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Stochastic finite element modelling of elementary random media. / Chenfeng Li
Swansea University Author: Chenfeng Li
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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...
Published: |
2006
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Institution: | Swansea University |
Degree level: | Doctoral |
Degree name: | Ph.D |
URI: | https://cronfa.swan.ac.uk/Record/cronfa42770 |
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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 |
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Chenfeng Li |
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E-Thesis |
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2006 |
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Swansea University |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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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 |
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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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1763752665152487424 |
score |
11.021648 |