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\usepackage{epstopdf}

 
\usepackage[absolute,overlay]{textpos}



\usepackage{ulem}
\usepackage{amsmath}
\usepackage{bm}
\usepackage{IEEEtrantools}
\usepackage{setspace}
\usepackage{scalerel}


% %% 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
% %*****************************************


%% ovo je za cirilicu
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% % for not showing eq numbers unless eq is references
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% FEI  LOGO definition
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{{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}

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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 ...

  \setbeamercovered{transparent}


%  \setbeamercovered{transparent}
% or whatever (possibly just delete it)
%  \usecolortheme{albatross} % teget sa svetlim slovima
%  \usecolortheme{beetle} % siva pozadina (vrh plav)
  \usecolortheme{seagull} % sivo
%%%%%%%
%  \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}
\usepackage{amsfonts}

\newcommand{\ud}{{\rm d}}


\usepackage{array}



%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
\definecolor{webgreen}{rgb}{0, 0.35, 0} % less intense green
\definecolor{webblue}{rgb}{0, 0, 0.50} % less intense blue
\definecolor{webred}{rgb}{0.35, 0, 0} % less intense red
%\usepackage[colorlinks=true,linkcolor=webblue,citecolor=webred,urlcolor=webgreen]{hyperref}


\usepackage{hyperref}
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  pdfmenubar=true,
  pdftoolbar=true,
  pdfpagemode={None}
             colorlinks=true,
             linkcolor=webblue,
             citecolor=webblue,
             urlcolor=webblue,
}
% \usepackage[pdfauthor={Boris Jeremic},
%             colorlinks=true,
%             linkcolor=webblue,
%             citecolor=webblue,
%             urlcolor=webblue,
%             linktocpage,
%             pdftex]{hyperref}


\usepackage{pause}
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%\usepackage{url}

\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.



%      Site Specific Dynamics of Structures: 
%From Seismic Source to 
%the Safety of Occupants and Content


\title[Real ESSI Simulator]
        {The Real ESSI Simulator System \\
         Status Report}


%\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[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}
}

%\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\\
%  and\\
%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
  Lawrence Berkeley National Laboratory, Berkeley, CA}
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.


\date[] % (optional, should be abbreviation of conference name)
{\small LBNL, 14Mar2019}

\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}{3}
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     \frametitle{Outline}
     \tableofcontents[currentsection,currentsubsection]
%    \tableofcontents[currentsection]
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 }


% 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{Outline}

   \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{Introduction}




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\subsection{Motivation}



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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



%\vspace*{0.3cm}
  \item  Improve  modeling  and  simulation  for  infrastructure objects
 

% \vspace*{2mm}
%  \item[]  Expert numerical modeling and simulation tool

\vspace*{1mm}
  \item      Use of numerical models to
  analyze statics and dynamics of soil-structure systems


\vspace*{1mm}
  \item  Reduction  of modeling uncertainty

\vspace*{1mm}
  \item  Desired level
  of sophistication (high  $\leftrightarrow$ low) analysis


\vspace*{1mm}
  \item  Follow and direct  the  flow of seismic  energy, 


\vspace*{1mm}
  \item  Practical  system  for modeling and simulation of
  Earthquakes,    Soils,    Structures    and    their    Interaction, 
%    Real-ESSI:
 \\
% \vspace*{3mm}
%  \hspace*{1mm} 
%  \hspace*{15mm} 
\vspace*{2mm}
    {\href{http://real-essi.info/}{http://real-essi.info/}} 
% \\
%     \small{\href{http://sokocalo.engr.ucdavis.edu/\~{}jeremic/Real\_ESSI\_Simulator/}{http://sokocalo.engr.ucdavis.edu/\~{}jeremic/Real\_ESSI\_Simulator/}}






\end{itemize}
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Motivation: Modeling Uncertainty}
% 
% \begin{itemize}
% 
% 
% 
%   \item         Simplified  modeling:    Features (important ?)   are neglected,
%   simplified out (6C ground motions, inelasticity)
% 
% \vspace*{3mm}
%      \item   Modeling   Uncertainty:   unrealistic   (unnecessary?)  modeling
%      simplifications
% 
% %\vspace*{3mm}
% %     \item  Modeling  simplifications   are  justifiable  if  one  or  two  level  higher
% %     sophistication  model  shows  that  features  being  simplified out are not
% %     important
% 
% 
% %\vspace*{3mm}
% %     \item   Chief Engineer in my old company: "I would really love to know what
% %     would a realistic response this object be"
% 
% 
% \end{itemize}
% \end{frame}
% 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}

\begin{itemize}

   \item {  Prediction under Uncertainty}:  use  of  computational  model
   to  predict  the  state  of SSI system under
   conditions for which the computational model has not been validated.


\vspace*{1mm}
     \item  {{  Verification}  provides  evidence  that  the  model is solved
     correctly.} Mathematics issue.

\vspace*{1mm}
     \item  {{  Validation}  provides  evidence  that  the  correct  model is
     solved.} Physics issue.

\vspace*{1mm}
   \item  Modeling  and  parametric uncertainties are always present, need to be
   addressed 

% \vspace*{1mm}
%    \item Predictive capabilities with {low Kolmogorov Complexity}
% 

\vspace*{1mm}
     \item Goal: Predict and Inform rather than (force) Fit

\end{itemize}


\end{frame}



% 


 
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\section{Real-ESSI Simulator System}

      
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection*{Real-ESSI Simulator System}
\subsection{Real ESSI Components}



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

\frametitle{Real-ESSI Simulator System}

The  Real-ESSI, 
{\underline {\bf Real}}istic  
%{\underline {\bf M}}odeling  and  
%{\underline {\bf S}}imulation  of  
{M}odeling  and  
{S}imulation  of  
{\underline {\bf E}}arthquakes,  
{\underline {\bf S}}oils,
{\underline {\bf S}}tructures  and  their  
{\underline {\bf I}}nteraction.  Simulator  is  a  software,  hardware  and
documentation   system   for   time  domain,
linear  and  nonlinear,  inelastic,  deterministic  or probabilistic, 3D, finite
element modeling and simulation of:

    \begin{itemize}
%\vspace*{1mm}
      \item statics and dynamics of soil,
%\vspace*{1mm}
      \item    statics and dynamics of rock,
%\vspace*{1mm}
      \item    statics and dynamics of structures,
%\vspace*{1mm}
      \item    statics of soil-structure systems, and
%\vspace*{1mm}
      \item    dynamics of earthquake-soil-structure system interaction
    \end{itemize}



Used for:
\begin{itemize}
%\vspace*{1mm}
  \item Design, linear elastic, load combinations, dimensioning


%\vspace*{1mm}
  \item Assessment, nonlinear/inelastic, safety margins
\end{itemize}




\end{frame}



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

\frametitle{Real-ESSI Simulator System}

 
\begin{itemize}


  \item Real-ESSI System Components
    \begin{itemize} 
     \item Real-ESSI Pre-processor (gmsh/gmESSI, X2ESSI) 
     \item Real-ESSI Program (local, remote, cloud)
     \item Real-ESSI Post-Processor (Paraview, Python, Matlab)

    \end{itemize} 

\vspace*{1mm}
  \item Real-ESSI System availability:                   
    \begin{itemize}
%\vspace*{1mm}
     \item Educational  Institutions: Amazon Web Services (AWS), free 
     \item Government Agencies, National Labs: AWS GovCloud
     \item Professional  Practice: AWS, commercial
%\vspace*{1mm}
%%\vspace*{1mm}
%      \item Sources available to collaborators
    \end{itemize}



\vspace*{1mm}
  \item Real-ESSI Short Courses, online, worldwide



\vspace*{1mm}
  \item System description and documentation at  \url{http://real-essi.info/}



% \vspace*{2mm}
%   \item
% 


\end{itemize}


\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Quality Assurance}

\begin{itemize}

\item Full verification suit for each element, model, algorithm

\vspace*{4mm}
\item Certification process in progress for NQA-1 and ISO-90003-2014

%\vspace*{3mm}
%\item[] Verification examples given below

\end{itemize}




\end{frame}

%  % 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Real-ESSI}
%  
%  \begin{itemize}
%  
%  
%  
%  %\vspace*{2mm}
%    \item    A  system  for  time domain, nonlinear/inelastic,  deterministic  or 
%    probabilistic, modeling and simulation of
%  
%      \begin{itemize}
%        \item  statics and dynamics of soil,
%        \item  statics and dynamics of rock,
%        \item  statics and dynamics of structures,
%        \item  statics of soil-structure systems, and
%        \item  dynamics of earthquake-soil-structure system interaction.
%        \end{itemize}
%  
%  
%  \vspace*{1mm}
%    \item Design, linear elastic, load combinations, dimensioning
%  
%  
%  \vspace*{1mm}
%    \item Assessment, nonlinear/inelastic, safety margins
%  
%  
%  
%  %\vspace*{1mm}
%  %  \item  Develops methods and models that inform and predict rather than (force) fit.
%  
%  \vspace*{1mm}
%          \item Collaboration and financial support from the US-DOE, US-NRC,
%          US-NSF, Caltrans, CNSC-CCSN, UN-IAEA, Shimizu, Basler\&Hofmann, etc.
%  
%  
%  
%  \end{itemize}
%   
%  \end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Modeling Features}

\begin{itemize}



%\vspace*{2mm}
  \item Solid elements, dry, (un-)saturated, elastic, inelastic

\vspace*{1mm}
  \item Structural elements, beams, shells, elastic, inelastic 

\vspace*{1mm}
  \item Contact elements, dry, coupled/saturated, 

\vspace*{1mm}
  \item Super element, stiffness and mass matrices

\vspace*{1mm}
  \item Material models, soil, concrete, steel... 
  
