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Chris Nkinthorn, 10-03-2019

Motivation for this project is to use a literature review to study the applications stochastic finite elements and methods to solve such problems: Markov and Monte Carlo models, use of polynomial chaos to study the propagation of variability in the system. Motivation for stochastic finite elements allow for modeling of the inherent variation between expected sample measurements and the true mean, which is immeasurable without knowing the distribution of population. Current applications of these methods include uncertainty quantification in field quantities in both fluid and solid mechanics. Theory to be studied include Karhunen-Loeve and Homogenous Chaos Expansion and their application to random processes. Literature to be studied include a paper which explores application with sparse data. Another paper applies Spectral Stochastic Finite Element Methods (SSFEM) to composite structures. Paper applies SSFEM to experimental data. Additional literature will be added to both works cited and reference as the project progresses. A finalized list will be presented with the midterm project progress report.

Works Referenced

:Dridger, A. & Caylak, Ismail & Mahnken, R. & Penner, Eduard. (2019). A possibilistic finite element method for sparse data. Safety and Reliability. 38. 1-25. 10.1080/09617353.2018.1552477.

:M.F. Ngah, A. Young. Application of the spectral stochastic finite element method for performance prediction of composite structures. Composite Structures, Volume 78, Issue 3, 2007

:C. Desceliers, et. al. Maximum likelihood estimation of stochastic chaos representations from experimental data. International Journal for Numerical Methods in Engineering, Wiley, 2006, 66 (6), pp.978-1001. ff10.1002/nme.1576ff. ffhal-00686154f