结构可靠度分析的一次二阶矩方法与二次二阶矩方法

Simple and Quadratic of the Two Ranks Quadrature of the Structure Reliability

以中心点法和验算点法为代表的一次二阶矩方法计算简便,但对非线性程度较高的结构功能函数,其计算结果与精确度相差过大.应用数学逼近中的拉普拉斯渐进方法将非线性功能函数在验算点处作二次展开来研究结构的可靠度问题,能较高精度的逼近精确结果.算例分析表明,当随机变量的数目较多时,由一次二阶矩方法计算的结果与精确解相差较大,而二次二阶矩方法的计算结果与精确解非常接近.

Representative methods of the simple and two ranks quadrature are the method of the center and the method of the checking computations which are simple and convenient, but when structural function is non-linear, these methods are not enough nicety. Gradual method of the Laplace deploys quadraticly the non-linear structural function at the center of the checking computations, which can obtain better results. The analysis of the example indicates that the results by the method of simple and two ranks quadrature are inadequately inaccurate and the results by the method of quadratic and two ranks quadrature are enough niceties when random variables are more.