\vspace*{1mm}
  \item Seismic input, 1C and 3C, deterministic or probabilistic

\vspace*{1mm}
  \item Energy dissipation calculations

\vspace*{1mm}
  \item Solid/Structure -- Fluid interaction, full coupling

\vspace*{1mm}
  \item Intrusive probabilistic inelastic modeling

%
%\vspace*{1mm}
%  \item Modeling features listed at
%  \hspace*{5mm}
%  \href{http://real-essi.info/}{http://real-essi.info/} 
%%  \hspace*{5mm} 
%%  and 
%%  \hspace*{5mm} 
%%  \href{http://real-essi.info/}{http://real-essi.info/}


\end{itemize}
 
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Simulation Features}

\begin{itemize}




  \item Static loading stages



\vspace*{2mm}
  \item Dynamic loading stages

\vspace*{2mm}
  \item Restart, simulation tree

\vspace*{2mm}
  \item Solution advancement methods/algorithms, on global and
  constitutive levels, with and without enforcing equilibrium


%\vspace*{1mm}
%  \item Load combinations, elastic, for design

\vspace*{2mm}
  \item High Performance Computing
%  clusters, cloud, supercomputers 
    \begin{itemize}
\vspace*{1mm}
      \item[] Fine grained, template mataprograms, small matrix library
\vspace*{1mm}
      \item[] Coarse grained, distributed memory parallel 
    \end{itemize}


% \vspace*{1mm}
%   \item All  Simulation Features are listed at  
%   \hspace*{5mm}
%   \href{http://real-essi.info/}{http://real-essi.info/} 
% %  \hspace*{5mm} 
% %  and 
% %  \hspace*{5mm} 
% %  \href{http://real-essi.info/}{http://real-essi.info/}



\end{itemize}
 
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Model Development}

\begin{itemize}

    \item Pre-Processing, model development gmsh/gmESSI

\vspace*{2mm}
    \item Existing model translation, SASSI$\rightarrow$Real-ESSI

\vspace*{2mm}
    \item Choose level of sophistication

\vspace*{2mm}
    \item Reduce modeling uncertainty

\vspace*{2mm}
    \item Model developed in phases

\vspace*{2mm}
    \item Verify model components


\vspace*{2mm}
    \item  Build confidence in inelastic modeling

\end{itemize}
 
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Real-ESSI  Modeling Phases}



\begin{figure}[htbp]
\begin{center}
  \includegraphics[width = 2.3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
\vspace*{-1mm}
\\
  \includegraphics[width = 0.35cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_1D/DRM_1D_motion_3D_just_column.jpg}
\hspace*{5mm}
%  \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_1D/DRM1D_Motion3D.png}
  \includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_3D/motion3D_DRM3D_free_field.png}
\hspace*{5mm}
%  \includegraphics[width = 1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/soil_foundation.png}
%  \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/slice.png}
  \includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/foundation_results.png}
%  \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
\\
\vspace*{-3mm}
  \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/structure-only.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen1.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen2.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen3.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen4.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen5.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen6.png}
\hfill
%  \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/imposed_motion/structure-only.png}
%\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/imposed_motion/imposed_motion_results.png}
%   \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
\\
\vspace*{-1mm}
  \includegraphics[width = 6cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/DRM3D_motion3D_structure.png}
\end{center}
\end{figure}



\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Results Post Processing}

\begin{itemize}


      \item All output is saved (stress, strain, displacements, energy...)

\vspace*{5mm}
      \item Time histories, scripts to plot or extract in preferred format

\vspace*{5mm}
      \item 3D visualization, Paraview with pvESSI plugin

% OVDE dodaj primere vizualizacije


\end{itemize}
 
\end{frame}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Verification}
% 
% \begin{itemize}
% 
% 
%   \item Implementation  verification
% 
% \vspace*{2mm}
%   \item Solution verification for each component
%     \begin{itemize}
%        \item Finite elements
%        \item Constitutive algorithms
%        \item Solution advancement, static and dynamic 
% 
%     \end{itemize}
% 
% 
% \vspace*{2mm}
%   \item Error quantification for ranges of modeling parameters
% 
% \vspace*{2mm}
%   \item Automatic verification, a 13 hour process on multiple CPUs
% 
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Validation}
% 
% %OVDE
% \begin{itemize}
% 
%   \item Validation partially done, need for high quality data
% 
% \vspace*{1mm}
%   \item Validation, UNR soil box tests in the near future
%     \begin{itemize}
% 
% %\vspace*{1mm}
%       \item Soil testing, range of strains, confinements, stress paths
%       
% %\vspace*{1mm}
%       \item Contact testing,  axial, shear, soil-concrete, formed, poured
% 
% %\vspace*{1mm}
%       \item Wave propagation through soil, equivalent elastic and inelastic, 
%       1C and 2C, dilatancy influence
% 
% %\vspace*{1mm}
%             \item Inelastic structural behavior for beams, walls, plates, shells, use of
%             already published high quality test data
% 
% %\vspace*{1mm}
%       \item ESSI tests for a complete simplified SSI systems
% 
%     \end{itemize}
% 
% 
% \end{itemize}
%  
% 
% \begin{figure}[!htbp]
% \begin{flushleft}
% \includegraphics[width=2cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/soilbox_model_gmsh.png}
% \hspace*{1mm}
% \includegraphics[width=1.2cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mesh_detail.pdf}
% \end{flushleft}
% \end{figure}
% 
% 
% 
% \vspace*{-30mm}
% \begin{figure}[!htbp]
% \begin{flushright}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode1_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode2_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode3_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode4_side.pdf} 
% \\
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode5_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode6_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode7_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode8_side.pdf} 
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode9_side.pdf} 
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode10_side.pdf}
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode11_side.pdf}
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode12_side.pdf}
% \end{flushright}
% \end{figure}
% 
% 
% 
% \end{frame}
% 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Training and Education}

\begin{itemize}


  \item Short Courses: 
    \begin{itemize}
\vspace*{1mm}
      \item Online short course, soon
\vspace*{1mm}
     \item Professional practice 
% %   \vspace*{1mm}
%        \item Developers 
\vspace*{1mm}
     \item Examples available in lecture notes, and documentation
\vspace*{1mm}
      \item Real-ESSI Simulator system, with examples on Amazon Web Services 
      (AWS)

    \end{itemize}

%\vspace{1mm}
%  \item Documentation, extensive

\vspace{2mm}
  \item Full lecture notes (2600+ pages) available online


\vspace{2mm}
  \item Up to date information on Real-ESSI at: 
  \\ \vspace*{2mm}
  \hspace*{5mm} 
  \href{http://real-essi.info/}{http://real-essi.info/}


\end{itemize}
 
\end{frame}

% OVDE  OVDE  OVDE   


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Real-ESSI Core Functionality}

\begin{itemize}



%\vspace*{2mm}
  \item  Introduction to inelastic, nonlinear analysis for practicing engineers

% 
%  % \vspace*{3mm}
%    \item Usable models for professional practice
%  
%  %\vspace*{2mm}
%   \item  Core  functionality  needed  for  nonlinear  modeling  in professional
%   practice
%  % 
%  


%  %\vspace*{0.3cm}
%  %\vspace*{2mm}
%    \item Hierarchy of modeling capabilities, 
%    
%       \begin{itemize}
%  
%  %\vspace*{1mm}
%          \item Linear elastic models, elastic constants, viscous damping
%  
%  %\vspace*{1mm}
%          \item    Nonlinear  models,  core  functionality,  does not require much
%          material data however, sensitivity study is advised
%    
%  %\vspace*{1mm}
%          \item High sophistication  nonlinear models, require material data
%       
%       
%       \end{itemize}
%  


\vspace*{2mm}
  \item    Use  of prescribed, required (low, medium, high) fidelity numerical
  models to analyze ESSI behavior


\vspace*{2mm}
  \item  Set of suggested modeling and simulation parameters

\vspace*{2mm}
  \item  Investigate  sensitivity  of  response  to model sophistication

\vspace*{2mm}
  \item  Investigate  sensitivity  of response  to model parameters

% 
% \vspace*{1mm}
%   \item[]  Accurately   follow  the  flow   of  seismic  energy  in  a
%   soil structure system
% 
% \vspace*{1mm}
%   \item[]   The  goal is to create methodology and numerical tool that is used to 
%   predict and inform and not to fit
% 
% 
% 
% %\vspace*{1mm}
% %  \item[]   Directing,   in   space   and   time,   seismic  energy  flow  in  the
% %  soil structure system
% 


\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Real-ESSI Core Functionality Components}

\begin{itemize}


   \item Structural elements: Truss, Beam, Shell, Super-Element

\vspace*{2mm}
   \item Soil, solids:  elastic, $G/G_{max}$

\vspace*{2mm}
   \item Contacts: Bonded, Frictional, Gap open/close


\vspace*{2mm}
   \item Loads: Static, Dynamic (earthquake, 1C or 3$\times$1C), Restart   

\vspace*{2mm}
   \item Simulation: Explicit no-equilibrium, Implicit equilibrium

\vspace*{2mm}
   \item Core Functionality Application programs: APPs
% 


\end{itemize}


\end{frame}









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%  
%  \frametitle{NPP, Inelastic Response, Energy Dissipation}
%  
%  % Elastoplastic soil with contact elements
%  %% Both solid and contact elements dissipate energy
%  
%  
%  % \vspace*{-5mm}
%  \begin{center}
%  % \hspace*{-15mm}
%  \movie[label=show3,width=10cm,poster,autostart,showcontrols]
%  {\includegraphics[width=10cm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation_grab.jpg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%  \end{center}
%  
%  
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animation/NPP_Plastic_Dissipation.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  %
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\subsection{Stochastic Modeling}





% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
%\vspace{0.5cm}
% 
% \begin{tabular}{c  c}
% \begin{minipage}{0.45\textwidth}
% %
% \hspace{-1cm} {\color{blue} Soils are spatially non-uniform}
% \begin{itemize}
% 
% \footnotesize
% \item Spatial non-uniformity is a function of soil formation process.
% \vspace*{0.1cm}
% \item Spatial non-uniformity is usually 'uncertain', due to limited data! 
% \vspace*{0.1cm}
% \item Soil parameters are ideally described as non-Gaussian random fields 
% \end{itemize}
% 
% \end{minipage} &
% %
% \hspace*{0.75truecm} 
% \begin{minipage}{0.50\textwidth}
% 
% \begin{figure}
% \includegraphics[height=5.45cm]{Fangbo_figs/TypicalSoilVariability.jpg} 
% \end{figure}
% \vspace*{-0.5truecm}
% \centering
% \scriptsize Schematic profile of a soil deposit \\
% \hspace*{0.1cm} {\tiny(Terzaghi, Peck and Mesri, 1996)}
% \end{minipage}
% \end{tabular}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
% 
% \begin{columns}
% 
% \column{0.5\textwidth}
% 
% {\color{blue} Bedrock motion is also uncertain}
% \begin{itemize}
% \small
% \item Factors lead to uncertainty: 
% \begin{itemize}
% \item Mechanism of source
% \item Source parameters
% \item Earthquake propagation path
% \item ...
% \end{itemize}
% 
% \item Bedrock motion is ideally described as a non-stationary random process
% \end{itemize}
% \vspace{0.5cm}
% 
% 
% \column{0.5\textwidth}
% \includegraphics[scale=0.2]{Fangbo_figs/Three_stages_of_ground_mtion_Jie_Li.pdf} \\
% \vspace{-0.6cm}
% \begin{flushright}
% \scriptsize{Three stages explicitly indicate the non-stationarity of seismic wave}
% \end{flushright}
% \centering
% \vspace{-0.3cm}
% \hspace{0.5cm} \tiny(Li and Chen, 2009)
% 
% 
% \end{columns}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
% \vspace{0.2cm}
% {\color{blue}{Design frameworks can account for uncertainties:}}
% \footnotesize
% \begin{itemize}
% \item ASD $\rightarrow$ a single factor of safety
% \item LRFD $\rightarrow$ load and resistance factors
% \item Performance-based design (PBD):
% \end{itemize}
% 
% \vspace{-0.4cm}
% \begin{figure}
% \includegraphics[scale=0.3]{Fangbo_figs/Performance_design_framework.jpg} 
% \vspace{-0.3cm}
% \caption{ \scriptsize{Schematic of PBD framework} {\tiny(Moehle and Deierlein, 2004)} }
% \end{figure}
% 
% \end{frame}
% 
% 
% \begin{frame}[t]
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
% 
% {\footnotesize \color{blue}{However, numerical simulations -- which are used to feed design framework -- still remain exclusively deterministic:}}
% \vspace{-0.2cm}
% \begin{columns}
% \column{0.5\textwidth}
% \minipage[c][0.6\textheight][s]{\columnwidth}
% \begin{figure}
%   \includegraphics[width=0.8\textwidth, angle=90]{Fangbo_figs/SSI_model_deterministic}
%   \tiny{\linespread{1.0} Schematic of a Soil-Foundation-Structure system subjected to earthquake}
% \end{figure}
% 
% \endminipage
% 
% \column{0.5\textwidth}
% \footnotesize
% 
% \begin{itemize}
% \item Although high-fidelity models that reduce modeling uncertainty are increasingly being used
% \item Uncertainties in model parameters are ignored:
%  \begin{itemize}
%      \scriptsize
%      \item Material parameters
%      \item Forcing function
%  \end{itemize}
%  \item Resulting in negation of the effects of nonlinear stochastic dynamics
% \end{itemize}
% 
% \end{columns}
% 
% \end{frame}
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% \begin{frame}{Effects of nonlinear stochastic dynamics must be captured for accurate prediction}
% 
% \begin{columns}
% 
% \column{0.4\textwidth}
% \scriptsize
% 
% %\begin{center}
% %traditional SSI model \\
% %+ \\
% %uncertain soil deposit \\
% %+ \\
% %uncertain bedrock motion \\
% %$\Downarrow$ \\
% %stochastic SSI model
% %\end{center}
% Dynamic interaction of:
% \vspace{0.3cm}
% \begin{itemize}
% \item Non-Gaussian characteristics and spatial correlation of material parameters
% \item Temporal correlation of the forcing function
% \item Probabilistic evolution of material parameters as materials plastify
% \end{itemize}
% 
% \column{0.60\textwidth}
% \vspace{-1cm}
% %  \hspace{-0.9cm}
% \begin{figure}
%   \begin{flushleft}
%   \includegraphics[width=0.7\textwidth, angle=90]{Fangbo_figs/SSI_model_stochastic}
%   \end{flushleft}
%   \caption{\scriptsize Schematic illustration of a stochastic soil-foundation-structure system.}
% \end{figure}
% 
% \end{columns}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %\begin{frame}{Governing equations of solid mechanics}
% %\footnotesize
% %{
% %\begin{itemize}
% % \item Equilibrium equation: 
% %   \begin{flushleft}
% %     \begin{equation*}
% %        \frac{\partial \sigma_{ij}}{\partial x_j}+ {\color{blue}{b_j}} = \rho u_i
% %     \end{equation*}
% %   \end{flushleft}
% % \item Strain compatibility equation: 
% %     \begin{equation*}
% %        \epsilon_{ij} = \frac{1}{2} \left( \frac{\partial u_{i}}{\partial x_j}+ \frac{\partial u_{j}}{\partial x_i} \right)
% %     \end{equation*}
% % \item Constitutive equation:   
% %           \begin{equation*}
% %       \dot{\sigma}_{ij} = {\color{blue}{D_{ijkl}}} \dot{\epsilon}_{kl}
% %     \end{equation*}
% %\end{itemize}
% %}
% %\vspace{0.5cm}
% %\centering Input uncertainties (${\color{blue}{D_{ijkl}}}$, ${\color{blue}{b_j}}$) $\rightarrow$ stochastic PDE
% %\end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Existing Simulation Methods for Stochastic PDEs}

\begin{itemize}
\item Analytical, stochastic differential equation approach: difficult to solve with complex random coefficients
\vspace*{2mm}
\item Monte Carlo method : Computationally expensive
\vspace*{2mm}
\item Perturbation approach: Small variation with respect to mean, closure problem
\vspace*{2mm}
\item Stochastic collocation method: Global error minimization
\vspace*{2mm}
\item Stochastic Galerkin method: Local error minimization
%    \begin{itemize}
%         \item \color{blue}{ \footnotesize Previous studies$\rightarrow$ Uncertain static loading, linear elastic material.}
%         \item \color{blue}{ \footnotesize My research$\rightarrow$ Uncertain dynamic loading, nonlinear material.}
%    \end{itemize}
\end{itemize}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section[Formulation]{Stochastic Dynamic Finite Element Formulation}
%\subsection[Time domain stochastic Galerkin method]{Time domain stochastic Galerkin method}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Time Domain Stochastic Galerkin Method}

\begin{itemize}
\item Input random field/process{\normalsize{(non-Gaussian, heterogeneous/ non-stationary)}}
 \begin{itemize}
 \item[] Multi-dimensional Hermite Polynomial Chaos (PC) with {known coefficients}
 \end{itemize}
\vspace{0.05in}
\item Output response process
 \begin{itemize}
 \item[] Multi-dimensional Hermite PC with {unknown coefficients}
 \end{itemize}
 \vspace{0.05in}
 \item Galerkin projection: minimize the error to compute unknown coefficients of response process
\vspace{0.05in}
 \item Time integration using Newmark's method
  \begin{itemize}
   \item[] Update coefficients following an elastic-plastic constitutive law at each time step
  \end{itemize}
 
\end{itemize}

\scriptsize 
Note: PC = Polynomial Chaos

\end{frame}

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

\begin{frame}{Discretization of Input Random Process/Field $\beta(x,\theta)$}
\begin{center}
\includegraphics[scale=0.35]{Fangbo_figs/PC_KL_explanation.PNG} \\
\end{center}


\footnotesize{Note: $\beta(x,\theta)$ is an input random process with any
marginal distribution,  \\ \hspace{21mm} with any covariance structure;} \\
\footnotesize{\hspace{8mm} $\gamma(x,\theta)$ is a zero-mean unit-variance Gaussian random process.} \\

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Polynomial Chaos Representation}

%\scriptsize{
Material random field:
%\vspace{-0.3cm}
%\begin{equation*} 
$D(x, \theta)= \sum_{i=1}^{P1} a_i(x) \Psi_i(\left\{\xi_r(\theta)\right\})$      
%\end{equation*}


\vspace{3mm}

Motion random process:
%\vspace{-0.3cm}
%\begin{equation*} 
$f_m(t, \theta)=\sum_{j=1}^{P_2} f_{mj}(t) \Psi_j(\{\xi_k(\theta)\})$         
%\end{equation*}

\vspace{3mm}

Displacement response:
%\vspace{-0.3cm}
%\begin{equation*} 
$u_n(t, \theta)=\sum_{k=1}^{P_3} d_{nk}(t) \Psi_k(\{\xi_l(\theta)\})$         
%\end{equation*}

\vspace{3mm}

%Acceleration response:
%%\vspace{-0.3cm}
%%\begin{equation*} 
%$\ddot u_n(t, \theta)=\sum_{k=1}^{P_3} \ddot d_{nk}(t) \Psi_k(\{\xi_l(\theta)\})$         
%%\end{equation*}

\vspace{3mm}
\vspace{3mm}

where $a_i(x), f_{mj}(t)$ are {known PC coefficients}, while $d_{nk}(t)$
are {unknown PC coefficients}.
%}

\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{FEM and Stochastic Elastic-Plastic FEM, SEPFEM}


