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% \usetheme{Singapore} % ima sadrzaj i tackice gore
% \usetheme{Antibes} % ima sadrzaj gore i kao graf ...
% \usetheme{Berkeley} % ima sadrzaj desno
% \usetheme{Berlin} % ima sadrzaj gore i tackice
% \usetheme{Goettingen} % ima sadrzxaj za desne strane
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\title[{\cyrosam
ElastoPlastichnost i verovatno\cj{}e}]
{{\cyrsesnaest
Modelovanje elastoplastichnih sistema primenom teorije verovatno\cj{}a}}
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
%  Give the names in the same order as the appear in the paper.
%  Use the \inst{?} command only if the authors have different
% affiliation.
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%\author[Boris Jeremi{\'c}, CompGeoMech \includegraphics[width=8cm]{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}] % (optional, use only with lots of authors)
\author[{\cyrosam Jeremi\cj{}}] % (optional, use only with lots of authors)
{\cyrsesnaest Boris~Jeremi\cj{}}
%  Give the names in the same order as the appear in the paper.
%  Use the \inst{?} command only if the authors have different
% affiliation.
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA, USA\\
% and\\
% Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Lawrence Berkeley National Laboratory, Berkeley, CA, USA }
%  Use the \inst command only if there are several affi`liations.
%  Keep it simple, no one is interested in your street address.
\date[] % (optional, should be abbreviation of conference name)
{\cyrdeset Institut za vodoprivredu "Jaroslav Cherni" \\ Jun 2017}
\subject{}
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{
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% \frametitle{\cyrsesnaest Pregled}
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}
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\begin{frame}
\frametitle{\cyrdvanaest Sadrzhaj}
\begin{scriptsize}
\tableofcontents
% You might wish to add the option [pausesections]
\end{scriptsize}
\end{frame}
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% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:
%  Exactly two or three sections (other than the summary).
%  At *most* three subsections per section.
%  Talk about 30s to 2min per frame. So there should be between about
% 15 and 30 frames, all told.
%  A conference audience is likely to know very little of what you
% are going to talk about. So *simplify*!
%  In a 20min talk, getting the main ideas across is hard
% enough. Leave out details, even if it means being less precise than
% you think necessary.
%  If you omit details that are vital to the proof/implementation,
% just say so once. Everybody will be happy with that.
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\section{\cyrdeset Uvod}
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\subsection{\cyrdevet Motivacija}
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\begin{frame}
\frametitle{{\cyrsesnaest Motivacija}}
\begin{itemize}
%\vspace*{0.3cm}
\item {\cyrdvanaest Poboljshanje modelovanja i simulacija za sisteme tla i konstrukcije}
\vspace*{1mm}
\item {\cyrdvanaest Razvoj ekspertnog sistema za numerichke analize}
\vspace*{1mm}
\item {\cyrdvanaest Upotreba preciznih modela za analize statike i dinamike
sistema tla i konstrukcije}
%\vspace*{1mm}
% \item {\cyrdvanaest Pra\cj{}enje protoka mehanichke energije kroz sistem tla
% i konstrukcije sa ciljem}
% \begin{itemize}
% \item {\cyrdvanaest pove\cj{}anja sigurnosti}
% \item {\cyrdvanaest smanjenja troshkova objekta}
% \end{itemize}
\vspace*{1mm}
\item {\cyrdvanaest Cilj je razvoj metodologije za
numerichka predvidjanja i informisanje korisnika, struchnjaka,
a ne rezultati koji prate neku zadatu liniju, na silu}
%\vspace*{1mm}
% \item Directing, in space and time, seismic energy flow in the
% soil structure system
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Seismic Hazard, World}
\vspace*{3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=11truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/worldseismap.png}
%
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Seismic Hazard, Europe}
\vspace*{2mm}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Seismic_Hazard_Europe.jpg}
%
\end{center}
\end{figure}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Seismic Hazard, USA}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/USA_Seismic_hazard_Map.jpg}
% %
% \end{center}
% \end{figure}
%
% \end{frame}
%
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\begin{frame}
\frametitle{Seismic Hazard, DOE Facilities}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/DOE_Sites_and_Seismic_Hazard.jpg}
%
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{{\cyrsesnaest Pretpostavka}}
\begin{itemize}
%OVDE
%\vspace*{0.5cm}
\item {\cyrdvanaest Interakcija dinamichkih karakteristika zemljotresa,
tla i konstrukcije kontrolishe nivo oshte\cj{}enja konstrukcije}
\vspace*{3mm}
\item {\cyrdvanaest Mesto i vreme disipacije zemljotresne energije
odredjuje lokaciju i
nivo oshte\cj{}enja konstrukcije}
\vspace*{3mm}
\item {\cyrdvanaest Kontrolisanjem protok
zemljotresne energije kroz tlo i konstrukciju,
mozhemo da poboljshamo}
\begin{itemize}
\vspace*{1mm}
\item {\cyrdvanaest Sigurnost}
\vspace*{1mm}
\item {\cyrdvanaest Ekonomichnost}
\end{itemize}
\end{itemize}
\end{frame}
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%
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\begin{frame}
\frametitle{\cyrsesnaest Tachnost Modelovanja i Simulacija}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}
\begin{itemize}
\item {\cyrdvanaest Verifikacija: dokaz da je model tachno
reshen, matematichki problem}
\vspace*{1mm}
\item {\cyrdvanaest Validacije: dokaz da je reshen pravi model,
mehanichki problem}
\vspace*{1mm}
\item {\cyrdvanaest Numerichko analiza:
korish\cj{}enje numerichkog
modela za predvicjanje stanja sistema za optere\cj{}enja koja nisu
korish\cj{}ena pri testiranju (validaciji)}
\vspace*{1mm}
\item {\cyrdvanaest Predvidjanje/analiza uz teoriju verovatno\cj{}a:}
\begin{itemize}
%OVDE vidi opet kako da pravilno kazes uncertainty, pitaj Beku
\item {\cyrdvanaest Nesigurnost modela}
\item {\cyrdvanaest Nesigurnost parametara}
\end{itemize}
%\vspace*{0.2cm}
% \item Goal: predictive capabilities
% with {\bf low Kolmogorov Complexity}
% %% % \vspace*{0.2cm}
% % \item {\bf The Finite Element
% % Interpreter \FEI{}} might be one such
% % predictive tool (application program)
\end{itemize}
\end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Role of Verification and Validation}
%
%
% \begin{figure}[!h]
% \begin{center}
% \hspace*{2cm}
% {\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/ASME_V_and_V_symposium/presentetation/RoleVV_NEW_knowledge.pdf}}
% {\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
% \hspace*{2cm}
% \end{center}
% \end{figure}
%
% {Oberkampf et al. \hspace*{4cm} Oden et al.}
% %
% %\item Models available (some now, some later)
% %\vspace*{2.0cm}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
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\subsection{Modeling and Parametric Uncertainty}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Modeling Uncertainty: Simplified Models}
\begin{itemize}
\item Simplified modeling: Features (important ?) are neglected (6D
ground motions, inelasticity)
%\vspace*{1mm}
\item Modeling Uncertainty: unrealistic and unnecessary modeling
simplifications
%\vspace*{1mm}
\item Modeling simplifications: justifiable iff higher level
sophistication model shows are features not important
\end{itemize}
\begin{center}
{\includegraphics[width=45mm]{movie_ff_3d_mp4_icon.jpeg}}
%
%\hspace*{10mm}
%
{\includegraphics[width=45mm]{movie_ff_1d_mp4_icon.jpeg}}
\end{center}
\end{frame}
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\begin{frame}
\frametitle{Parametric Uncertainty: Material and Loads}
\begin{itemize}
\item Significant uncertainty in material and loads
%\vspace*{1mm}
\item Need to propagate uncertainty through simulation, to give
regulators and engineers information for design, licensing...
