Univariate dimension-reduction integration, maximum entropy principle, and finite element method are employed to present a computational procedure for estimating probability densities and distributions of stochastic responses of structures. The proposed procedure can be described as follows: 1. Choose input variables and corresponding distributions. 2. Calculate the integration points and perform finite element analysis. 3. Calculate the first four moments of structural responses by univariate dimension-reduction integration. 4. Estimate probability density function and cumulative distribution function of responses by maximum entropy principle. Numerical integration formulas are obtained for non-normal distributions. The non-normal input variables need not to be transformed into equivalent normal ones. Three numerical examples involving explicit performance functions and solid mechanic problems without explicit performance functions are used to illustrate the proposed procedure. Accuracy and efficiency of the proposed procedure are demonstrated by comparisons of the estimated probability density functions and cumulative distribution functions obtained by maximum entropy principle and Monte Carlo simulation.
Non-Gaussian probability distribution functions from maximum-entropy-principle considerations
