Difference Method for Probability Density Evolution Equation of Stochastic Structural Response

Probability density evolution method is a prospective approach for stochastic structural analysis. Difference method for probability density evolution equation of the stochastic structural response was studied. The computational performances of one-sided difference scheme and Lax-Wendroff scheme were discussed, respectively. The two schemes can both satisfy the compatibility of probability and ensure the linear increase with loading parameter increasing. An 8-story frame structure was taken as an example to verify the numerical method. The researches show that the two schemes are both convergent and stable, and there is corner effect around the discontinuous point. The one-sided difference scheme can keep the nonnegativeness of computed probability while the Lax-Wendroff scheme usually has more rapid convergence. As far as the coefficient of variance is concerned, the one-sided scheme provides an asymptotic value. In contrast the Lax-Wendroff scheme can provide a stable value from the beginnings.