%\vspace{4mm} 
\vspace{-2mm} 

\small
{
%FEM:
\begin{eqnarray*}
  \sum_{e} [ \int_{D_e} N_m(x)\rho(x)N_n(x)d\Omega \; {\color{blue}{\ddot{u}_n(t)}} + 
	 \\
	 \int_{D_e}\nabla N_m(x) {\color{blue}{E(x)}} \nabla N_n(x)d\Omega \; {\color{blue}{u_n(t)}} - {\color{blue}{f_m(t)}} ]=0   
 \end{eqnarray*}

%SEPFEM: 
 \begin{eqnarray*} 
     &&\lefteqn{\sum_{n=1}^N \sum_{k=1}^{P_3} \langle \Psi_k \Psi_l \rangle \int_{D_e}N_m(x)\rho(x)N_n(x)d\Omega \; \; \ddot{d}_{nk}(t)  \; \; +}  
				 \\  
     &&\sum_{n=1}^N \sum_{k=1}^{P_3} \sum_{i=1}^{P_1} \langle \Psi_i \Psi_k \Psi_l \rangle  
				 \int_{D_e}B_m(x) {\color{blue}{a_i(x,t)}} B_n(x)d\Omega \; \; d_{nk}(t) 
     = 
				 \\
				 &&\sum_{j=1}^{P_2} \langle \Psi_j \Psi_l \rangle f_{mj}(t) \\
\end{eqnarray*}
}
\vspace{-0.3cm} 

%\scriptsize{Note: update \textcolor{blue}{$a_i(x,t)$} for elastic-plastic material}

\vspace{0.4cm} 

%\begin{beamercolorbox}{section in head/foot}
%\usebeamerfont{framesubtitle}\tiny{Wang, F. and Sett, K., "Time-Domain Stochastic Finite Element Simulation of Uncertain Seismic Wave Propagation through Uncertain Heterogeneous Solids", \textit{Soil Dynamics and Earthquake Engineering}, 88:369-385, 2016.}
%\end{beamercolorbox}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{SEPFEM}
Matrix form:
\begin{equation*}
\bm{M} \ddot{\bm{d}} + \bm{K} \bm{d} = \bm{f}
\end{equation*}
For damped systems:
\begin{equation*}
\label{eqno_19}
\bm{M} \ddot{\bm{d}} + \bm{C} \dot{\bm{d}} + \bm{K} \bm{d} = \bm{f}
\end{equation*}
\hspace{5cm}    {\huge $\Downarrow$  }   \\
\hspace{2.2cm}   Newmark's method to solve in time domain \\

\vspace{1cm}
\scriptsize{
\noindent where $\bm{M}$, $\bm{C}$ and $\bm{K}$ are generalized mass, damping and stiffness matrices,\\
 \hspace{0.9cm} $\bm{f}$, $\bm{d}$, and $\ddot {\bm{d}}$ are generalized force, displacement, and acceleration vectors. 
}

\end{frame}


%\begin{frame}{Physical significance of stochastic DOFs} \label{matrix_form}
%
%{\scriptsize Finite element system of equation --- \only<1> {deterministic} \only<2> {stochastic}}
%\vspace{-0.5cm}
%
%\begin{equation}
%\nonumber
%\tiny
%\left[ \begin{array}{ccccc}
%\uncover<2-> {\displaystyle \sum_{i=1}^{P_1} C_{i11}} \only<1> {K_1} \only<2> {K_i} & \uncover<2-> {\displaystyle \sum_{i=1}^{P_1} C_{i12} K_i} & \uncover<2-> \dots & \uncover<2-> \dots & \uncover<2-> {\displaystyle \sum_{i=1}^{P_1} C_{i 1 P_{\scaleto{3}{3pt}}} K_i} \\
%\uncover<2-> {\displaystyle \sum_{i=1}^{P_1} C_{i21} K_i} & \uncover<2-> {\displaystyle \sum_{i=1}^{P_1} C_{i22} K_i} & \uncover<2-> \dots & \uncover<2-> \dots & \uncover<2-> \vdots \\
%\uncover<2-> \vdots & \uncover<2-> \vdots & \uncover<2-> \ddots &  & \uncover<2-> \vdots \\
%\uncover<2-> \vdots & \uncover<2-> \vdots &  & \uncover<2-> \ddots & \uncover<2-> \vdots \\
%\uncover<2-> {\displaystyle \sum_{i=1}^{P_1} C_{i P_{\scaleto{3}{3pt}} 1} K_i} & \uncover<2-> {\dots} & \uncover<2->{\dots} & \uncover<2-> {\dots}  & \uncover<2-> {\displaystyle \sum_{i=1}^{P_1} C_{i P_{\scaleto{3}{3pt}} P_{\scaleto{3}{3pt}}} K_i}
%\end{array} \right]
%%
%\left[ \begin{array}{c}
%\vec{d}_1 \\
%\\
%\uncover<2-> {\vec{d}_2} \\
%\\
%\uncover<2-> \vdots \\
%\\
%\uncover<2-> \vdots \\
%\\
%\uncover<2-> {\vec{d}_{P_{\scaleto{3}{3pt}}}} 
%\end{array} \right]
%%
%=
%%
%\left[ \begin{array}{c}
%\uncover<2-> {\displaystyle \sum_{j=1}^{P_{\scaleto{2}{3pt}}} C_{j1}} \only<1> {\vec{f}_1} \only<2> {\vec{f}_j}\\
%\uncover<2-> {\displaystyle \sum_{j=1}^{P_{\scaleto{2}{3pt}}} C_{j2} \vec{f}_j} \\
%\uncover<2-> \vdots \\
%\uncover<2-> \vdots \\
%\uncover<2-> {\displaystyle \sum_{j=1}^{P_{\scaleto{2}{3pt}}} C_{j P_{\scaleto{3}{3pt}}} \vec{f}_j}
%\end{array} \right]
%\end{equation}
%
%\tiny
%{
%
%\only<1>
%{
%Note: $K_1$ is the deterministic stiffness matrix; \\
%\vspace{0.1cm}
%\hspace{0.55cm} $\vec{d}_1$ is the displacement vector for all the nodes; \\
%\vspace{0.1cm}
%\hspace{0.55cm} $\vec{f}_1$ is the forcing vector for all the nodes; \\
%\vspace{0.1cm}
%\hspace{0.55cm} Size of the stiffness matrix is $N \times N$, $N$ is the number of deterministic DOFs. \\
%\vspace{0.1cm}
%\hspace{0.55cm} \color{white}{deterministic DOFs;} \\
%}
%\only<2> 
%{
%Note: $C_{ijk}= \langle \Psi_i \Psi_j \Psi_k \rangle$, $C_{ij}= \langle \Psi_i \Psi_j \rangle$;  \\
%\vspace{0.1cm}
%\hspace{0.55cm} $K_i$ is the block stiffness matrix with $i$th PC coefficients of modulus, {\tiny for example, $K_1$ is the deterministic matrix};  \\
%\vspace{0.1cm}
%\hspace{0.55cm} $\vec{d}_i$ is the block vector for $i$th PC coefficients of displacement for all the nodes; \\
%\vspace{0.1cm}
%\hspace{0.55cm} $\vec{f}_i$ is the block vector for $i$th PC coefficients of forcing for all the nodes; \\
%\vspace{0.1cm}
%\hspace{0.55cm} Size of the global matrix is $(N \times P_3) \times (N \times P_3)$, $N$ is the number of deterministic DOFs; \\
%
%}
%}
%
%\begin{flushright}
%\tiny
%\hyperlink{3D_matrix}{\beamergotobutton{}}
%\end{flushright}
%
%
%\end{frame}


%\begin{frame}{Size of the stochastic stiffness matrix}
%\begin{itemize}
%
%\item Governed by:
%\begin{itemize}
%\item PC dimension $\rightarrow$ function of correlation length
%\item PC order $\rightarrow$ function of COV
%\end{itemize}
%
%\begin{small}
%
%\begin{table}
%\begin{center}
%\begin{tabular}{|c|l|r|}
%\hline
%PC dimension           & Order of PC         & Size of Stiffness Matrix \\
% \hline \hline
%2                   & 1         & Real DOFs x 3 \\
%      & 2  & x 6 \\
%      & 4         & x 15 \\
% \hline
%4      & 1         & Real DOFs x 5 \\
%      & 2  & x 15 \\
%                    & 4         & x 70 \\
% \hline
%6      & 1         & Real DOFs x 7 \\
%      & 2  & x 28 \\
%                    & 4         & x 210 \\
% \hline
%\end{tabular}        
%\end{center}
%\end{table}
%
%\end{small}
%
%\end{itemize}
%\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection[Constitutive update]{Intrusive constitutive update}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Stochastic Elastic-Plastic Response}

\begin{flushleft}
Governing equation: $d\sigma_{ij} = E_{ijkl} d\epsilon_{kl}$
\end{flushleft}
    
%\vspace*{-1.0truecm}

    \begin{eqnarray}
    \nonumber
     E_{ijkl} = \left\{\begin{array}{ll}
%
     E^{el}_{ijkl}
%
%
        \;\;\; & \mbox{\large{~for elastic}} \\
%
           \\
%
           E^{el}_{ijkl}
           -
           \displaystyle \frac{E^{el}_{ijmn} m_{mn}  n_{pq}  E^{el}_{pqkl}}
           { n_{rs} E^{el}_{rstu} m_{tu}
           -
           \xi_* h_* }

           \;\;\; & \mbox{\large{~for elastic--plastic}}
%
           \end{array} \right.
           \end{eqnarray}

%\footnotesize{If the material properties ($D^{el}$, $f$, $U$, $q_*$, and $r_*$) are uncertain, then the above equation becomes a nonlinear SDE with random coefficients!}