\end{itemize}
%
%\vspace{1cm}
%\hspace{0.5cm}
%Example: Elastic Stiffness
%\vspace*{3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
% \hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{0.8cm}
%\hspace*{3.3cm}
\begin{flushleft}
{\tiny
Transformation of SPT $N$value:
1D Young's modulus, $E$
(cf. Phoon and Kulhawy (1999B))
~}
\end{flushleft}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Strength}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{7mm}
% \includegraphics[width=6.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_RawData_and_MeanTrendMod.pdf}
% \hspace*{7mm}
% % \hfill
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_Histogram_PearsonIVFineTunedMod.pdf}
% %
% \end{center}
% \end{figure}
%
% % \vspace*{1.8cm}
% % %\hspace*{3.3cm}
% % \begin{flushright}
% % {\tiny
% % Transformation of SPT $N$value: \\
% % 1D Young's modulus, $E$ \\
% % (cf. Phoon and Kulhawy (1999B))\\
% % ~}
% % \end{flushright}
% % %
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Properties}
%
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% % %
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
% \\
% %\vspace*{2mm}
% \hspace*{2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
% %\vspace*{45mm}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
% \\
% %\vspace*{8mm}
% \hspace*{2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
% \end{center}
% \end{figure}
%
% \end{frame}
%
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Uncertainty in Modeling Ground Motions}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Complexity of and Uncertainty in Ground Motions}
%
% \begin{itemize}
% %\vspace*{0.3cm}
% \item 6D (3 translations, 3 rotations)
%
% \vspace*{0.3cm}
% \item Vertical motions usually neglected
%
% \vspace*{0.3cm}
% \item Rotational components usually not measured and neglected
%
% \vspace*{0.3cm}
% \item Lack of models for such 6D motions (from measured data))
%
% \vspace*{0.3cm}
% \item Sources of uncertainties in ground motions (Source, Path (rock), soil (rock))
% \end{itemize}
%
%
%
% \end{frame}
%
%
%
%
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Uncertainty in Modeling Material}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Material Behavior Inherently Uncertain}
%
%
% %\begin{itemize}
%
% %\vspace*{0.5cm}
% %\item
% %Material behavior is inherently uncertain (concrete, metals, soil, rock,
% %bone, foam, powder etc.)
%
% \begin{itemize}
%
% \vspace*{0.5cm}
% \item Spatial \\
% variability
%
% \vspace*{0.5cm}
% \item Pointwise \\
% uncertainty, \\
% testing \\
% error, \\
% transformation \\
% error
%
% \end{itemize}
%
% % \vspace*{0.5cm}
% % \item Failure mechanisms related to spatial variability (strain localization and
% % bifurcation of response)
% %
% % \vspace*{0.5cm}
% % \item Inverse problems
% %
% % \begin{itemize}
% %
% % \item New material design, ({\it pointwise})
% %
% % \item Solid and/or structure design (or retrofits), ({\it spatial})
% %
% % \end{itemize}
%
% %\end{itemize}
%
% \vspace*{5cm}
% \begin{figure}[!hbpt]
% %\nonumber
% %\begin{center}
% \begin{flushright}
% %\includegraphics[height=5.0cm]{/home/jeremic/tex/works/Conferences/2006/KragujevacSEECCM06/Presentation/MGMuzorak01.jpg}
% \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/FrictionAngleProfile.jpg}
% \\
% \mbox{(Mayne et al. (2000) }
% \end{flushright}
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% \frametitle{Soil Uncertainties and Quantification}
%
% \begin{itemize}
% %
% %\vspace*{0.5cm}
% \item Natural variability of soil deposit (Fenton 1999)
%
% \begin{itemize}
%
% \item Function of soil formation process
%
% \end{itemize}
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% %
% \vspace*{0.2cm}
% \item Testing error (Stokoe et al. 2004)
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% \begin{itemize}
%
% \item Imperfection of instruments
%
% \item Error in methods to register quantities
%
% \end{itemize}
%
% %
% \vspace*{0.2cm}
% \item Transformation error (Phoon and Kulhawy 1999)
%
% \begin{itemize}
%
% \item Correlation by empirical data fitting (e.g. CPT data $\rightarrow$ friction angle etc.)
%
% \end{itemize}
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% \end{itemize}
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% \frametitle{SPT Based Determination of Shear Strength}
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% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_RawData_and_MeanTrendMod.pdf}
% \hfill
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_Histogram_PearsonIVFineTunedMod.pdf}
% %
% \end{center}
% \end{figure}
%
% \vspace*{0.3cm}
% Transformation of SPT $N$value $\rightarrow$ undrained shear
% strength, $s_u$ (cf. Phoon and Kulhawy (1999B)
%
% Histogram of the residual
% (w.r.t the deterministic transformation
% equation) undrained strength,
% along with fitted probability density function
% (Pearson IV)
% \end{frame}
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% \begin{frame}
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%
% \frametitle{SPT Based Determination of Young's Modulus}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
% \hfill
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
% %
% \end{center}
% \end{figure}
%
% \vspace*{0.3cm}
% Transformation of SPT $N$value $\rightarrow$ 1D Young's modulus, $E$ (cf. Phoon and Kulhawy (1999B))
%
% Histogram of the residual (w.r.t the deterministic transformation equation) Young's modulus, along with fitted probability density function
%
% \end{frame}
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% \frametitle{Errors in Scientific Software}
%
%
% \begin{itemize}
%
% % \vspace*{0.2truecm}
% \item Les Hatton, Kingston University, the T Experiments
%
% \vspace*{0.1truecm}
% \item "Extensive tests showed that many software codes widely used in science
% and engineering are not as accurate as we would like to think."
