Abstract: A new way to obtain the probability density function (PDF) of response was presented.The sample of structure response was obtained using Neumann SFEM. Then, the PDF of response was fit by means of the linear combination of Hermite orthogonal polynomial. At last, the hypothesis test was used to verify if the fit PDF can represent the actual probability distribution of the random variable. Results show that the proposed approach is practically efficient and can be applied to engineering practice.

Key words: Structural response;Probability density function;Structural reliability;Finite element method

摘要： 为了提高结构可靠性分析的精度 ,提出一种获得结构响应概率密度函数的新方法。通过随机有限元法计算得到结构响应的样本及其各阶矩 ,利用Hermite正交多项式的线性组合来获得结构响应概率密度函数的最佳平方逼近式。算例表明 ,本文方法具有较高的计算精度和计算效率。

关键词: 结构响应;概率密度函数;结构可靠性;有限元法