\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Zero-Elastic Region Material}
% \footnotesize
% Assume material with zero-elastic region, the general form reduces to elastic-plastic steps only:
%  
% \begin{eqnarray}
%     \nonumber
%      D_{ijkl} = D^{el}_{ijkl} - 
%            \displaystyle \frac{ D^{el}_{ijmn}
%            \displaystyle \frac{\partial U}{\partial \sigma_{mn}}
%            \displaystyle \frac{\partial f}{\partial \sigma_{pq}}
%            D^{el}_{pqkl} }
%            {\displaystyle \frac{\partial f}{\partial \sigma_{rs}}
%            D^{el}_{rstu}
%            \displaystyle \frac{\partial U}{\partial \sigma_{tu}}
%            -
%            \displaystyle \frac{\partial f}{\partial q_*}r_*}    
% %           \;\;\; & \mbox{\large{~for elastic--plastic}} 
% \end{eqnarray} 
% 
% For 1D von-Mises material with Armstrong-Frederick hardening, the above equation simplifies to:
% 
% \begin{equation}
% \nonumber
% E=H_a \pm C_r \sigma
% \end{equation} 
% where $h_a$ and $C_r$ are the two material parameters. Use + sign for positive incremental strain; use - sign for negative incremental strain. 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}{zero-elastic von-Mises material with Armstrong-Frederick hardening}
% \footnotesize
% The incremental stress can be updated as:
% \begin{equation}
% \nonumber
% \Delta \sigma=H_a \Delta \epsilon \pm  C_r \sigma \Delta \epsilon
% \end{equation}  
% \begin{figure}
% \includegraphics[scale=0.3]{Fangbo_figs/constitutive_pureAF_deterministic_ha6e7_Cr600}
% \caption{\scriptsize hysteretic behavior of material using $H_a=6e7, C_r=600$}
% \end{figure}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}{Stochastic Galerkin projection at local level}
% 
% Represent uncertain material parameters $H_a, C_r$ with PC:
% \begin{equation*} 
% H_a(x)= \displaystyle \sum_{i=1}^{P_3} H_{a_i}(x) \Psi_i(\left\{\xi_r(\theta)\right\})      
% \end{equation*}
% \begin{equation*} 
% C_r(x)= \displaystyle \sum_{i=1}^{P_3} C_{r_i}(x) \Psi_i(\left\{\xi_r(\theta)\right\})      
% \end{equation*}
% 
% Apply stochastic Galerkin projection to get PC coefficients of $E$ and $\Delta \sigma$:
% \begin{align*}
% \Delta \sigma_i(x,t) & =\frac{ H_{a_j} \Delta \epsilon_l \langle \Psi_i \Psi_j \Psi_l \rangle 
% \pm 
% C_{r_j} \sigma_k \Delta \epsilon_l \langle \Psi_i \Psi_j \Psi_k \Psi_l \rangle }{\langle \Psi_i^2 \rangle} \\
% E_i(x,t) & =H_{a_i} \pm C_{r_j} \sigma_k \langle \Psi_i \Psi_j \Psi_k \rangle \mathbin{/} \langle \Psi_i^2 \rangle \\
% \end{align*}
% 
% 
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{frame}{Application of FP equation to material models}
%
%\begin{itemize}
%\item FP eq. is applicable to any material models
%\item Different material models $\rightarrow$ different $N_{ab}^{(1)}$ and $N_{abcd}^{(2)}$
%\end{itemize}
%
%\begin{equation}         
%\nonumber
%\frac{\partial P(\sigma_{ij},t)}{\partial t} = -\frac{\partial}{\partial \sigma_{ab}}\left[N_{ab}^{(1)}P(\sigma_{ij},t)-\frac{\partial}{\partial \sigma_{cd}}
%\left\{N_{abcd}^{(2)} P(\sigma_{ij},t)\right\} \right]
%\end{equation}
%
%Salient Features:
%
%\begin{itemize}
%
%\item Nonlinear SDE in real space to Linear PDE in probability density space $\rightarrow$ simplifies the numerical solution process
%\vspace*{0.1truecm}
%\item Complete probabilistic description of response $\rightarrow$ joint PDF
%\vspace*{0.1truecm}
%\end{itemize}
%
%
%\end{frame}

%\begin{frame}{Linearize the FP eq. to update tangent stiffness PC coefficients as the material plastifies}
%
%\begin{itemize}
%\item Linearized form of the FP eq.:
%\begin{equation}
%\nonumber         
%\frac{\partial P^{lin}(\sigma_{ij},t)}{\partial t} = - N_{(1)_{ab}}^{lin} \frac{\partial P(\sigma_{ij},t)}{\partial \sigma_{ab}} + N_{(2)_{mnab}}^{lin} \frac{\partial^2 P(\sigma_{ij},t)}{\partial \sigma_{mn} \sigma_{ab}} 
%\end{equation}
%where $N_{(1)_{ab}}^{lin}$ and $N_{(2)_{mnab}}^{lin}$ are functions of statistics of material parameters expressed in terms of PC coefficients
%
%\item Update the PC coefficients as material plastifies by solving an over-determined residual system of eqs.:
%\begin{equation}
%\nonumber
%\frac{\partial P^{lin}(\sigma_{ij}, t)}{\partial t} - \frac{\partial P(\sigma_{ij}, t)}{\partial t} =0
%\end{equation}
%
%\end{itemize}
%
%\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{High Performance Computing}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Course and Fine Grained HPC}


\begin{itemize}

 \vspace*{2mm}
 \item Hardware Aware Plastic Domain Decomposition (HAPDD) Method


 \vspace*{2mm}
 \item Small Tensor Library 

\end{itemize}

\begin{figure}[!Htbp]
\begin{center}
\hspace*{-5mm}
 \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Exit_Seminar_slides/img_slides_yuan_exit_seminar/1_speedup_analysis.jpg}
\end{center}
\end{figure}





\end{frame}


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

\begin{figure}[!Htbp]
\begin{center}
\hspace*{-5mm}
 \includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_14-15Mar2019/present/HAPDD01.jpg}
\end{center}
\end{figure}


\end{frame}

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

\begin{figure}[!Htbp]
\begin{center}
\hspace*{-5mm}
 \includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_14-15Mar2019/present/HAPDD02.jpg}
\end{center}
\end{figure}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Small Tensor Library}

\begin{figure}[!Htbp]
\begin{center}
\hspace*{-5mm}
 \includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_14-15Mar2019/present/Small_tensor_lib_01.jpg}
\end{center}
\end{figure}


\end{frame}











































%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Modeling and Simulation Examples}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seismic Motions}




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{ESSI: 6C or 1C Seismic Motions}
% 
% 
% \begin{itemize}
% 
% 
% \item Assume that a full 6C (3C) motions at the surface are only recorded in one
% horizontal direction
% 
% 
% \item  From such recorded motions one can develop a vertically propagating shear
% wave (1C) in 1D
% 
% \item  Apply  such  vertically propagating shear wave to 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{6C Free Field Motions (closeup)}
% 
% 
%   
% %\vspace*{-2mm}
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% \movie[label=show3,width=80mm,poster,showcontrols]
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% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% \end{center}
% 
% \begin{flushleft}
% \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}
%   {\tiny (MP4)}
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% 
% 
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1C vs 6C Free Field Motions}
% 
% 
% 
%  
% \begin{itemize}
% 
%   \item One component of motions (1D) from  3D
% %  or 3$\times$1D (it is done all the time!)
% 
%   \item  Excellent fit
% %  (goal is to predict and inform and not (force) fit)
% 
% 
% \end{itemize}
% 
% 
% 
% 
% % local
% %\vspace*{-2mm}
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% %
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% %  
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{1D vs 3$\times$1D vs 3D Seismic Motions}
% % 
% % 
% % \begin{itemize}
% % 
% % \vspace{2mm}
% %  \item 1D is required by the code
% % 
% % \vspace{4mm}
% %  \item 3$\times$1D can be used depending on frequency/wave length of interest, 
% % 
% % \vspace{4mm}
% %  \item 3D is more realistic, however it is challenging to define motions in full 3D
% % 
% % \end{itemize}
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 
% % 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{When to  use  3D and/or 3$\times$1D}
% % 
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % %
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% %  \frametitle{Free Field 3D vs 1D Convolution From Base Point}
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% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/motion_compare_surface_ax.pdf}
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% %  \frametitle{3D vs 3$\times$1D vs 1D, Top of SMR}
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% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/point1Ax.pdf}
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%   {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
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\begin{frame}
\frametitle{Seismic Motions}


%\vspace*{-10mm}  

\begin{itemize}

\item Variation in  inclination, frequency, energy, duration...

\item Deterministic and Probabilistic

\item Stress test the soil-structure system

\end{itemize}


\vspace*{10mm}  



%\vspace*{-4mm}  
\begin{figure}[!htb]
\begin{flushleft}
\hspace*{-5mm}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{flushleft}
\end{figure}


% 
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% \begin{figure}[!htb]
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% \includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
% \hspace*{-5mm}
% \end{flushright}
% \end{figure}


\hspace*{10mm}  
\vspace*{-35mm}  
\begin{figure}[!htb]
\begin{flushright}
\includegraphics[width=6cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
\hspace*{-5mm}
\end{flushright}
\end{figure}




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%   

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\frametitle{Free Field, Variation in Input Frequency, $\theta = 60^{o}$}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/Free_Field_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
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\begin{frame}

\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
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\begin{frame}

%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, Variation in Input Frequency, REAL TIME}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR-ESSI_real_time_four_freq.mp4}
\end{center}
        
% online   
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\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR-ESSI_real_time_four_freq.mp4}
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\begin{frame}