%
% \vspace*{0.1truecm}
% \item "Better software engineering practices would help solve this problem,"
%
% \vspace*{0.1truecm}
% \item "Realizing that the problem exists is an important first step."
%
%
% \vspace*{0.1truecm}
% \item Large experiment over 4 years measuring faults (T1) and failures (T2)
% of scientific and engineering codes
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% \frametitle{The T2 Experiments}
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%
% \begin{itemize}
%
% \item Specific application area: seismic data processing, geophysics, inverse analysis
%
% \vspace*{0.2truecm}
% \item Echo sounding of underground and reconstructing "images" of
% subsurface geological structure
%
% \vspace*{0.2truecm}
% \item Nine mature packages, using {same algorithms (same original code)}, on a
% {same data set}!
%
% \vspace*{0.2truecm}
% \item 14 primary calibration points for results check
%
% \vspace*{0.2truecm}
% \item Results "fascinating and disturbing"
%
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% \frametitle{T2: Disagreement at Calibration Points}
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% \begin{center}
% \hspace*{1.5cm}
% %\vspace*{2.5cm}
% {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_01.jpg}}
% \hspace*{1.5cm}
% %\vspace*{5.0cm}
% \end{center}
% \end{figure}
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%
% % \begin{itemize}
% %
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% % \end{itemize}
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% % \begin{frame}
% % \frametitle{T2: Stage 14, Interpretation of Data }
% %
% %
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% %
% % \begin{figure}[!h]
% % \begin{center}
% % %\vspace*{2.5cm}
% % \vspace*{1.0cm}
% % \hspace*{1.5cm}
% % {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_02.jpg}}
% % \hspace*{1.5cm}
% % \vspace*{1.5cm}
% % %\vspace*{5.0cm}
% % \end{center}
% % \end{figure}
% %
% % %
% % % % \begin{itemize}
% % % %
% % % %
% % %
% % % \end{itemize}
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% \frametitle{Realistic ESSI Modeling (Uncertainties)}
%
%
% \begin{itemize}
%
%
% \item Seismic Motions: 6D, inclined, body and surface waves
% (translations, rotations)
% %; Incoherency
%
% %\vspace*{3mm}
% \vspace*{1mm}
% \item Inelastic material: soil (dry, saturated), rock, concrete, steel
%
% \vspace*{1mm}
% \item Inelastic contact: foundationsoil, dry, saturated, slipgap
%
% \vspace*{1mm}
% \item Nonlinear buoyant forces
%
% \vspace*{1mm}
% \item Base Isolators, Dissipators
%
% \vspace*{1mm}
% \item Uncertain loading and material
%
% \vspace*{1mm}
% \item Verification and Validation $\Rightarrow$ Predictions
%
%
% \end{itemize}
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% \begin{frame}
% \frametitle{Development Team}
%
%
% \vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/YuanFeng01.jpg}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/SumeetKumarSinha01.jpg}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/FatmaBehbehani01.jpg}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/MaximeLacour.jpg}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/HanYang01.jpg}
% \end{center}
% \end{figure}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=2.2cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/JoseAbell.jpg}
% \includegraphics[width=2.6cm]{/home/jeremic/tex/works/Conferences/2016/DOE_panel_review_UNR_01June2016/present/Frank02.jpg}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2016/DOE_panel_review_UNR_01June2016/present/Boris01.jpg}
% \end{center}
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%
% \begin{frame}
% \frametitle{Recent Work}
%
% \begin{itemize}
%
% \item Wave propagation in local geology
%
% \item Stiff (concr. to concr.) and soft
% (concr. to soil) contacts
%
% \item SW4 for development of seismic wave fields,
%
% \item Coupling of SW4 with the Real ESSI (using DRM)
%
% \item Nonlinear/inelastic bending beam element
%
% \item Detailed modeling of the UNR cylinder,
% \begin{itemize}
%
% \item Nonlinear/inelastic soil, (variation of soil stiffness)
%
% \item Contact zone (frictional, gaping) (variation of frictional
% resistance (complementary shear?)
%
% \item Detailed model of a wall (beams, elastomers)
%
% \item Static pushovers (wall, full model...)
%
% \item Dynamic excitations, bottom shakes
%
% \item Dynamic excitations from within (dynamic sources)
%
% \end{itemize}
%
% \item Educational developments!!!
%
% \end{itemize}
% \end{frame}
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\section{\cyrdeset Program}
%
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\subsection{Real ESSI Simulator System}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator System}
\begin{itemize}
\item {\bf The Real ESSIProgram} is a 3D, nonlinear, time domain,
parallel finite element program specifically developed for
HiFi modeling and simulation of Earthquake Soil/Rock Structure
Interaction problems for NPPs (infrastructure objects) on ESSIComputers. \
%The NRC ESSI Program is based on
%a number of public domain numerical libraries developed at UCD as well as those
%available on the web, that are compiled and linked together to form the
%executable program (NRCESSIProgram). Significant effort is devoted to development
%of verification and validation procedures, as well as on development of
%extensive documentation. NRCESSIProgram is in public domain and is licensed
%through the Lesser GPL.
%\vspace*{0.3cm}
\vspace*{0.1cm}
\item {\bf The Real ESSIComputer} is a distributed memory
parallel computer, a cluster of clusters with multiple performance
processors and multiple performance networks.
%Compute nodes are Shared Memory Parallel
%(SMP) computers, that are connected, using high speed network(s), into a
%Distributed Memory Parallel (DMP) computer.
%\vspace*{0.3cm}
\vspace*{0.1cm}
\item {\bf The Real ESSINotes} represent a hypertext
documentation system
(Theory and Formulation, Software and Hardware, Verification and Validation, and
Case Studies and Practical Examples)
detailing modeling and simulation of ESSI
problems.
%
%the
%NRCESSIProgram code API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRCESSINotes, developed by Boris Jeremic and collaborators, are in public
%domain
%%and are licensed under a Creative Commons AttributionShareAlike 3.0 Unported
%%License.
%
%\vspace*{0.3cm}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator Modeling and Simulation Process}
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=3.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stageincrementsiterations.pdf}
%\caption{\label{loading_stagesincrements_iterations} }
\end{center}
\vspace*{0.5cm}
\end{figure}
%
\end{frame}
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\subsection{Real ESSI Simulator Components}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator: DSL}[fragile]
\begin{itemize}
\item Domain Specific Language (DSL), Yacc \& Lex
\vspace*{3mm}
\item English like modeling and simulation language
\vspace*{3mm}
\item Parser and compiler, can define functions, models, etc.
