求解结构可靠指标的线性可行方向算法  

Linear feasible direction algorithm for calculation of reliability index of structure

作　　者：蒋友宝[1] 冯健[1] 孟少平[1] 

机构地区：[1]东南大学混凝土及预应力混凝土结构教育部重点实验室,南京210096

出　　处：《东南大学学报（自然科学版）》2006年第2期312-315,共4页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(50478075);江苏省自然科学基金资助项目(BK2003061)

摘　　要：为克服当极限状态曲面方程非线性程度较高时应用一次二阶矩法求解可靠指标可能不收敛的问题,提出一种求解结构可靠指标的线性可行方向算法.该算法采用求解约束极值问题的可行方向策略,在迭代过程中综合考虑了目标函数和极限状态曲面方程的影响.算法在每步迭代中先计算极限状态曲面在前步迭代点处的切平面,然后在此切平面上选定一个点,使该点和原点的连线与极限状态曲面的交点满足可行方向和收敛的要求.数值算例表明,无论极限状态曲面方程非线性程度如何,该算法都具有较高的精度和效率.这为结构可靠指标的计算提供了新的方法.A linear feasible direction algorithm is proposed to calculate reliability index of structure. It overcomes the problem that calculation of reliability index is not converged with the first order reliability method （FORM） when limit state equation is nonlinear. Based on the feasible direction strategy, the effect of objective function and limit state equation on calculation of reliability index is considered in the iteration of the algorithm. In each step the tangent plane of limit state surface at the previous iterative point is calculated firstly, and then a line from origin to a point on the plane is determined whose intersection with limit state surface satisfies the requirement of feasible direction and convergence. Numerical examples show that the algorithm is of higher precision and efficiency whether limit state equation is nonlinear or not. It provides a new approach to calculate structural reliability index.

关 键 词：可靠指标 非线性 可行方向 初始值 

分 类 号：TU311[建筑科学—结构工程]