%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, 3C vs 3$\times$1C}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Free Field vs ESSI - Different Frequencies}
% 
% 
% \begin{textblock*}{8cm}(1.0cm,2.5cm) % {block width} (coords) 
%    \scriptsize Acceleration response - Surface center point A
% \end{textblock*}
% \begin{textblock*}{2cm}(0.2cm,4cm) % {block width} (coords) 
%    \tiny X direction
% \end{textblock*}
% \begin{textblock*}{2cm}(0.2cm,6.3cm) % {block width} (coords) 
%    \tiny Z direction
% \end{textblock*}
% \begin{textblock*}{3cm}(2.4cm,7.6cm) % {block width} (coords) 
%    \tiny  (a) $f=1Hz \ \ \theta=60^{o}$
% \end{textblock*}
% \begin{textblock*}{3cm}(5.6cm,7.6cm) % {block width} (coords) 
%    \tiny  (b) $f=5Hz \ \ \theta=60^{o}$
% \end{textblock*}
% \begin{textblock*}{3cm}(8.8cm,7.6cm) % {block width} (coords) 
%    \tiny  (c) $f=10Hz \ \ \theta=60^{o}$
% \end{textblock*}
% 
% \vspace*{-30mm}
%   \begin{figure}[!H]
%     \centering
%      % \begin{flushleft}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_ax.pdf}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_ax.pdf}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_ax.pdf}
%       \\
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_az.pdf}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_az.pdf}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_az.pdf}
%     % \end{flushleft}
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%      \hspace*{30mm}
%        \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/Points_configuration.pdf}
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\subsection{Plastic Energy Dissipation}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Energy Input and Dissipation}

\begin{itemize}

\vspace*{1mm}
     \item[] Energy input, dynamic forcing


\vspace*{4mm}
     \item[] Energy dissipation outside SSI domain:
       \begin{itemize}
         \item[] SSI system oscillation radiation
         \item[] Reflected wave radiation
       \end{itemize}
%\vspace*{1mm}
     \item[] Energy dissipation/conversion inside SSI domain:
       \begin{itemize}
         \item[] Inelasticity of soil, contact zone, structure, foundation, dissipators
         \item[] Viscous coupling with internal/pore fluids, and external fluids
% %         \item[] potential and kinetic energy
%          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



%\vspace*{1mm}
%   \item[] Numerical energy dissipation (numerical damping/production and period  errors)
%   \item[] Numerical energy dissipation (damping/production)
   \item[] Numerical energy dissipation/production


\end{itemize}

%
\end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
\frametitle{Plastic Energy Dissipation}


\vspace*{2mm}
 
 Single elastic-plastic element under cyclic shear loading
 
\begin{itemize}
\item[] Difference between plastic work and plastic dissipation
\item[] Plastic work can decrease
\item[] Plastic dissipation always increases
\end{itemize}
 
%\vspace*{-7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
  
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation Control Mechanisms}
% 
% \begin{figure}[!H]
% %\hspace*{-10mm}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
% \end{figure}
% 
% 
% % \hspace*{10mm} Numerical  \hspace*{20mm}  Viscous  \hspace*{20mm} Plasticity 
%  \hspace*{10mm} Plasticity \hspace*{20mm}  Viscous  \hspace*{20mm} Numerical
% 
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% \end{frame}
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\begin{frame}

\frametitle{Energy Dissipation Control}

\begin{figure}[!H]
%\hspace*{-10mm}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
     \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
\end{figure}




\end{frame}

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




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\begin{frame}
 \frametitle{Inelastic Modeling of Soil Structure Systems}

\begin{itemize}

%\vspace*{1mm}
     \item Soil, inelastic, elastic-plastic
       \begin{itemize}
         \item[] Dry, single phase
         \item[] Unsaturated, partially saturated
         \item[] Fully saturated
       \end{itemize}


%\vspace*{1mm}
     \item Contact, inelastic, soil/rock -- foundation
       \begin{itemize}
         \item[]  Dry,  single  phase,  
           \begin{itemize}
             \item[]  Normal, hard  and  soft, gap open/close
             \item[]  Friction, nonlinear
           \end{itemize}
         \item[] Fully saturated, suction, excess pressure, buoyant force
       \end{itemize}


%\vspace*{1mm}
     \item Structure, inelastic, damage, cracks
       \begin{itemize}
         \item[] Nonlinear/inelastic 1D reinforced concrete fiber beam
         \item[] Nonlinear/inelastic 3D reinforced concrete solid element
         \item[] Alcali Silica Reaction concrete modeling
       \end{itemize}


%%\vspace*{1mm}
%     \item Fluid-Solid interaction (open surface)



\end{itemize}

%
\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{NPP Model }
% 
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
%   \end{center}
% %  \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%   \end{figure}
% 
% 
% % \begin{tikzpicture}[remember picture,overlay]
% %     \node[xshift=3.5cm,yshift=-0.6cm] at (current page.center) {\includegraphics[width=0.5\textwidth]{images/Contact_In_Industry}};
% % \end{tikzpicture}
% 
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Structure Model}
% 
%  The nuclear power plant structure comprise of
%  \begin{itemize}
%   \item Auxiliary building, $f^{aux}_{1}= 8Hz$
%   \item Containment/Shield building, $f^{cont}_{1}= 4Hz$
%   \item Concrete raft foundation: $3.5m$ thick
%  \end{itemize}
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=0.8\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Model_Auxiliary_And_Containment_Building.pdf}
%   \end{center}
%   \caption{\label{Fig:NPP_Structure_Model_In_Real_ESSI} Auxiliary and Containment Building }
%   \end{figure}
% 
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}

 \frametitle{Inelastic Soil and Inelastic Contact}

 \begin{itemize}
  \item Shear velocity of soil $V_s=500m/s$
  \item Undrained shear strength (Dickenson 1994) $V_s [m/s] = 23 (S_u [kPa])^{0.475}$
  \item For $V_s=500m/s$ Undrained Strength $S_u=650kPa$ and Young's Modulus of $E=1.3GPa$
  \item von Mises, Armstrong Frederick kinematic hardening
  ($S_u=650kPa$ at $\gamma=0.01\%$; $h_a = 30MPa$, $c_r = 25$)
  \item Soft contact (concrete-soil), gaping and nonlinear shear
  \end{itemize}

 \begin{figure}[!h]
 \begin{center}
  \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Von_Mies_non_Linear_Hardening.pdf}
  \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/SoftContact.pdf}
 \end{center}
  \end{figure}


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Acc. Response, Top of Containment Building}
% 
%  \begin{figure}[!h]
%  \begin{center}
% \hspace*{-8mm}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% \\
% \hspace*{-8mm}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Z.pdf}
% % \caption{\label{Fig:Response_of_Top_of_Containment_Building} Seismic Response at Top of Containment Building}
%  \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
%  
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

 \frametitle{Acceleration Traces, Elastic vs Inelastic }


\hspace*{-35mm}
  \begin{figure}[!h]
  \vspace*{-2mm}
  \begin{center}
  \hspace*{-15mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
  \hspace*{-20mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
  \hspace*{-25mm}
  \end{center}
 \end{figure}
\hspace*{-35mm}

\hspace*{10mm} Elastic  \hspace*{40mm} Inelastic \hspace*{40mm} 

\end{frame}

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


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

 
 \frametitle{Displacement Traces, Elastic vs Inelastic}
 
\hspace*{-35mm}
  \begin{figure}[!h]
  \vspace*{-2mm}
  \begin{center}
  \hspace*{-15mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Elastic_Without_Contact_SMIRT_2017.pdf}
  \hspace*{-20mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Inelastic_With_Contact_SMIRT_2017.pdf}
  \hspace*{-25mm}
  \end{center}
 \end{figure}
\hspace*{-35mm}

\hspace*{10mm} Elastic  \hspace*{40mm} Inelastic \hspace*{40mm} 

\end{frame}
 
 

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



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

\frametitle{Elastic and Inelastic Response: Differences}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.mp4}
\end{center}



\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linear_Effects_Sumeet.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%


\end{frame}

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


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

\frametitle{Energy Dissipation in a Large-Scale Model}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}




\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%



\end{frame}

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

   
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation for a SMR}
% 
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
% 
%      
% % \vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% %\movie[label=show3,width=9cm,poster,autostart,showcontrols]
% \movie[label=show3,width=10cm,poster,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/Nonlinear_Analysis_of_ESSI_for_SMR/SMR_Energy_Dissipation_screen_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mpg}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_16Aug2017/SMR_Energy_Dissipation.mp4}
% \end{center}
% 
%  
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
% 
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


















% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction as Base Isolation, Model}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_04.jpg}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Wave Propagation}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_01.jpg}
% \end{center}
% \end{figure}
% 
% \hspace*{40mm} Dry  \hspace*{10mm} Liquefied \hspace*{40mm} 
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Stress-Strain Response}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_03.jpg}
% \end{center}
% \end{figure}
% 
% \hspace*{40mm} Dry  \hspace*{10mm} Liquefied \hspace*{40mm} 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Dissipation for Design}

\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/2D_Frame_Model.pdf}
\end{center}
\end{figure}


\end{frame}






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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Design Alternatives}


% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation_screen_grab.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation_screen_grab.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation.mp4}
\hspace*{-16mm}
\end{center}
% local


% online % online
% online \begin{center}
% online \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}
% online {\tiny (MP4)}
% online %
% online \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}
% online  {\tiny (MP4)}
% online \end{center}
% online % online





\end{frame}






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




\begin{frame}
 
 \frametitle{Wall, Regular and ASR Concrete}

%\vspace{-5mm}

   \begin{figure}[!h]
    \begin{center}
\hspace*{-15mm}
     \includegraphics[width=2truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Rebar_Plan.pdf}
     \includegraphics[width=4truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/3D_mesh.pdf}
\includegraphics[width=2.8truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Reg_A_Force_Displacement.pdf}
\includegraphics[width=2.8truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/ASR_A1_Force_Displacement.pdf}
\hspace*{-15mm}
    \end{center}
\end{figure}


\vspace{-2mm}
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_Natural_Hazartd_Oct2018/Present/OECD_wall_damage_3_stages.jpg}
\end{center}
\end{figure}