\vspace*{3mm}
\item Can extend models and methods
\vspace*{3mm}
\item Requires units!
\end{itemize}
%
%\begin{verbatim}
%add node \# 2 at (0*m, 0*m, 1*m) with 6 dofs;
%\end{verbatim}
%
%\begin{lstlisting}
%add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
%add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
%\end{lstlisting}
%
%\begin{lstlisting}
%add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
%\end{lstlisting}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
% \frametitle{Real ESSI DSL Example}
%
%
% \vspace*{2mm}
% \begin{lstlisting}
% model name "UNR Test Setup";
% new loading stage "First, static";
% add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
% add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
% add element # 1 type beam_elastic with
% nodes (1, 2) cross_section=1.0*m^2
% elastic_modulus=1.0e5*KN/m^2
% shear_modulus=2.0e4*KN/m^2
% torsion_Jx=2*0.083*m^4
% bending_Iy=0.083*m^4 bending_Iz=0.083*m^4
% mass_density=2500.0*kg/m^3
% xz_plane_vector = (0, 1, 0)
% joint_1_offset = (0.0*m, 0.0*m, 0.0*m)
% joint_2_offset = (0.0*m, 0.0*m, 0.0*m);
% \end{lstlisting}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
% \frametitle{Real ESSI DSL Example}
%
%
% \vspace*{2mm}
% \begin{lstlisting}
% fix node No 1 dofs all;
% add load # 1 to node # 2 type
% linear Fx=9*kN;
% define load factor increment 0.01;
% define solver UMFPack;
% define convergence test
% Norm_Displacement_Increment
% tolerance = 1e5
% maximum_iterations = 20
% verbose_level = 4;
% define algorithm Newton;
% simulate 100 steps using static algorithm;
%
% dovidjenja;
% \end{lstlisting}
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
% \frametitle{Real ESSI DSL Example}
%
%
% \begin{lstlisting}
% add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
% add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
% \end{lstlisting}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
% \frametitle{Beam Example, Model}
%
%
%
% \begin{figure}[!h]
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Cantilever_Beam_02.pdf}
% %\caption{8 node brick element}
% %\label{fig:8node_command}
% \end{center}
% \end{figure}
%
%
% %}
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
% \frametitle{Real ESSI DSL Example}
%
%
% \begin{lstlisting}
% model name "UNR Test Setup";
% new loading stage "First, static";
% // Nodal Coordinates
% add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
% add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
% add element # 1 type beam_elastic with
% nodes (1, 2) cross_section=1.0*m^2
% elastic_modulus=1.0e5*KN/m^2
% shear_modulus=2.0e4*KN/m^2
% torsion_Jx=2*0.083*m^4
% bending_Iy=0.083*m^4 bending_Iz=0.083*m^4
% mass_density=2500.0*kg/m^3
% xz_plane_vector = (0, 1, 0)
% joint_1_offset = (0.0*m, 0.0*m, 0.0*m)
% joint_2_offset = (0.0*m, 0.0*m, 0.0*m);
% \end{lstlisting}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
% \frametitle{Real ESSI DSL Example}
%
%
% \begin{lstlisting}
% fix node No 1 dofs all;
% add load # 1 to node # 2 type
% linear Fx=9*kN;
% define load factor increment 0.01;
%
% define solver UMFPack;
% define convergence test
% Norm_Displacement_Increment
% tolerance = 1e5
% maximum_iterations = 20
% verbose_level = 4;
% define algorithm Newton;
% simulate 100 steps using static algorithm;
%
% bye;
% \end{lstlisting}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
%
%
%
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% \subsection{Real ESSI Program}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator Program: Finite Elements}
%\vspace*{3mm}
\begin{itemize}
\item Dry/single phase solids (8, 20, 27, 827 node bricks),
%\vspace*{1mm}
\item Saturated/two phase solids (8 and 27 node bricks, liquefaction modeling),
%\vspace*{1mm}
\item Truss, Beams, linear and nonlinear
%\vspace*{1mm}
\item Nonlinear concrete shell and linear shell (ANDES)
% with 6DOF per node,
%\vspace*{1mm}
\item Contacts (dry and/or saturated soil/rock  concrete, gap
openingclosing, frictional slip),
%\vspace*{1mm}
\item Base isolators (elastomeric, frictional pendulum)
%\vspace*{1mm}
\item Stochastic ElasticPlastic FEM (1D and 3D solid)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator Program: Material Models}
%\vspace*{2mm}
\begin{itemize}
\item Elastic (solids): Linear, nonlinear, isotropic and anisotropic
\vspace*{2mm}
\item ElasticPlastic (solids): von Mises,
Drucker Prager,
Rounded MohrCoulomb,
Leon Parabolic,
CamClay,
SaniSand,
SaniClay,
Pisan{\` o}.
All elasticplastic models can be used as
perfectly plastic, isotropic hardening/softening
and kinematic hardening models.
\vspace*{2mm}
\item ElasticPlastic (structures, 1D fibers): concrete and steel
\vspace*{2mm}
\item Probabilistic ElastoPlasticity
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator Program: Seismic Input}
Analytic input of seismic motions using Domain Reduction Method (Bielak et al.)
\begin{itemize}
\vspace*{2mm}
\item Body (P, S) seismic waves
\vspace*{2mm}
\item Surface (Rayleigh, Love, etc.) seismic waves,
\vspace*{2mm}
\item Analytic radiation damping.
\end{itemize}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
% %\vspace*{2mm}
%
% \begin{equation}
% \boldsymbol{M \ddot{x}+C \dot{x}+Kx}=\boldsymbol{f}
% \end{equation}
%
% Forward propagation of uncertainty for uncertain inelastic/nonlinear material
% (LHS, $\boldsymbol{M, C, K}$) and uncertain loads (RHS, $\boldsymbol{f}$)
%
% \begin{itemize}
% %\vspace*{2.5mm}
% \item Constitutive: EulerLagrange form of FokkerPlanck (forward
% Kolmogorov) equation for probabilistic elastoplasticity (PEP) (meshless
% finite element method for solution at each Gauss point)
%
% \vspace*{1mm}
% \item Spatial: stochastic elastic plastic finite element method (SEPFEM)
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
% %\vspace*{2mm}
%
%
% \begin{itemize}
%
% \item Uncertainties in {\bf material} and {\bf load}
% are analytically taken into account
%
% \vspace*{1mm}
% \item Resulting displacements, stress and strain are obtained as very
% accurate (second order accurate for stress)
% Probability Density Functions (PDFs)
%
% \vspace*{1mm}
% \item PEP and SEPFEM are not based on Monte Carlo method!
