Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
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 (Autor:in)
01.01.2006
9 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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