% \vspace{-20mm}
% \begin{figure}[!htbp]
% \hspace*{-10mm}
% \begin{center}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_3000.pdf}
% \hspace*{-5mm}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_5000.pdf}
% \hspace*{-5mm}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_10000.pdf}
% \end{center}
% \end{figure}
% 
% 
% \vspace*{-5mm}
% \hspace*{12mm}
% \begin{footnotesize}
% $u_y$ = 1.4 mm
% \hspace{12mm}
% $u_y$ = 1.8 mm
% \hspace{12mm}
% $u_y$ = 3.0 mm
% \end{footnotesize}
  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Reinforced Concrete Wall, Evolution of Plastic Dissipation}
% 
% 
%  
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% \movie[label=show3,width=90mm,poster,showcontrols]
%   {\includegraphics[width=90mm]{/home/jeremic/tex/works/Conferences/2018/ENSI_meeting_Brugg_18May2018/Present/Shear_wall_frame.jpg}}{/home/jeremic/tex/works/Thesis/HanYang/Shear_Wall_Presentation_26Apr2018/Presentation/Figures/Shear_Wall_Plastic_Dissipation.mp4}
% \end{center}
%  
% % \begin{flushleft}
% % \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_01AApr2015/movie_input_closeup.mp4}
% % %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% %   {\tiny (MP4)}
% % \end{flushleft}
% % %
% 
% 
% % 
% % 
% % \vspace*{-3mm}
% % \begin{center}
% % % \hspace*{-15mm}
% % \includemedia[width=\linewidth,height=0.6\linewidth,activate=pageopen,addresource=/home/jeremic/tex/works/Thesis/HanYang/Shear_Wall_Presentation_26Apr2018/Presentation/Figures/Shear_Wall_Plastic_Dissipation.mp4,
% % flashvars={source=/home/jeremic/tex/works/Thesis/HanYang/Shear_Wall_Presentation_26Apr2018/Presentation/Figures/Shear_Wall_Plastic_Dissipation.mp4&autoPlay=true&loop=true}]{VPlayer.swf}
% % \end{center}
% %   
% 
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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

\begin{frame}

\frametitle{Buoyant Force Simulation}

\begin{figure}[!H]
\hspace*{-20mm}
     \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/upU_element_type_annotation.pdf}
     \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}
\hspace*{-20mm}
\end{figure}

% -  %
% -  % \begin{tikzpicture}[remember picture,overlay]
% -  %    \node[anchor=south west,inner sep=0pt] at ($(current page.south west)+(7.5cm,2.5cm)$) {
% -  %      \includegraphics[width=0.4\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}};
% -  % \end{tikzpicture}
% -
% -  %  \vspace{-1.4cm}
%  \begin{itemize}
%   \item \scriptsize Upward structural displacement under buoyant force
%  \end{itemize}
\end{frame}



%

     

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Solid, Structure-Fluid Interaction: gmFoam}
 \begin{columns}[T]
 \begin{column}{.65\textwidth}
 \begin{itemize}
%  \vspace{-0.4cm}
  \item[] Mesh separation
   \begin{itemize}
     \item[] integrated geometry model %(solid \& fluid) based on gmsh
     \item[] FEM \& FVM mesh conversion
     \item[] handle discontinuous mesh  
   \end{itemize}
  \item[] Incorporate gmESSI
%     \begin{itemize}
%      \item[] conveniently set BCs
%      \item[] input files easy generation
%     \end{itemize}
  \item[] Interface geometry extraction  

  \item[] Interface class \textbf{SSFI} in Real-ESSI 
%     \begin{itemize}
%      \item[] interface geometrical mapping
%      \item[] handle different mesh size
%      \item[] BCs interpolation \& updating 
%      \item[] boundary mass conservation iteration 
%     \end{itemize}
  \item[]  Real-ESSI $\leftrightarrow$ SSFI $\leftrightarrow$ OpenFoam 
%  \item[] Shepherd method
%   \begin{itemize}
%    \item[] Real-ESSI $\Longleftrightarrow$ SSFI $\Longleftrightarrow$ OpenFoam
%    \item[] explicit transient algorithm
%    \item[] handle different time step length
%   \end{itemize} 


 \end{itemize}
 \vspace{0.2cm}
% \scriptsize gmFoam: https://github.com/hexiang6666/gmFoam
 \end{column}
 \begin{column}{.35\textwidth}
 \vspace{-1cm}
   \begin{figure}[!H]
    \begin{center}
     \includegraphics[width=\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_08June2017/pic/gmFoam.pdf}
    \end{center}                       
   \end{figure}
 \end{column}
 \end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
%  \begin{frame}
%   \frametitle{Semi-Coupled Solid Fluid Interaction}
%   \begin{itemize}
%    \item[] Utilize VOF implemented in interFoam
%    \setbeamertemplate{itemize items}[circle]
%     \begin{itemize}
%     \item[] avoid tracking free surface
%     \item[] relatively fixed BCs
%     \item[] relatively fixed background mesh
%     \end{itemize}
%   \end{itemize}
%   \vspace{-0.3cm}
%   \begin{itemize}
%   \item[] Interface class \textbf{SSFI} added in Real-ESSI 
%     \setbeamertemplate{itemize items}[circle]
%     \begin{itemize}
%     \item[] interface geometrical mapping
%     \item[] handle different mesh size
%     \item[] BCs interpolation \& updating 
%     \item[] boundary mass conservation iteration 
%     \end{itemize}
%   \end{itemize}
%   \vspace{-0.3cm}
%   \begin{itemize}
%    \item[] Shepherd method
%     \setbeamertemplate{itemize items}[circle]
%     \begin{itemize}
%     \item[] Real-ESSI $\Longleftrightarrow$ SSFI $\Longleftrightarrow$ InterFoam
%     \item[] explicit transient algorithm
%     \item[] handle different time step length
%     \end{itemize} 
%   \end{itemize}
%  
%  \end{frame}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{Semi-Coupled Solid Fluid Interaction}
%   Implemented in Real-ESSI based on explicit transient algorithm
%   \begin{figure}[!H]
%    \begin{center}
%      \includegraphics[width=.5\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_08June2017/pic/No_SSFI.pdf}\enspace
%      \includegraphics[width=0.5\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_08June2017/pic/SSFI.pdf}\enspace
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%   \quad \href{http://cml08.engr.ucdavis.edu/for_professor/fluid_model_simulation.mp4}{Water Break without SFI}\quad \quad \quad \quad \quad \href{http://cml08.engr.ucdavis.edu/for_professor/Solid_Fluid_Interaction.mp4}{Box Sloshing with SFI}
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\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
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% \vspace*{1mm}
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% \vspace*{6mm}
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%          \item Reflected wave radiation
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% \vspace*{1mm}
%      \item[] Energy dissipation/conversion inside SSI domain:
%        \begin{itemize}
%          \item Inelastic soil, contacts, structure, foundation, dissipators
%          \item Viscous coupling with internal and external fluids
% % %         \item[] potential and kinetic energy
% %          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
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% %   \item[] Numerical energy dissipation (numerical damping/production and period  errors)
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% %  %$d W_p = \sigma_{ij} \, d\epsilon_{ij}^{pl}$
% %  }
% %   
% %  \begin{itemize}
% %  \item Negative incremental energy dissipation
% %  %\item Plastic work is NOT plastic dissipation
% %  \end{itemize}
% %   
% %  \begin{figure}[!H]
% %  \begin{center}
% %  \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem.png}
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% 
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% %\begin{itemize}
% %\item[] Difference between plastic work and plastic dissipation
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% %\item[] Plastic work can decrease, plastic dissipation always increases
% Plastic work can decrease, plastic dissipation always increases
% %\end{itemize}
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% %\vspace*{-7mm}
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{-5mm}
% \includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
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% %  % \item Direct violation of the second law of thermodynamics
% %  % % \item Where is the problem?
% %  % \item Missing is the plastic free energy
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% %  \item Multi-scale effect of particle interlocking/rearrangement
% %  \item Strain energy on particle level
% %  \end{itemize}
% %   
% %  \begin{figure}[!h]
% %  \begin{center}
% %  \includegraphics[width=7truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Plastic_Free_Energy.png}
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% %   
% %  \frametitle{Energy Transformation in Elastic-Plastic Material}
% %   
% %  \begin{figure}[!H]
% %  \begin{center}
% %  \includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Energy_Transformation.png}
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%      \includegraphics[width=3.0cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
%      \includegraphics[width=3.0cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
%      \includegraphics[width=3.0cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
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% % \hspace*{10mm} Numerical  \hspace*{20mm}  Viscous  \hspace*{20mm} Plasticity 
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% %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
% %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
%      \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
% %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
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% % \frametitle{Energy Dissipation Control}
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% % \begin{figure}[!H]
% % %\hspace*{-10mm}
% % %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
% % %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
% %      \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
% % %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
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% %   \frametitle{Inelastic Modeling for NPP Soil Structure System}
% %  
% %  \begin{itemize}
% %  
% %  %\vspace*{1mm}
% %       \item Soil elastic-plastic
% %         \begin{itemize}
% %           \item Dry, single phase
% %           \item Unsaturated (partially saturated)
% %           \item Fully saturated
% %         \end{itemize}
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% %  
% %  %\vspace*{1mm}
% %       \item Contact, inelastic, soil/rock -- foundation
% %         \begin{itemize}
% %           \item  Dry,  single  phase,  Normal  (hard  and  soft, gap open/close),
% %                  Friction (nonlinear)
% %           \item Fully saturated, suction and excess pressure (buoyant force)
% %         \end{itemize}
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% %  
% %  %\vspace*{1mm}
% %       \item Structural inelasticity/damage
% %         \begin{itemize}
% %           \item Nonlinear/inelastic fiber beams
% %           \item Nonlinear/inelastic reinforced concrete walls. plates, shells
% %           \item Alcali Silica Reaction concrete modeling
% %         \end{itemize}
% %  
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% %  %     \item Fluid-Solid interaction (open surface)
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%  \frametitle{Nuclear Power Plant Model }
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%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
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% %  \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
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% % \begin{tikzpicture}[remember picture,overlay]
% %     \node[xshift=3.5cm,yshift=-0.6cm] at (current page.center) {\includegraphics[width=0.5\textwidth]{images/Contact_In_Industry}};
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% % \begin{frame}
% % 
% %  \frametitle{Structure Model}
% % 
% %  The nuclear power plant structure comprise of
% %  \begin{itemize}
% %   \item Auxiliary building, $f^{aux}_{1}= 8Hz$
% %   \item Containment/Shield building, $f^{cont}_{1}= 4Hz$
% %   \item Concrete raft foundation: $3.5m$ thick
% %  \end{itemize}
% %   \begin{figure}[!h]
% %   \begin{center}
% %    \includegraphics[width=0.8\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Model_Auxiliary_And_Containment_Building.pdf}
% %   \end{center}
% %   \caption{\label{Fig:NPP_Structure_Model_In_Real_ESSI} Auxiliary and Containment Building }
% %   \end{figure}
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% 
% \begin{frame}
% 
%  \frametitle{Inelastic Soil and Inelastic Contact}
% 
%  \begin{itemize}
%   \item Shear velocity of soil $V_s=500m/s$
%   \item Undrained shear strength (Dickenson 1994) $V_s [m/s] = 23 (S_u [kPa])^{0.475}$
%   \item For $V_s=500m/s$ Undrained Strength $S_u=650kPa$ and Young's Modulus of $E=1.3GPa$
%   \item von Mises, Armstrong Frederick kinematic hardening
%   ($S_u=650kPa$ at $\gamma=0.01\%$; $h_a = 30MPa$, $c_r = 25$)
%   \item Soft contact (concrete-soil), gaping and nonlinear shear
%   \end{itemize}
% 
%  \begin{figure}[!h]
%  \begin{center}
%   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Von_Mies_non_Linear_Hardening.pdf}
%   \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/SoftContact.pdf}
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% % \begin{frame}
% % 
% %  \frametitle{Simulation Result}
% % 
% %  \begin{figure}[!h]
% %  \begin{center}
% % %\subfigure[Selected Locations
% % %  \label{Specific_Locations}]
% % {\includegraphics[width=0.45\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Selected_Location_For_Study.pdf}}
% % %\subfigure[Total Displacement
% % %  \label{Total_Displacement}]
% % {\includegraphics[width=0.40\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Total_Displacement_Z.pdf}}
% %  \end{center}
% % % \caption{\label{Fig:NPP_Selected_Location_For_Study} Locations selected to study non-linear effects and plot of total displacement at center of model}
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% %  \begin{figure}[!h]
% %  \begin{center}
% % \hspace*{-8mm}
% %   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
% %   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
% %   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% % \\
% % \hspace*{-8mm}
% %   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
% %   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
% %   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Z.pdf}
% % % \caption{\label{Fig:Response_of_Top_of_Containment_Building} Seismic Response at Top of Containment Building}
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%    \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
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%    \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
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% % \hspace*{-15mm}
% \movie[label=show3,width=10cm,poster,autostart,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
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% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
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% % \movie[label=show3,width=10cm,poster,autostart,showcontrols]
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% % {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% % \end{center}
% % 
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% % \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
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% %    \begin{figure}[!h]
% %     \begin{center}
% %      \includegraphics[width=2truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Rebar_Plan.pdf}
% %      \includegraphics[width=4truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/3D_mesh.pdf}
% % \includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Reg_A_Force_Displacement.pdf}
% % \includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/ASR_A1_Force_Displacement.pdf}
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% % % \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_5000.pdf}
% % % \hspace*{-5mm}
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% % % \end{center}
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% % % \begin{footnotesize}
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% % %OVDE dodaj link na online...
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\subsection{Uncertain Inelasticity}
%\section[1-D stochastic structural dynamic analysis]{1-D stochastic structural dynamic analysis}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
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\begin{frame}{Uncertain Stiffness}