%
% \vspace*{1mm}
% \item PEP and SEPFEM expand uncertain input variables and uncertain
% degrees of freedom (unknowns) into spectral probabilistic spaces
% (KarhunenLoeve, Polynomial Chaos)
%
% \vspace*{1mm}
% \item Solve for PDFs of resulting displacement, stress and strain in a
% single run
%
% \end{itemize}
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
% %\vspace*{2mm}
%
% Backward propagation of uncertainty (future work):
%
% \begin{itemize}
% %\vspace*{2.5mm}
% \vspace*{3mm}
% \item Backward Kolmogorov problem: for given/required
% final risk,
% prescribe uncertainties in input material parameters and loads
%
% \vspace*{3mm}
% \item Constitutive level backward Kolmogorov to use
% FeynmanKac analytic
% solution ('48, '49)
%
%
% \vspace*{3mm}
% \item Spatial level backward Kolmogorov to use a
% variant of Monte Carlo
% method
%
% \end{itemize}
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator Program: V\&V}
\begin{itemize}
%\vspace*{2mm}
\item Verification: mathematics issue,
\begin{itemize}
\vspace*{1mm}
\item Each element, model, algorithm and procedure has been extensively
verified (math issue),
\end{itemize}
\vspace*{4mm}
\item Validation: physics issue,
\begin{itemize}
\vspace*{1mm}
\item Limited, current DOE project will provide a wealth of data for soil, SSI, \&c.
\end{itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Simulator Status}
%
% \begin{scriptsize}
%
% \begin{itemize}
%
% \item[] Real ESSI Simulator. '05 
%
% \item[] C++ standard (current !)
%
% \item[] Input: Domain Specific Language (DSL), Yacc and Lex,
%
% \item[] Model development: gmsh, gmESSI, Python,
%
% \item[] Output: HDF5 (VisIt, ParaView, Matlab, Python...)
%
% %\item[] Vis: Visit, Paraview, Matlab ...
%
% \item[] E: Solids (bricks 8n, 20n, 820n, 27n 827n)
%
% \item[] E: Coupled solids, upU and up,
%
% \item[] E: Structural (Truss, beams B12, B9, ANDES Shell, Nonlinear Beam,
% Shell
%
% \item[] E: Contact, dry and saturated
%
%
% \item[] Material: template/template elastoplasticity (small and large def.),
%
% \item[] Seismic: DRM for seismic input
%
% \item[] Probabilistic ElastoPlasticity and Stochastic ElasticPlastic FEM
%
% \item[] HPC: Template Metaprograms and Expression Templates
%
% \item[] HPC: Parallel, Plastic Domain Decomposition (PDD) (dyn comp load bal),
%
% \item[] HPC: Adaptive PDD (multiple networks/connectivity)
%
%
% \item[] Portable: local clusters, SDSC, TACC, NERSC (Edison)
%
% \end{itemize}
% \end{scriptsize}
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Modelling and Simulation Process}
%
% \begin{itemize}
%
% %\vspace*{4mm}
% \item Mesh Development: gmsh, gmESSI
% % FeConv (Vlaski)
%
% %\vspace*{2mm}
% % \item Model Development: sublime text editor
%
% \vspace*{2mm}
% \item Model Simulation:
% \begin{itemize}
% \item Domain Specific Language (DSL) for input
% \item Real ESSI
% \item Output everything (HDF5), Great (!) and a problem (!)
% \end{itemize}
%
% \vspace*{2mm}
% \item Result visualization: VisIt, visitESSI plugin (all
% displacements, stress, strain, really large output!), ParaView
%
% \end{itemize}
% %
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Real ESSI Program Features}
%
%
%
% \begin{itemize}
%
%
% \item Finite Elements: solids (dry/single, coupled); truss; beams;
% shell; wall; plate; contact; base isolator/dissipator
%
% \vspace*{1mm}
% \item Material Models: Lin., nonlin, iso. and aniso.
% elastic; ElasticPlastic (vMises, DrPr, RMC, LeonP, CClay, SSand, SClay, P);
% Damping, Rayleigh and Caughey
%
% \vspace*{1mm}
% \item Seismic input: the Domain Reduction Method (DRM, Bielak et al.,
% Analytic input of seismic motions)
%
% \vspace*{1mm}
% \item High Performance Computing: Parallel (Plastic Domain Decomposition
% Method), Template Metaprograms
%
% \vspace*{1mm}
% \item Probabilistic Modeling: (analytic) PEP and SEPFEM
%
%
% \end{itemize}
%
% \end{frame}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{\cyrdeset Analize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Examples}
\begin{itemize}
\item Earth and Concrete Dam: level of sophistication and the influence of
human factor (expert opinion)
% \vspace*{3mm}
% \item Concrete Bridge: matching of earthquake, soil and structure dynamic
% characteristics
\vspace*{4mm}
\item Nuclear Power Plant: 3D (6D) vs 1D seismic motions
\vspace*{4mm}
\item Stochastic Elastic Plastic Finite Element Method: risk of
undesirable performance
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{{\cyrdevet Nasuta Brana} }
\subsection{{\cyrdevet Brana} }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dam, Satellite Photo}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView01.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dam, 3D Slope, Satellite Photo}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView02.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{3D Slope}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SatelliteView_with_slope01.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{3D Slope, Ground Photo}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=9.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/img0188.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dam, Construction Photo}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_Q261_621_Embankment_Sep_30_48.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{3D Dam  Slope Stability}
\begin{itemize}
\item 3D earth slope part of a concrete, earth dam
% \vspace*{3mm}
\item Movements recorded during lowering of reservoir (and significant rain!)
% \vspace*{3mm}
\item 3D slope unstable (?), no one could tell, all commercial software
does 2D slope stability
% \vspace*{3mm}
\item 2D vs 3D slope stability
% \vspace*{3mm}
\item Shear strength (?) as the only material parameter
\item (")Expert(") increased value of (a single) measured shear strength
\item Load cases: lowering and raising reservoir, slow and fast
\item Dam build using untreated alluvium
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dam, Section}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_PerpendicularSection.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dam, Model}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final02.jpg}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg}
//
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final05.jpg}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final_Top.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dam Slope, Failure Modes}
% \vspace*{5mm}
\begin{itemize}
\item 3D failure pattern
\item 3D has lower FS than 2D (!)
