劲性支撑穹顶结构找形分析

Form- finding Analysis of Rigid Bracing Dome

针对索垂度在施工成形过程中不可忽略的问题,采用悬链线单元模拟索,依据胡克定律、小应变假设和变形协调方程等条件,推导了索原长的计算公式,给出了一种已知任意一个正值求解索原长度的二分法。在正交索网结构中,采用该二分法求得的索原长与已知条件给出的索原长进行对比,其误差均不超过0.16%,且不同初始值计算得到的索原长差别不大。针对劲性支撑穹顶结构的找形分析问题,给出了一种FEDR法,即有限元动力松弛法,以期提高动力松弛法的计算精度和可靠性。给出了找形分析的求解策略,并通过FORTRAN语言和ANSYS的APDL语言编制找形分析程序。对正交索网和跨度为71.2 m设两道环杆的肋环型劲性支撑穹顶结构进行找形分析,ANSYS有限元分析与FORTRAN语言找形程序求得的杆件内力进行对比,其误差均不超过0.42%。

In order to solve the problem that the cable sag of rigid bracing dome can not be ignored, cables were simulated by catenary cable element. According to Hooke＇ s law, small strain assuming and deformation compatibility equation, the calculation formula of cable original length was deduced. With any known positive value, the able original length was calculated by dichotomy. For orthogonal cable net,the initial length of cable was compared with known cable original length. The errors are less than 0.16%. And the difference of the calculated cable original lengths is very small for different initial values. According to the form-finding analysis of rigid bracing dome, FEDR method was given to improve the accuracY and reliability of DR method. Solving strategies of form-finding analysis were given. Form-finding analysis program was programmed by FORTRAN language and ANSYS APDL language. Form-finding analysis was done for cable net and the span 71.2 m of rigid bracing dome. Internal forces of rods that were calculated by form finding program were compared with internal forces of rods of finite element analysis software, and the errors are less than 0.42%.