation of cable element into accounts, a calculation method of nodal forces is presented considering temperature change combining the physical and geometrical implications of deformation for cable element. Cases 1 and 2 indicate that the developed program and calculation method of nodal forces considering temperature change are correct, and the maximum error of longitudinal tension force of cable element is within 0.862% between the results from the presented method considering temperature method and those from references. Case 3 shows that the method presented in this paper considering rigid arm is more rational compared with that in existed references. Therefore, for the calculation capacity, the methods in existed references can not reach convergence when the load is 2.52kN, which is far less than 35kN obtained from this paper. For the calculation efficiency, the number of iteration steps in most existed references is more than that in this paper, the iteration steps in some existed references is 8 times higher than that in this paper.

关 键 词：索梁混合结构 悬链线索单元 刚臂 温度变化 切线刚度矩阵 

分 类 号：TU378.2[建筑科学—结构工程]