\item Original $S_u$: FS barely enough
\item With "increased" $S_u$, FS a bit higher
\item Seismic: immediate slope failure
\end{itemize}
\vspace*{40mm}
\begin{figure}[!htbp]
\begin{flushright}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/UndrainedSu440VectorPlan_snapshot.jpg}
\end{flushright}
\end{figure}
\vspace*{10mm}
%
\begin{figure}[!htbp]
\begin{center}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_3D_AbsVal_L680_E680_Phi18_FS178.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_3D_Vector_L680_E680_Phi18_FS178.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_drained_case_40_FS_1_89_displacement_vectors_factor_42_39.jpg}
% \\
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_L680_E680_Phi17_FS189.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_undrained_case_41_FS_1_43__displacement_vectors_factor_1_80.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su1200_FS167.jpg}
% \\
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su800_Alluvium_Su1500_FS250.jpg}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su900_Alluvium_Su1000_FS222.jpg}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E720_Su1300_FS154.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{{\cyrdevet Nuklearna Elektrana}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Nuclear Power Plants, Modelling Issues}
\begin{itemize}
\item Nuclear Power Plants (NPPs), early use of SSI analysis (SASSI, CLASSI, \&c.)
%\vspace*{2mm}
\item State of practice for ESSI analysis of NPPs:
\begin{itemize}
\item Linear elastic material
\item 1D seismic motions
\item Incoherent seismic motions
\end{itemize}
%\vspace*{1mm}
\item Current state of art for ESSI analysis of NPPs:
\begin{itemize}
\item Nonlinear soil, rock, contact, structure
\item 3D (6D) seismic motions
\end{itemize}
%\vspace*{1mm}
\item Seismic motions issue/problem
%
%\vspace*{1mm}
% \item
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Example Earthquake: M 6.6, Norcia, Italy, 30Oct2016}
%
%
% %\vspace*{10mm}
% \begin{figure}[!hpbt]
% %\hspace*{30mm}
% \begin{center}
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Norcia_30Oct2016_ACC_3D.jpg}
% \hspace*{10mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Norcia_30Oct2016_ACC_2D_PGA.jpg}
% \\
% \vspace*{3mm}
% %
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Norcia_30Oct2016_DISP_3D.jpg}
% \hspace*{10mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Norcia_30Oct2016_DISP_2D_PGD.jpg}
% \end{center}
% \end{figure}
%
% \begin{flushright}
% \vspace*{10mm}
% \hspace*{50mm}
% \tiny{StrongMotions.com}
% \end{flushright}
% %
% %
% % \begin{itemize}
% % %\vspace*{0.3cm}
% % \item
% %
% % \vspace*{1mm}
% % \item
% %
% % \end{itemize}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{1D, 2D, 3D Earthquakes?}
\vspace*{4mm}
\begin{figure}[!hpbt]
\begin{center}
\hspace*{8mm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/consulting/2016/IAEA/Report/Chapter_4_Free_Field_Ground_Motions/Lotung_LSST07_FA25.jpeg}
\hspace*{3mm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/consulting/2016/IAEA/Report/Chapter_4_Free_Field_Ground_Motions/Lotung_LSST12_FA25.jpeg}
\end{center}
\end{figure}
%
\vspace*{4mm}
\begin{itemize}
\item SMART1 array, Lotung, Taiwan,
\item LSST07: almost 2D (the only one!)
\item LSST12: full 3D
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Modeling and Simulation of Nuclear Power Plants}
%
%
% \begin{itemize}
%
%
% \item Nuclear Power Plants (NPPs) design based on a number of simplified assumptions!
%
% \vspace*{1mm}
% \item Linear elastic material behavior
%
% \vspace*{1mm}
% \item Seismic Motions: $1$D or $3 \times 1$D, or real 3D (6D)
%
%
% \vspace*{1mm}
% \item Savings in construction cost possible with more accurate modeling of
% NPPs
%
%
% \vspace*{1mm}
% \item Improvements in safety of NPPs also possible, even with higher seismic
% motions, as inelastic effects "eat up" (dissipate) seismic energy
%
%
% \end{itemize}
%
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{3D (6D) or 1D Seismic Motions for NPPs}
\begin{itemize}
\item Assume that a full 6D (3D) motions at the surface are only recorded in one
horizontal direction
\item From such recorded motions one can develop a vertically propagating shear
wave in 1D
\item Apply such vertically propagating shear wave to the same soilstructure
system
\end{itemize}
\vspace*{3mm}
\begin{figure}[!H]
\begin{center}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CompDyn/Present/6D_to_1D_01.jpg}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Stress Testing NPP SSI Systems}
%
%
%
% \begin{itemize}
%
% \item Excite SSI system: different waves, energies and durations
%
% \item Try to "break" the system, shakeout strong and weak links
%
%
% %\vspace*{3mm}
% %\item
%
% \end{itemize}
%
% \vspace*{2mm}
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
% \hspace*{5mm}
% \end{center}
% \end{figure}
%
%
%
% \end{frame}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Synthetic (Realistic) Test Motions}
% online
% online
% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
{\includegraphics[width=55mm]{movie_input_mp4_icon.jpeg}}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
{\includegraphics[width=50mm]{movie_input_closeup_mp4_icon.jpeg}}
\end{center}
% online
% online
% online
% local % local
% local % local
% local % local
% local \vspace*{2mm}
% local \begin{center}
% local %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
% local \hspace*{12mm}
% local %\movie[label=show3,width=6.0cm,poster]
% local % {\includegraphics[width=70mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% local %
% local %\hspace*{2mm}
% local %%\hfill
% local %%\hspace*{7mm}
% local %\movie[label=show3,width=80mm,poster,toolbar,mouse=true]
% local \movie[label=show3,width=61mm,poster]
% local {\includegraphics[width=80mm]{movie_input_closeup_mp4_icon.jpeg}}{movie_input_closeup.mp4}
% local \hspace*{12mm}
% local \end{center}
% local % local
% local % local
% local
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Synthetic Test Motions, 6D vs 1D}
\begin{itemize}
\item Danger of picking one component (1D) of motions
\item Excellent (forced) fit, but it is not a prediction
% and information is lost
% (goal is to predict and inform and not (force) fit)
\end{itemize}
% local % local
% local % local
% local % local
% local \vspace*{4mm}
% local \begin{center}
% local \hspace*{16mm}
% local \movie[label=show3,width=61mm,poster]
% local {\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}{movie_ff_3d.mp4}
% local %\hspace*{2mm}
% local %\hfill
% local \movie[label=show3,width=61mm,poster]
% local {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}{movie_ff_1d.mp4}
% local \hspace*{16mm}
% local \end{center}
% local % local
% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
{\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
{\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
\end{center}
% online
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D vs 1D NPP ESSI Response Comparison}
% local % local
% local
% local % local
% local \vspace*{2mm}
% local \begin{center}
% local \hspace*{7mm}
% local \movie[label=show3,width=88mm,poster]
% local {\includegraphics[width=88mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% local \end{center}
% local % local
% local % \vspace*{2mm}
% local % \begin{center}
% local % \hspace*{7mm}
% local % \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% local % {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% local % \end{center}
% online
% online
% online
\begin{center}
%\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
{\includegraphics[width=80mm]{movie_2_npps_mp4_icon.jpeg}}
\end{center}
% online
% online
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D vs 1D NPP ESSI, Top of Containment, Differences}
% An example of a Mises probabilistic yield surface is given in Fig.~\ref{ProbCylinder}.
