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Galerkin Method for Stochastic Algebraic Equations and Plates on Random Elastic Foundation
Abstract 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 suboptimal 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.
Galerkin Method for Stochastic Algebraic Equations and Plates on Random Elastic Foundation
Abstract 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 suboptimal 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.
Galerkin Method for Stochastic Algebraic Equations and Plates on Random Elastic Foundation
Grigoriu, Mircea (author)
2006-01-01
9 pages
Article/Chapter (Book)
Electronic Resource
English
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