线性化极限状态方程及归一型算法

Linearizing Limit-State Equations and the Merge-Variable Iterations

对β通常的几何涵义进行了补充说明;讨论分析了几种可靠度计算中常用的线性化极限状态方程的迭代法,导出了几种方法基本方程间的关系。在迭代算法中,收敛性不仅决定着计算量的大小,而且决定着算法的可行性。在分析各种算法的收敛性之后,针对这些算法存在的问题提出了计算可靠指标β的归一型迭代法,并给出了两点迭代格式的迭代步骤。这个算法可以同时计算设计验算点。通过计算实例比较了几种算法的计算量和计算效果。结果表明,归一型算法计算速度快、计算量小,是一种实用的算法。

At first an additional explanation of common geometric meanings of reliability index β is presented.Then two types of iterations of linearzed limit-state equations for structural reliability anal- ysis are discussed and the fundamental relationships between them are derived.In iterations,the con- vergence of algorithm affects not only computing work load but also the workability of it.Through dissecting the convergence of two types of iterations,the merge-variable iterations which are directed toward the problems existing in the iterations are proposed and the steps of two-point-iteration are illus- trated.This algorithm can compute the design points simultaneously.At last both computing work load and efficiency are compared through computing examples.The results show that the new type of itera- tions has the advantages of better convergence and less computing work load and is a practical method.