结构可靠度FORM方法的混沌动力学分析

引入混沌动力学理论讨论了FORM收敛失败的非线性动力学根源. 给出了几个典 型函数在参数区间上的可靠指标分岔图，展示了极限状态函数经过FORM迭代成为 非线性映射后计算结果的周期振荡、分岔和混沌等复杂动力学现象，计算了非线性映射的 Lyapunov指数. 结果表明，极限状态函数设计点的曲率大小与FORM的收敛性没有简单的联 系，判别FORM迭代计算收敛性的指标是非线性映射的Lyapunov指数.

FORM in structural reilianbility analysis and chaotic dynamics

The HL-RF algorithm of First Order Reliability Method (FORM) in structural reliability analysis is recommended to use by the Joint Committee of Structural Safety. However, there exists the phenomenon of convergent failure with the FORM when calculating the reliability index for some nonlinear limit state functions. The essential factors of nonlinear dynamics for the convergent failure are investigated by using chaotic dynamics theory in the present paper. The bifurcation plots of reliability index are presented for several typical limit state functions. From the computational solutions of those mapping functions due to FORM iterations, it is shown that there are the complicated dynamics phenomena such as the periodic oscillation, bifurcation and chaos. Furthermore, the Lyapunov exponents of nonlinear map from FORM are analyzed. It is concluded that there is not a simple relationship between the curvature value of design points of limit state function and the convergence of FORM iteration, and the quantitative index for identifying the convergence of FORM iterative computation is the Lyapunov exponents of nonlinear map corresponding to that limit state function.