摘要
该文建立了分析大坝可靠度的计算方法。首先,使用Monte-Carlo法得到服从一定分布的随机参数,运用复合失效准则建立不同的功能函数,从而得出相应的功能函数的样本点。然后,采用二次多项式拟合相应的响应面。运用拉格朗日乘数法,将在响应面约束下求解设计验算点的非线性的约束最优化问题转化为解线性方程组问题,使用Jacobi迭代法求解线性方程组进行迭代。最后,使用二分法通过迭代得出拉格朗日乘子,反推出设计验算点,从而得出复合失效准则下大坝各个单元可靠度。取大坝各个单元可靠度的最小值作为其最终的可靠度。与常规求大坝各个单元可靠度的方法相比,该方法有其优点:一是中间过程不用求梯度,适用范围广;二是将非线性问题转化为线性问题进行求解,可以用于极限状态方程非线性程度较高的可靠度分析。
In this paper, an improved method for reliability analysis of dam is established. Firstly, random parameters in accord with certain distribution are obtained using Monte-Carlo simulation method. Based on composite failure criterion, different performance functions are established, and then sample points of performance functions are obtained accordingly. Secondly, quadratic polynomial is used to model response surface. Using Lagrange multiplier rule, the nonlinear optimization constraint problem, which generates the design checking points under constraint of response surface, is converted into the problem of solving linear equations, which can be implemented by Jacobi iterative method. Finally, Lagrange multiplier and the design checking points are obtained by using bisection method. And the reliability of each element of the dam under composite failure criterion is calculated. The element reliability is defined as the minimum among all elements＇ reliabilities. Compared with other conventional algorithm, this method has some advantages： 1） the gradient is not required in analysis; 2） wider application scope; 3） a nonlinear optimization constraint problem is converted into a problem of solving linear equations, so this method can analyze structure reliability with highly nonlinear limit states.
出处
《工程力学》
EI
CSCD
北大核心
2009年第11期108-113,共6页
Engineering Mechanics
基金
国家重点基础研究发展计划(973项目2007CB714107)
教育部新世纪优秀人才计划项目(NCET-06-0270)
