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% %% Jose Antonio Abell Mena provided this for DSL descriptions
% % (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% % This is added for listing FEI DSL
% %   since   he   customized   it,   it   needs   to   be   changed   (linked  to
% % /usr/share/texmf/tex/latex/misc)
% %\usepackage{myListings}
% \input{essi_listings_options.tex}
% 
      
\usepackage{multimedia}

% for inclusion of other PDF pages, in this case Frank's presentation
\usepackage{pdfpages}

%This is a macro to  convert eps to pdf files on the fly.
% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
%
% \ifx\pdfoutput\undefined
% % we are running LaTeX, not pdflatex
% \usepackage{graphicx}
% \else
% % we are running pdflatex, so convert .pdf files to .pdf
% \usepackage[pdftex]{graphicx}
% \usepackage{epstopdf}
% \fi
% %*****************************************


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% % for not showing eq numbers unless eq is references
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\setbeamertemplate{navigation symbols}{}
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%  \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
%  \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
%  \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
%  \usetheme{Montpellier} % ima graf sadrzaj gore
%  \usetheme{Warsaw}
%  \usetheme{Warsaw}
  \usetheme{Dresden}
    \usecolortheme[RGB={20,0,128}]{structure}

% or ...

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%  \setbeamercovered{transparent}
% or whatever (possibly just delete it)
%  \usecolortheme{albatross} % teget sa svetlim slovima
%  \usecolortheme{beetle} % siva pozadina (vrh plav)
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%%%%%%%
%  \usecolortheme{BorisJeremic}
%%%%%%%
%  \usecolortheme{rose}
%   \usefonttheme[onlylarge]{structuresmallcapsserif}
%   \usefonttheme{structuresmallcapsserif}
}

\definecolor{mycolor}{rgb}{0,0.08,0.45}%


\usepackage[greek,english]{babel}



\usepackage{amsmath}
\usepackage{mathrsfs}
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\newcommand{\ud}{{\rm d}}


\usepackage{array}



%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
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\usepackage{pause}
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\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.






\title[{\cyrosam
Elasto-Plastichnost i verovatno\cj{}e}]
        {{\cyrsesnaest
Modelovanje elasto-plastichnih 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.
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}


%\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{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (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{}
% This is only inserted into the PDF information catalog. Can be left
% out.



% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:

%\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{university-logo}}

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}




% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{2}
 \AtBeginSubsection[]
% \AtBeginSection[]
 {
   \begin{scriptsize}
   \begin{frame}<beamer>
%     \frametitle{\cyrsesnaest Pregled}
     \tableofcontents[currentsection,currentsubsection]
%    \tableofcontents[currentsection]
   \end{frame}
   \end{scriptsize}
 }


% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command:





\begin{document}

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\begin{frame}
  \titlepage
\end{frame}

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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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}

\vspace*{-0.8cm}
%\hspace*{-3.3cm}
\begin{flushleft}
{\tiny
Transformation  of SPT $N$-value: 
1-D 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/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
% \hspace*{-7mm}
% % \hfill
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}
% 
% % \vspace*{-1.8cm}
% % %\hspace*{-3.3cm}
% % \begin{flushright}
% % {\tiny
% % Transformation  of SPT $N$-value: \\
% % 1-D 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}
% 
% 
% 
% 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %\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 Point-wise \\ 
%               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 point-wise})
% % 
% %       \item Solid and/or structure design (or retrofits),  ({\it spatial})
% % 
% %       \end{itemize}
%                                   
% %\end{itemize}
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% \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) }
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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}
% 
% 
% %
% \vspace*{0.2cm}
% \item Testing error (Stokoe et al. 2004)
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%   \begin{itemize}
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%     \item Imperfection of instruments 
%  
%     \item Error in methods to register quantities
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%   \end{itemize}
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% %
% \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.)
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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/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
% \hfill
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.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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% \frametitle{SPT Based Determination of Young's Modulus}
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% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf} 
% \hfill
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% %
% \end{center}
% \end{figure}                                                          
% 
% \vspace*{-0.3cm}
%  Transformation of SPT $N$-value $\rightarrow$ 1-D 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
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% \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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% \end{itemize}
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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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% {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_01.jpg}}
% \hspace*{-1.5cm}
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% %  \frametitle{T2: Stage 14, Interpretation of Data  }
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% % \begin{center}
% % %\vspace*{-2.5cm}
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% % {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_02.jpg}}
% % \hspace*{-1.5cm}
% % \vspace*{-1.5cm}
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% \begin{frame}
% \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: foundation--soil, dry, saturated, slip--gap
% 
% \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}
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% 
% 
% \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}
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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 ESSI-Program} is a 3D, nonlinear, time domain,
parallel finite element program specifically developed for
Hi-Fi modeling  and  simulation  of  Earthquake  Soil/Rock  Structure
Interaction problems for NPPs (infrastructure objects) on ESSI-Computers. \
%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 (NRC-ESSI-Program). Significant effort is devoted to development
%of  verification  and  validation  procedures,  as  well  as  on  development of
%extensive  documentation.  NRC-ESSI-Program  is  in  public  domain  and is licensed
%through the Lesser GPL.

