结构连续变更定理在可靠性分析中的应用

THE USE OF THEOREM OF STRUCTURE CONTINUAL VARIATION IN RELIABILITY ANALYSIS

以平面桁架为例将结构连续变更定理用于结构的可靠性分析,以分枝限界法为基础编制了电算程序。避免了由于结构拓朴不断变更引起的总刚度阵多次组装及多次求逆运算,引入了结构退化为机构的新判据。实现了不断变更结构的连续分析,还连续生成极限状态函数。从而边进行结构分析,边进行失效链失效概率计算。在搜索中,有效地筛选出可能失效链并得到可能失效模式的集合。因此提出的理论和方法可以用来解决某些工程实际问题。算例表明结果令人满意。

The theorem of structural continual variation is applied to the analysis of the reliability of plane truss structures. On the basis of the branch-bound method, a computing program is developed. The repeated assemblies of the global stiffness matrix and the repeated inverse operations of the matrix caused by uninterrupted changes of structure topology can be avoided. A new criterion for degeneration of structure into a mechanism is introduced. Both the sequential analysis for the structure continual variation and the generation of the limit state functions of structure can be realized. Moreover, the generation of the probable failure chain and the calculation of the failure probability may be simultaneously accomplished. In the searching the probable failure chain is efficiently selected and the set of the probable failure models is also given. Therefore, the theorem and the method indicated in this paper is useful to solve some practical engineering problems. The results of the calculating example are satisfactory.