New developments in computational stochastic mechanics, part II: applications
New developments in computational stochastic mechanics, part II: applications
In a companion paper (Nair, P.B., and Keane, A.J., 'New Developments in Computational Stochastic Mechanics, Part I: Theory', AIAA-2000-1827), stochastic reduced basis approximation (SRBA) methods were presented for analysis of systems governed by stochastic partial differential equations (PDEs). The fundamental idea proposed was to use the terms of the Neumann expansion series as stochastic basis vectors along with undetermined coefficients for representing the response process. Solution procedures based on variants of the stochastic Bubnov-Galerkin scheme were developed for determining the coefficients of the reduced basis representation. This paper presents detailed numerical studies for two example problems from the domain of stochastic structural mechanics. The main objective here is to study the numerical characteristics of SRBA methods, and to compare the results with the Neumann expansion scheme. It is demonstrated that the SRBA methods give significantly better results as compared to the Neumann expansion scheme, particularly for large stochastic variations in the random system parameters.
1-10
American Institute of Aeronautics and Astronautics
Nair, P.B.
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Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def
2000
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def
Nair, P.B. and Keane, A.J.
(2000)
New developments in computational stochastic mechanics, part II: applications.
In Proceedings of AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibition.
American Institute of Aeronautics and Astronautics.
.
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Conference or Workshop Item
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Abstract
In a companion paper (Nair, P.B., and Keane, A.J., 'New Developments in Computational Stochastic Mechanics, Part I: Theory', AIAA-2000-1827), stochastic reduced basis approximation (SRBA) methods were presented for analysis of systems governed by stochastic partial differential equations (PDEs). The fundamental idea proposed was to use the terms of the Neumann expansion series as stochastic basis vectors along with undetermined coefficients for representing the response process. Solution procedures based on variants of the stochastic Bubnov-Galerkin scheme were developed for determining the coefficients of the reduced basis representation. This paper presents detailed numerical studies for two example problems from the domain of stochastic structural mechanics. The main objective here is to study the numerical characteristics of SRBA methods, and to compare the results with the Neumann expansion scheme. It is demonstrated that the SRBA methods give significantly better results as compared to the Neumann expansion scheme, particularly for large stochastic variations in the random system parameters.
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nair_00a.pdf
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Published date: 2000
Additional Information:
AIAA-2000-1441
Venue - Dates:
AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Atlanta, USA, 2000-04-03 - 2000-04-06
Identifiers
Local EPrints ID: 23605
URI: http://eprints.soton.ac.uk/id/eprint/23605
PURE UUID: 277d0828-580c-4891-b4fb-297e28b0cf53
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Date deposited: 23 Feb 2007
Last modified: 16 Mar 2024 02:53
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Author:
P.B. Nair
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