\begin{columns}
\column{0.5\textwidth}
\vspace{-0.5cm}
\begin{figure}
\includegraphics[scale=0.4]{Fangbo_figs/four_story_building.pdf} 
\end{figure}
%\hspace{1.5cm} \footnotesize{Schematic model}

\column{0.5\textwidth}
{\footnotesize
{Lognormal random field for stiffness $\bar{k}$:} \\
Marginal mean: 9.84 MN/m \\
Marginal COV: 10\% \\
Correlation structure: \\
\vspace{0.2cm}
\hspace{0.5cm}
$ \begin{bmatrix}
1.0 & 0.6 & 0.3 & 0.2 \\
0.6 & 1.0 & 0.5 & 0.2 \\
0.3 & 0.5 & 1.0 & 0.7 \\
0.2 & 0.2 & 0.7 & 1.0 
\end{bmatrix}  $

PC rep: dimension 4 order 2
}

\end{columns}   

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\begin{frame}{Uncertain Motion}

\vspace{-0.4cm}
\begin{columns}
\column{0.35\textwidth}

\scriptsize
{
Uncertain bedrock seismic motion:
\begin{itemize}
\item Stochastic ground motion modeling
\item Marginal PDF: Gaussian $\rightarrow$ order 1
\item PC dimension 150 order 1 to quantify motion random process
\end{itemize}
}
\vspace{0cm} 
\flushleft  \scriptsize{PC synthesized statistics $\Longleftarrow$ of bedrock motion} 

\column{0.65\textwidth}

\vspace{-0.4truecm}
\begin{figure}
\includegraphics[scale=0.23]{Fangbo_figs/KL_mean_dis_from_dis_equal_scale.pdf}
\includegraphics[scale=0.23]{Fangbo_figs/KL_var_dis_from_dis.pdf}   \\
\tiny{(a) Displacement} \\

\includegraphics[scale=0.23]{Fangbo_figs/KL_mean_acc_from_acc_equal_scale.pdf}
\includegraphics[scale=0.23]{Fangbo_figs/KL_var_acc_from_acc.pdf}   \\
\tiny{(b) Acceleration} \\
\end{figure}

\end{columns}

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\begin{frame}{Uncertain Motion: Non-stationary Correlation Structure}

\hspace{2.0cm}     \underline{Displacement}    \hspace{2.0cm}  \underline{Acceleration}
\begin{figure}
\includegraphics[scale=0.25]{Fangbo_figs/KL_exact_dis_correlation_from_dis.pdf}    \hspace{1cm}
\includegraphics[scale=0.25]{Fangbo_figs/KL_exact_acc_correlation_from_acc.pdf}   \\
\end{figure}
\end{frame}


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\begin{frame}{Uncertain Response on Top}

\begin{columns}
\column{0.6\textwidth}
\begin{figure}
\includegraphics[height=3cm]{Fangbo_figs/dynamic_disp_linear_vs_nonlinear.pdf} \\
\includegraphics[height=3cm]{Fangbo_figs/dynamic_acc_linear_vs_nonlinear.pdf} \\
%\caption{\footnotesize Synthesized displacement and acceleration at the top of structure}
\end{figure}
\column{0.4\textwidth}
\begin{itemize}
\footnotesize
\item Smaller St.Dev. for nonlinear case
\item Magnitude of mean is negligible compared to standard deviation
\end{itemize}

\end{columns}
\end{frame}

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\begin{frame}{Evolution of Stress and Stiffness at Top Floor}

\begin{columns}
\column{0.6\textwidth}
\begin{figure}
\includegraphics[height=3cm]{Fangbo_figs/dynamic_stress_linear_vs_nonlinear.pdf} \\
\includegraphics[height=3cm]{Fangbo_figs/dynamic_stiffness_linear_vs_nonlinear.pdf} \\
%\caption{\footnotesize Synthesized displacement and acceleration at the top of structure}
\end{figure}
\column{0.4\textwidth}
\begin{itemize}
\footnotesize
\item Smaller St.Dev. of stress for nonlinear case
\item Larger St.Dev. of stiffness introduced by nonlinearity
\end{itemize}

\end{columns}
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\section{Conclusion}

\subsection{\ }


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% 
% 
% \begin{frame} 
% 
% \frametitle{Science Quotes}
% 
% \begin{itemize}
% 
% 
% \item Max  Planck: 
% "A    new    scientific  truth does not triumph by convincing  its opponents and
% making  them see the light, but rather because its opponents eventually die, and
% a  new  generation  grows  up  that  is familiar with it." (Science advances one
% funeral at a time)
% 
% 
%  \vspace*{3mm}
% 
% \item  Fran{\c c}ois-Marie Arouet,  Voltaire: 
% "Le doute n'est pas une condition agr{\'e}able, mais la certitude est absurde."
% 
%  \vspace*{3mm}
% 
% \item  Niklaus  Wirth:   
% "Software is getting slower more rapidly than hardware becomes faster."
% w
% \end{itemize}
% 
% 
% \end{frame}
% 
% 




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\begin{frame}
  \frametitle{Summary}

  \begin{itemize}

%    \item Importance   of   using  proper  models  correctly  (verification,
%    validation, level of sophistication)
%     
 
%    \item Reduction of modeling uncertainty 
%
\vspace*{1mm}
    \item Numerical modeling to predict and inform, rather than fit

%\vspace*{1mm}
%    \item Change of demand due to inelastic effects

%\vspace*{-1mm}
%      \begin{itemize}
%         \item Reduction of dynamic motions
%         \item Increase in deformations
%      \end{itemize}



\vspace*{1mm}
    \item  Sophisticated inelastic/nonlinear modeling and simulations need to be
    done carefully and in phases


\vspace*{1mm}
    \item Education and Training is the key!


\vspace*{1mm}
   \item     Collaborators:   Wang, Feng,  Yang,  Behbehani,  Sinha,  Wang,
   Pisan{\'o}, Abell, Yang, Cheng, Jie, Tafazzoli, Preisig, Tasiopoulou, Watanabe
   

\vspace*{1mm}
  \item  Funding  from  and  collaboration  with  the US-DOE, US-NRC, US-NSF, 
  CNSC-CCSN, UN-IAEA, and Shimizu Corp. is greatly appreciated,


\vspace*{1mm}
  \item \url{http://real-essi.info/}

      

\end{itemize}



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