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《Acta Mechanica Sinica》 2003-06
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THE PROBABILITY DENSITY EVOLUTION METHOD FOR ANALYSIS OF DYNAMIC NONLINEAR RESPONSE OF STOCHASTIC STRUCTURES

Li Jie Chen Jianbing (School of Civil Engineering, Tongji University, Shanghai 200092, China)  
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.
【Fund】: 国家杰出青年科学基金资助项目(59825105)
【CateGory Index】: O342
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