摘要
提出了随机结构非线性动力响应分析的概率密度演化方法.根据结构动力响应的随机状态方程,利用概率守恒原理,建立了随机结构非线性动力响应的概率密度演化方程.结合Newmark-Beta时程积分方法与Lax-Wendroff差分格式,提出了概率密度演化方程的数值分析方法.通过与Monte Carlo分析方法对比,表明所给出的概率密度演化方法具有良好的计算精度和较小的计算工作量.研究表明:随机结构非线性动力响应概率密度具有典型的演化特征,随着时间增长,概率密度曲线分布趋于复杂.
The probability density evolution method (PDEM) for dynamic nonlinear response analysis of stochastic structures is proposed. In the paper, an uncoupled augmented state equation, based on existence and uniqueness of solution of well-posed dynamic systems, is firstly presented. According to the principle of preservation of probability, the probability density evolution equation of the structural nonlinear dynamic response is put forward and then uncoupled into a one-dimensional partial differential equation. The instantaneous probability density function of any response quantity can be obtained by solving the initial value partial differential equation problem. In the computational aspect, the proposed method can be carried out through a hybrid algorithm, where a deterministic nonlinear dynamic response analysis, say, the Newmark-Beta time integration method, is employed firstly to gain the coefficient of the probability density evolution equation and then a finite difference method with Lax-Wendroff scheme is used to solve the partial differential equation. The dynamic responses of an 8-story shear-story structure with bilinear hysteretic restoring force model are studied. The investigations indicate that the probability density functions of nonlinear dynamic responses evolves and tends more complex against time, usually far from well known distribution types such as the normal distribution and Rayleigh distribution, etc. This may have obvious influence on dynamic reliability assessment of the structure and therefore the traditional dynamic reliability theory may need to be revisited. The computations demonstrate that the proposed PDEM is of high accuracy and efficiency, without the limitation of the degree of variance of the source random parameters, neither influenced by the so-called secular terms problem. Therefore, it is a promising method worth further investigation.
出处
《力学学报》
EI
CSCD
北大核心
2003年第6期716-722,共7页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家杰出青年科学基金资助项目(59825105)
