GALERKIN METHOD FOR STOCHASTIC ALGEBRAIC EQUATIONS AND PLATES ON RANDOM ELASTIC FOUNDATION

摘要

A new perspective is presented on the Galerkin solution for linear stochastic algebraic equations, that is, linear algebraic equations with random coefficients. It is shown that (1) a stochastic algebraic equation has an optimal Galerkin solution, that is, a Galerkin solution that is best in the mean square sense, and (2) the optimal Galerkin solution is equal to the conditional expectation of the exact solution with respect to a σ-field coarser than the σ-field relative to which this solution is measurable. Galerkin solutions that are not optimal are called sub-optimal. Both optimal and sub-optimal Galerkin solutions are defined and constructed. Optimal and sub-optimal Galerkin solutions are used to calculate statistics of the displacement of a simply supported plate sitting on a random elastic foundation. The accuracy of these Galerkin solutions is assessed by Monte Carlo simulation.