IMPROVED FINITE-ELEMENT METHOD FOR STOCHASTIC PROBLEMS

The conventional finite element method dealing with stochastic problem s is based on series expansion of stochastic quantities with respect t o basic stochastic deviations, by means of either Taylor expansion, pe rturbation technique or Neumann expansion. The first-order approximati on of the mean response, which is utilized to calculate the required p robabilistic characteristics of the response, is just the deterministi c solution obtained by fixing stochastic parameters at their mean valu e. However, such a mean response differs from the exact mean value and its use may cause significant error when the coefficients of variatio n of stochastic parameters are relatively large. In this paper, we pro pose an improved finite element method for stochastic problems. The me thod takes into account the first-order and second-order probabilistic information of stochastic parameters for computing the mean solution. The variance and covariance of the solution are calculated by utilizi ng the improved mean solution instead of 'deterministic' mean solution . The present improved method requires only means, variances and covar iances of stochastic parameters. However, it has been found that the p roposed improved method is much more accurate than the conventional fi rst-order approximate method. Moreover, the present method is more acc urate than the conventional second-order approximation method, which r equires third and fourth-order probabilistic characteristics of stocha stic parameters.