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Stochastic finite element modelling of elementary random media. / Chenfeng Li

Swansea University Author: Chenfeng Li

Abstract

Following a stochastic approach, this thesis presents a numerical framework for elastostatics of random media. Firstly, after a mathematically rigorous investigation of the popular white noise model in an engineering context, the smooth spatial stochastic dependence between material properties is id...

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Published: 2006
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42770
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last_indexed 2018-08-03T10:11:03Z
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spelling 2018-08-02T16:24:30.4453992 v2 42770 2018-08-02 Stochastic finite element modelling of elementary random media. 964b9fdf7eb6b65ba568903478fcb1e3 NULL Chenfeng Li Chenfeng Li true true 2018-08-02 Following a stochastic approach, this thesis presents a numerical framework for elastostatics of random media. Firstly, after a mathematically rigorous investigation of the popular white noise model in an engineering context, the smooth spatial stochastic dependence between material properties is identified as a fundamental feature of practical random media. Based on the recognition of the probabilistic essence of practical random media and driven by engineering simulation requirements, a comprehensive random medium model, namely elementary random media (ERM), is consequently defined and its macro-scale properties including stationarity, smoothness and principles for material measurements are systematically explored. Moreover, an explicit representation scheme, namely the Fourier-Karhunen-Loeve (F-K-L) representation, is developed for the general elastic tensor of ERM by combining the spectral representation theory of wide-sense stationary stochastic fields and the standard dimensionality reduction technology of principal component analysis. Then, based on the concept of ERM and the F-K-L representation for its random elastic tensor, the stochastic partial differential equations regarding elastostatics of random media are formulated and further discretized, in a similar fashion as for the standard finite element method, to obtain a stochastic system of linear algebraic equations. For the solution of the resulting stochastic linear algebraic system, two different numerical techniques, i.e. the joint diagonalization solution strategy and the directed Monte Carlo simulation strategy, are developed. Original contributions include the theoretical analysis of practical random medium modelling, establishment of the ERM model and its F-K-L representation, and development of the numerical solvers for the stochastic linear algebraic system. In particular, for computational challenges arising from the proposed framework, two novel numerical algorithms are developed: (a) a quadrature algorithm for multidimensional oscillatory functions, which reduces the computational cost of the F-K-L representation by up to several orders of magnitude; and (b) a Jacobi-like joint diagonalization solution method for relatively small mesh structures, which can effectively solve the associated stochastic linear algebraic system with a large number of random variables. E-Thesis Computer engineering. 31 12 2006 2006-12-31 COLLEGE NANME Engineering COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:30.4453992 2018-08-02T16:24:30.4453992 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Chenfeng Li NULL 1 0042770-02082018162520.pdf 10807539.pdf 2018-08-02T16:25:20.5830000 Output 12173208 application/pdf E-Thesis true 2018-08-02T16:25:20.5830000 false
title Stochastic finite element modelling of elementary random media.
spellingShingle Stochastic finite element modelling of elementary random media.
Chenfeng Li
title_short Stochastic finite element modelling of elementary random media.
title_full Stochastic finite element modelling of elementary random media.
title_fullStr Stochastic finite element modelling of elementary random media.
title_full_unstemmed Stochastic finite element modelling of elementary random media.
title_sort Stochastic finite element modelling of elementary random media.
author_id_str_mv 964b9fdf7eb6b65ba568903478fcb1e3
author_id_fullname_str_mv 964b9fdf7eb6b65ba568903478fcb1e3_***_Chenfeng Li
author Chenfeng Li
author2 Chenfeng Li
format E-Thesis
publishDate 2006
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description Following a stochastic approach, this thesis presents a numerical framework for elastostatics of random media. Firstly, after a mathematically rigorous investigation of the popular white noise model in an engineering context, the smooth spatial stochastic dependence between material properties is identified as a fundamental feature of practical random media. Based on the recognition of the probabilistic essence of practical random media and driven by engineering simulation requirements, a comprehensive random medium model, namely elementary random media (ERM), is consequently defined and its macro-scale properties including stationarity, smoothness and principles for material measurements are systematically explored. Moreover, an explicit representation scheme, namely the Fourier-Karhunen-Loeve (F-K-L) representation, is developed for the general elastic tensor of ERM by combining the spectral representation theory of wide-sense stationary stochastic fields and the standard dimensionality reduction technology of principal component analysis. Then, based on the concept of ERM and the F-K-L representation for its random elastic tensor, the stochastic partial differential equations regarding elastostatics of random media are formulated and further discretized, in a similar fashion as for the standard finite element method, to obtain a stochastic system of linear algebraic equations. For the solution of the resulting stochastic linear algebraic system, two different numerical techniques, i.e. the joint diagonalization solution strategy and the directed Monte Carlo simulation strategy, are developed. Original contributions include the theoretical analysis of practical random medium modelling, establishment of the ERM model and its F-K-L representation, and development of the numerical solvers for the stochastic linear algebraic system. In particular, for computational challenges arising from the proposed framework, two novel numerical algorithms are developed: (a) a quadrature algorithm for multidimensional oscillatory functions, which reduces the computational cost of the F-K-L representation by up to several orders of magnitude; and (b) a Jacobi-like joint diagonalization solution method for relatively small mesh structures, which can effectively solve the associated stochastic linear algebraic system with a large number of random variables.
published_date 2006-12-31T03:53:37Z
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score 11.016593

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