相关正态空间中改进的有限步长迭代法

MODIFIED LIMIT STEP LENGTH ITERATION ALGORITHM IN CORRELATION NORMAL SPACE

针对有限步长迭代法在结构功能函数非线性程度极高时,保证收敛的初始步长难于确定的问题,提出了改进的有限步长迭代法。通过实例说明有限步长迭代法出现迂回迭代甚至不收敛的原因。为了保证每一迭代步长为最优步长,该文引入黄金分割法对步长进行一维搜索,并根据增广拉格朗日函数的极值条件构造了一个新的评价函数,给出了相关正态空间中改进的有限步长迭代法的计算步骤。数值算例表明改进的有限步长迭代法的迭代结果正确,在结构功能函数非线性程度极高时收敛性较好,迭代步数少于修正迭代法的步数。

When the structural failure function is highly nonlinear, the initial step length is difficult to determine for the application of the limit step length iteration method. To solve this problem, the modified limit step length iteration algorithm is presented in this paper. Illustrative examples demonstrate the reason of zigzagging movements and non-convergence in the application of the limit step length iteration method. To ensure that each iteration step length is optimized, the golden section method is introduced for one dimensional search of the step length. A new merit function is given according to the extreme value condition of extensive Lagrange function, and the calculation procedure of the modified limit step length iteration method is presented in correlation normal space. Numerical examples demonstrate the accuracy of the modified limit step length iteration method. It has better convergence when the structural failure function is highly nonlinear, and the number of iteration step is less than that of modified iterative algorithm.