%\vspace*{0.3cm}
\vspace*{0.1cm}
\item {\bf The Real ESSI-Computer} 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  ESSI-Notes} 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
%NRC-ESSI-Program  code  API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRC-ESSI-Notes,    developed  by Boris Jeremic and collaborators, are in public
%domain
%%and  are  licensed  under a Creative Commons Attribution-ShareAlike 3.0 Unported
%%License.
%
%\vspace*{0.3cm}
\end{itemize}

\end{frame}


    
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\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/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
%\caption{\label{loading_stages-increments_iterations} }
\end{center}
\vspace*{-0.5cm}
\end{figure}
%
\end{frame}

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\subsection{Real ESSI Simulator Components}



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\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 = 1e-5
%   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 = 1e-5
%    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}


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\begin{frame}
\frametitle{Real ESSI Simulator Program: Finite Elements}


%\vspace*{-3mm}
   \begin{itemize}
     \item Dry/single phase solids (8, 20, 27, 8-27 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
     opening-closing, frictional slip),
%\vspace*{1mm}
     \item Base isolators (elastomeric, frictional pendulum)
%\vspace*{1mm}
     \item Stochastic Elastic-Plastic 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  Elastic-Plastic (solids):  von Mises,
                                Drucker Prager,
                                Rounded Mohr-Coulomb,
                                Leon Parabolic,
                                Cam-Clay,
                                SaniSand,
                                SaniClay,
                                Pisan{\` o}.
                                All    elastic-plastic    models  can be used as
                                perfectly plastic, isotropic hardening/softening
                                and kinematic hardening models.

\vspace*{2mm}
       \item  Elastic-Plastic (structures, 1D fibers): concrete and steel

\vspace*{2mm}
     \item Probabilistic Elasto-Plasticity 

   \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:   Euler-Lagrange   form   of  Fokker-Planck  (forward
%      Kolmogorov)  equation  for  probabilistic elasto-plasticity (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
%      (Karhunen-Loeve, 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
%      Feynman-Kac 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, 8-20n, 27n 8-27n)
% 
% \item[-] E:  Coupled solids,      u-p-U and u-p,
% 
% \item[-] E:   Structural  (Truss,  beams  B12,  B9,  ANDES Shell, Nonlinear Beam,
% Shell
% 
% \item[-]  E: Contact, dry and saturated
% 
% 
% \item[-]  Material:   template/template elasto-plasticity (small and large def.),
% 
% \item[-]  Seismic:   DRM for seismic input
% 
% \item[-]   Probabilistic Elasto-Plasticity and Stochastic Elastic-Plastic 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  plug-in  (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; Elastic-Plastic (vMises, DrPr, R-MC, Leon-P, 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/Figure-files/_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/Figure-files/_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/Figure-files/_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/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/img-0188.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/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_Q2-61_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/Figure-files/_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/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final02.jpg}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg}
//
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final05.jpg}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_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/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/Undrained-Su440-Vector-Plan_snapshot.jpg}
\end{flushright}
\end{figure}

 \vspace*{-10mm}

%
\begin{figure}[!htbp] 
\begin{center}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_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/Figure-files/_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/Figure-files/_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/Figure-files/_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/Figure-files/_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/Figure-files/_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/Figure-files/_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/Figure-files/_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/Figure-files/_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 SMART-1 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 soil-structure
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, shake-out 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/Figure-files/_Chapter_Applications_ESSI_for_NPPs/02_displacements_Containment_building_top.jpg}
\hspace*{-5mm}
\includegraphics[width=6.6cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_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}}

            
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}












%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}

% 




                                          
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{Uncertainty Propagation through 
Inelastic System}

% 

\begin{itemize}

\item Incremental el--pl 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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%







 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%    END FORMULATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%    BEGGINING PEP    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\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 Armstrong-Frederick 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}
%  


% % % % % % % % % % % % % % % % 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%    END PEP    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}

% % % % % % % % % % % % % % % % % % % % % % % % % % % % %


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%    BEGGINING KL EXPANSION     %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\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 Karhunen-Loeve 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 Kahrunen-Loeve 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 3-dimensional exponential correlation structure
 \end{center}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%    END KL EXPANSION      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\begin{frame}
\frametitle{SEPFEM : Probabilistic Elastic-Plastic 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}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





























































































%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Summary}
% 
% 
\section{\cyrdeset Zakljuchak}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{\cyrdevet Zakljuchak}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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 US-NRC,
  US-NSF,  US-DOE, 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 US-NRC,
%   US-NSF,  US-DOE, 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}