\begin{figure}[!htbp]
\begin{center}
\hspace*{10mm}
\includegraphics[width=6.6cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_for_NPPs/02_displacements_Containment_building_top.jpg}
\hspace*{5mm}
\includegraphics[width=6.6cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_ESSI_for_NPPs/02_accelerations_Containment_building_top.jpg}
\end{center}
\end{figure}
\end{frame}
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\subsection{{\cyrdevet Mehanika i Teorija Verovatno\cj{}a}}
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\begin{frame}
\frametitle{Uncertain Material Parameters and Loads}
\begin{itemize}
\item Decide on modeling complexity
\vspace*{2mm}
\item Determine loads and model/material parameters
\vspace*{2mm}
\item Loads are uncertain!
\vspace*{2mm}
\item Model/material parameters are uncertain!
\begin{itemize}
\item Measurements
\item Transformation
\item Spatial variability
\end {itemize}
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Parametric Uncertainty: Material Properties}
\begin{figure}[!hbpt]
\begin{center}
% %
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
\\
%\vspace*{2mm}
\hspace*{2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
%\vspace*{45mm}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
\\
%\vspace*{8mm}
\hspace*{2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
\end{center}
\end{figure}
\end{frame}
%
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\begin{frame}
\frametitle{Uncertainty Propagation through
Inelastic System}
%
\begin{itemize}
\item Incremental elpl constitutive equation
%
\begin{eqnarray}
\nonumber
\Delta \sigma_{ij}
=
% E^{EP}_{ijkl}
E^{EP}_{ijkl} \; \Delta \epsilon_{kl}
=
\left[
E^{el}_{ijkl}

\frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
{\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
\right]
\Delta \epsilon_{kl}
\end{eqnarray}
\vspace*{5mm}
\item Dynamic Finite Elements
%
\begin{equation}
{\bf M} \ddot{\bf u} +
{\bf C} \dot{\bf u} +
{\bf K}^{ep} {\bf u} =
{\bf F}
\nonumber
\end{equation}
\item What if all (any) material and load parameters are uncertain
\end{itemize}
\end{frame}
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\begin{frame}{Stochastic Elastoplastic Finite Element Method (SEPFEM)}
\begin{itemize}
\item Material uncertainty expanded along stochastic shape functions:
\\
$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$
\vspace*{1mm}
\item Loading uncertainty expanded along stochastic shape functions:
\\
$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$
\vspace*{1mm}
\item Resulting displacement expanded along stochastic shape functions:
\\
$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{SEPFEM : Formulation}
Stochastic system of equation resulting from Galerkin approach
\begin{tiny}
\[
\begin{bmatrix}
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\ \\
\vdots & \vdots & \vdots & \vdots\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)} & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
u_{10} \\
\vdots \\
u_{N0}\\
\vdots \\
u_{1P_u}\\
\vdots \\
u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
\sum_{i=0}^{P_f} f_i <\Psi_0\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_1\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_2\zeta_i> \\
\vdots \\
\sum_{i=0}^{P_f} f_i <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
\]
\end{tiny}
% \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
\scalebox{0.7}{
\begin{tabular}{ c c c c}
\# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
4 & 4 & 10 & 43758 \\
4 & 4 & 20 & 3 108 105 \\
4 & 4 & 30 & 48 903 492 \\
6 & 6 & 10 & 646 646 \\
6 & 6 & 20 & 225 792 840 \\
6 & 6 & 30 & 1.1058 $10^{10}$ \\
% 8 & 8 & 10 & 5 311 735 \\
% 8 & 8 & 20 & 7.3079 $10^{9}$ \\
% 8 & 8 & 30 & 9.9149 $10^{11}$\\
... & ... & ... & ...\\ \hline
\end{tabular}}
\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%% END FORMULATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%% BEGGINING PEP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}{SEPFEM : Probabilistic Constitutive Modeling}
\begin{itemize}
% \vspace{0.5cm}
\item<1> Probabilistic constitutive modeling :
\begin{itemize}
\item<1> Evolution of stress and stiffness via stochastic ArmstrongFrederick kinematic hardening rule
$ \Delta\sigma =\ Ha \Delta \epsilon  c_r \sigma \Delta \epsilon $
\item<1> Initial stiffness Ha and shear strength Ha/cr are now uncertain :
%
$ Ha = \Sigma h_i \Phi_i$
\hspace*{5mm}
$ Cr = \Sigma c_i \Phi_i$
\item<1> Resulting stress and stiffness are also uncertain :
$ \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i \Phi_i = \sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k \Phi_i \Phi_k  \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_i \Delta \epsilon_k \sigma_l \Phi_j \Phi_k \Phi_l$
\end{itemize}
%\vspace{0.5cm}
\item<1> Polynomial Chaos decomposition of stress and stiffness is updated incrementally at each Gauss Point via stochastic Galerkin projection
%\vspace{1cm}
\item<1> Time integration is done via Newmark algorithm
\end{itemize}
\end{frame}
% % % % % % % % % % % % % % % %
%
% \begin{frame}{SEPFEM : probabilistic constitutive modeling}
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}
% \end{frame}
%
% % % % % % % % % % % % % % % %
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\begin{frame}{SEPFEM: Solution}
\begin{itemize}
\item<1> Solution is probability density function (PDF) of :
\begin{itemize}
\item<1> displacement
\item<1> velocity
\item<1> acceleration
\item<1> stress
\item <1> strain
\end{itemize}
%\vspace{0.5cm}
\item<1> These PDFs evolve in space and time
%\vspace{1cm}
\item<1> PDFs include dynamic uncertainty from materials and loads \vspace{1cm}
\end{itemize}
\end{frame}
% % % % % % % % % % % % % % % % % % % % % % % % % % % % %
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%%%%%%%%%%%%%%%%%%%%%%%%%% BEGGINING KL EXPANSION %%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}{ SEPFEM : Correlation Structure Representation}
% \vspace{0.5cm}
\begin{itemize}
\item Material properties $E(x, y, z ; \theta)$ are spatially correlated, with correlation structure $C(x_1, y_1, z_1 ; x_2, y_2, z_2)$ between two point locations\\ %$(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ \\
% \vspace{1cm}
\item Eigenvalue analysis of 3D correlation structure (KL Expansion)
