A reproducing kernel particle method for solving generalized probability density evolution equation in stochastic dynamic analysis

Analysis of stochastic dynamic system is still an open research issue. Recently a family of generalized probability density evolution equation, which provides an available way for general nonlinear systems, is put forward. In this paper, a numerical method based on reproducing kernel particle method (RKPM) for the solution of generalized probability density evolution equation, named the refined algorithm based on RKPM, is developed. Besides, the corresponding implementation procedure is elaborated. In this method, the time dependent probability distributions of the responses of interest can be obtained with less computational efforts. In addition, the mesh sensitivity problem in traditional probability density evolution method is settled well. Some details of parameter analysis are also discussed. To verify both the efficiency and accuracy of the method, a single-degree-of-freedom example and a 10-story frame structure are investigated. The refined algorithm based on RKPM can be applied to uni-variable and multi-variable, one-dimensional and multi-dimensional systems.