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Finite element methods for stochastic structures and conditional simulation

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Date Issued:
1998
Summary:
This dissertation deals with the non-perturbative finite element methods for stochastic structures and conditional simulation techniques for random fields. Three different non-perturbative finite element schemes have been proposed to compute the first and second moments of displacement responses of stochastic structures. These three methods are based, respectively, on (i) the exact inverse of the global stiffness matrix for simple stochastic structures; (ii) the variational principles for statically-determinate beams; and (iii) the element-level flexibility for general stochastic statically indeterminate structures. The non-perturbative finite element method for stochastic structures possesses several advantages over the conventional perturbation-based finite element method for stochastic structures, including (i) applicability to large values of the coefficient of variation of random parameters; (ii) convergence to exact solutions when the finite element mesh is refined; (iii) requirement of less statistical information than that demanded by the high-order perturbation methods. Conditional simulation of random fields has been an extremely important research field in most recent years due to its application in urban earthquake monitoring systems. This study generalizes the available simulation technique for one-variate Gaussian random fields, conditioned by realizations of the fields, to multi-variate vector random field, conditioned by the realizations of the fields themselves as well as the realizations of the fields derivatives. Furthermore, a conditional simulation for non-Gaussian random fields is also proposed in this study by combining the unconditional simulation technique of non-Gaussian fields and the conditional simulation technique of Gaussian fields. Finally, the dissertation incorporates the simulation technique of random field into the non-perturbation finite element method for stochastic structures, to handle the cases where only one-dimensional probability density function and the correlation function of the random parameters are available, the demanded two-dimensional probability density function is unavailable. Simulation technique is applied to generate the samples of random fields which are used to estimate the correlation between flexibilities over elements. The estimated correlation of flexibility is then used in finite element analysis for stochastic structures. For each proposed approach, numerous examples and numerical results have been implemented.
Title: Finite element methods for stochastic structures and conditional simulation.
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Name(s): Ren, Yongjian.
Florida Atlantic University, Degree grantor
Elishakoff, Isaac, Thesis advisor
College of Engineering and Computer Science
Department of Ocean and Mechanical Engineering
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 1998
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 191 p.
Language(s): English
Summary: This dissertation deals with the non-perturbative finite element methods for stochastic structures and conditional simulation techniques for random fields. Three different non-perturbative finite element schemes have been proposed to compute the first and second moments of displacement responses of stochastic structures. These three methods are based, respectively, on (i) the exact inverse of the global stiffness matrix for simple stochastic structures; (ii) the variational principles for statically-determinate beams; and (iii) the element-level flexibility for general stochastic statically indeterminate structures. The non-perturbative finite element method for stochastic structures possesses several advantages over the conventional perturbation-based finite element method for stochastic structures, including (i) applicability to large values of the coefficient of variation of random parameters; (ii) convergence to exact solutions when the finite element mesh is refined; (iii) requirement of less statistical information than that demanded by the high-order perturbation methods. Conditional simulation of random fields has been an extremely important research field in most recent years due to its application in urban earthquake monitoring systems. This study generalizes the available simulation technique for one-variate Gaussian random fields, conditioned by realizations of the fields, to multi-variate vector random field, conditioned by the realizations of the fields themselves as well as the realizations of the fields derivatives. Furthermore, a conditional simulation for non-Gaussian random fields is also proposed in this study by combining the unconditional simulation technique of non-Gaussian fields and the conditional simulation technique of Gaussian fields. Finally, the dissertation incorporates the simulation technique of random field into the non-perturbation finite element method for stochastic structures, to handle the cases where only one-dimensional probability density function and the correlation function of the random parameters are available, the demanded two-dimensional probability density function is unavailable. Simulation technique is applied to generate the samples of random fields which are used to estimate the correlation between flexibilities over elements. The estimated correlation of flexibility is then used in finite element analysis for stochastic structures. For each proposed approach, numerous examples and numerical results have been implemented.
Identifier: 9780599104976 (isbn), 12580 (digitool), FADT12580 (IID), fau:9466 (fedora)
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): College of Engineering and Computer Science
Thesis (Ph.D.)--Florida Atlantic University, 1998.
Subject(s): Finite element method
Stochastic processes
Random fields--Mathematical models
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fcla/dt/12580
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Owner Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.