%$\exists \lambda_k \in \Re, \ \exists \ f_k : \Re^{3}>\Re, \ \exists \xi_k \in \Omega, \ k = 1...\infty ;
%$\gamma(x, y, z) = \sum_{k = 1}^{\infty} \sqrt{\lambda_k} \ f_k(x, y, z) \ \xi_k(\theta) $
%where $\lambda_k$ and $f_k$ are the eigenvalues and eigenfunctions of the Fredholm integral equation defined by : \\
$\int_{\Re^3} C(x_1, y_1, z_1 ; x_2, y_2, z_2) \ f_k(x_1, y_1, z_1)dx_1dy_1dz_1 = \lambda \ f_k(x_2, y_2, z_2)$
\item 3D eigenfunctions can be included in stochastic shape functions $\Psi$ to propagate correlation structure of materials
$E(x, y, z ; \theta) = \sum_{k = 1}^{\infty} \sqrt{\lambda_k} \ f_k(x, y, z) \ \Psi\{\xi_k(\theta) \} $
%and where $\{\xi_1, \xi_2, ..., \xi_k \}$ form a set of independent random variables. \\
%\textbf{The KarhunenLoeve expansion allows us to prescribe a target correlation structure for the random process $\gamma$}, solving an eigenvalue problem involving this correlation structure, as defined in the previous equation. \\
%\underline{\textbf{N.B.}} : for the case where $\gamma$ is a Gaussian random process, the random variables $\xi_1, \xi_2, ...$ are also Gaussian. \\
%\underline{\textbf{N.B.}} : if we can now express our random process with a prescribed correlation structure, we also increase the number of random variables ($\xi_k$) in our system (one new random variable for each term in the expansion). The number of unknowns therefore the dimension of the SFEM system becomes much bigger with the nummber of unknowns added in the KahrunenLoeve expansion. \\
%\underline{\textbf{N.B.}} : to solve this eigenvalue analysis, we use a separate deterministic finite element approach...(FEM can be employed to solve partial differential/integral equations...)
\end{itemize}
\end{frame}
\begin{frame}{ SEPFEM : Correlation Structure Representation}
\includegraphics[width=11cm, height=7.5cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_27Jun2017/Summer_Slides/img/figure_KL.pdf}
\begin{center}
First nine eigenfunctions of a 3dimensional exponential correlation structure
\end{center}
\end{frame}
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\begin{frame}
\frametitle{SEPFEM : Probabilistic ElasticPlastic Modeling}
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% {NPP_without_Contact_vonMises.mp4}
% \end{center}
% local % local
% local % local
% local % local
% local %\vspace*{5mm}
% local \begin{center}
% local % \hspace*{15mm}
% local \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% local {\includegraphics[width=9cm]
% local {/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% local % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% local %{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
% local {PEP_Animation.mp4}
% local \end{center}
% local
% local
% online
% online
% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
{\includegraphics[width=85mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/figure_PEP_25.png}}
\end{center}
% online
% online
% online
%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}
\end{frame}
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\begin{frame}
\frametitle{SEPFEM : Example in 1D}
% local % local
% local
% local \vspace*{2mm}
% local \begin{center}
% local % \hspace*{15mm}
% local \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% local {\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% local % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% local %{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
% local {SEPFEM_Animation_Elastic.mp4}
% local \end{center}
% local
% local
% online
% online
% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4}
{\includegraphics[width=85mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/figure_elastic_900.png}}
\end{center}
% online
% online
% online
% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}
\end{frame}
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\begin{frame}
\frametitle{SEPFEM : Example in 3D}
% local % local
% local % local
% local % local
% local %\vspace*{5mm}
% local \begin{center}
% local % \hspace*{15mm}
% local \movie[label=show3,width=11cm,poster,autostart,showcontrols]
% local {\includegraphics[width=11cm]
% local {/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/SFEM_3D.png}}
% local % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% local {SFEM_Animation_3D.mp4}
% local \end{center}
% local % local
% local % local
% local % local
% online
% online
% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SFEM_Animation_3D.mp4}
{\includegraphics[width=85mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SFEM_3D.png}}
\end{center}
% online
% online
% online
% \includegraphics[width = 12cm]{./img/SFEM_3D.pdf}
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Summary}
%
%
\section{\cyrdeset Zakljuchak}
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\subsection{\cyrdevet Zakljuchak}
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\begin{frame}
\frametitle{Summary}
\begin{itemize}
\item High fidelity modeling and simulation allows reduction of
modeling uncertainty and direct propagation of parametric uncertainties
through the dynamic ESSI system
%\vspace*{1mm}
\item Development and expert use of high fidelity modeling and simulation numerical
tools: Real ESSI Simulator System
%\vspace*{1mm}
\item { Education} and {training} of users (researchers, designers, regulators,
owners) will prove essential
%\vspace*{1mm}
\item Collaborators:
Yang, Cheng, Jie, Sett, Taiebat, Tafazzoli, Karapiperis, Abell,
Pisan{\`o}, Feng, Sinha, Lacour, Yang, Behbehani, Wang, Petrone, Wong,
McKenna, McCallen
%\vspace*{0.1cm}
\item Funding from and collaboration with the USNRC,
USNSF, USDOE, CNSC, LBNL, LLNL, INL, ILEE,
AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,
\end{itemize}
\end{frame}
%
% \vspace*{0.1cm}
% \item Funding from and collaboration with the USNRC,
% USNSF, USDOE, CNSC, LLNL, INL,
% AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,
%
% % \vspace*{0.5cm}
% % \item Collaborators, students:
% % Mr. Abell, Mr. Jeong, Mr. Aldridge. Mr. Kamranimoghadam, Mr. Karapiperis,
% % Mr. Watanabe, Mr. Chao,
% % Dr. Tafazzoli, Prof. Pisan{\`o} (TU Delft),
% % Prof. Sett (U. Bufallo), Prof. Taiebat (U. British Columbia), Prof. Yang (U. Alaska)
% %
%
% \end{itemize}
%
%
% \end{frame}
% %
%
\end{document}