基于可靠度理论及非线性规划的索杆体系索长误差控制限值研究

Research on control limit of cable length error of cable-strut systems based on reliability theory and non-linear programming

为多维度地考虑索杆体系的安全边界,提出了索杆体系基于两种极限状态的三种失效模式,并结合可靠度理论构建了三种失效模式下索杆体系各构件的临界状态方程,推导了索杆体系中索长初始误差对于索力及节点位移的影响系数矩阵,然后采用主要目标法对此非线性规划问题进行求解,提出了考虑结构可靠度、加工要求和制造成本的索杆体系初始索长误差限值确定方法,并进行了算例验证。结果表明,综合考虑三种失效模式后,Levy索穹顶的-初始索长制造误差允许值小于现行规范规定值,应严格控制这类索杆体系的初始制造误差,否则容易发生松弛失效与变形失效。

Considering the safety boundary of the cable and rod system in multiple dimensions,three failure modes of cable-strut systems based on two kinds of limit states were proposed.The critical state equations of members of the cable-strut system under the three failure modes were derived making use of the reliability theory.The factor matrices of cable-strut systems were derived considering the influence of the initial error of the cable length on the cable force and the node displacement.Making use of the main target method which is one of the main methods for solving the non-linear programming problem,the paper then proposed a set of methods to calculate the initial error limits of cable length of the cable-strut system,considering the structural reliability,processing requirements and manufacturing costs.And the methods are validated by a case study.The numerical results show that after considering the three failure modes,the allowable initial error of cable length of the Levy cable dome is less than that specified in the current standard.Therefore,the initial manufacturing error should be tightly controlled for the cable-strut system.Otherwise,the structure is prone to relaxation failure and deformation failure.