\documentclass[fleqn]{beamer}
%\documentclass[handout]{beamer}
%\usepackage{pgfpages}
%\pgfpagelayout{2 on 1}[letterpaper, border shrink=5mm]

\mode<handout>{\setbeamercolor{background canvas}{bg=black!3}}

\usepackage{epstopdf}


\usepackage{multimedia}


%% 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}



%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
\input vuk.def
\newfont{\cyr}{wncyr10 scaled 1000 }
\newfont{\cyb}{wncyb10 scaled 1000 }
\newfont{\cyi}{wncyi10 scaled 1000 }
\newfont{\cysc}{wncysc10 scaled 1000 }
\newfont{\cyss}{wncyss10 scaled 1200 }
\newfont{\romjba}{cmss10 scaled 1000}
\newfont{\cyrjbnaslov}{wncyss10 scaled 1400 }



% % for not showing eq numbers unless eq is references
% \usepackage[fleqn,tbtags]{mathtools}
% \mathtoolsset{
%   showonlyrefs
%   }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FEI  LOGO definition
\newcommand{\FEI}
{{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}

% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % ovo je za cirilicu
% % \input vuk.def
% % %\newfont{\cyr}{wncyr10 scaled 1200}
% % %\newfont{\cyrimena}{wncyb10 scaled 1800}
% % %\newfont{\cyrnaslov}{wncyb10 scaled 2600}
% % %\newfont{\cyrpodnaslov}{wncyr10 scaled 1400}
%
% \newfont{\cyr}{wncyss10 scaled 1200}
% \newfont{\cyrimena}{wncyss10 scaled 2000}
% \newfont{\cyrnaslov}{wncyss10 scaled 2800}
% \newfont{\cyrpodnaslov}{wncyss10 scaled 1400}
%
% \newfont{\cyn}{wncyss10 scaled 2200}
% %% JB sig
% \newfont{\cyrjb}{wncyr10 scaled 600}
% \newcommand{\JB}
% {{\cyrjb \lower0.50ex\hbox{\uppercase{J}}\kern-.58em\hbox{\uppercase{B}}}}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\setbeamertemplate{navigation symbols}{}
\mode<presentation>
{
%  \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, 0.15, 0} % less intense green
\definecolor{webblue}{rgb}{0, 0, 0.15} % less intense blue
\definecolor{webred}{rgb}{0.15, 0, 0} % less intense red
%\usepackage[colorlinks=true,linkcolor=webblue,citecolor=webred,urlcolor=webgreen]{hyperref}

%\usepackage{html}
%\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.



\usepackage{hyperref}
% \hypersetup{
%   pdfmenubar=true,
%   pdftoolbar=true,
%   pdfpagemode={None}
% % % Commenting this out fixes Windows acrobat problem (?!)
% %              colorlinks=true,
% %              linkcolor=webblue,
% %              citecolor=webblue,
% %              urlcolor=webblue,
% }

\usepackage{pause}
% or whatever

% \usepackage[pdfauthor={Boris Jeremic},
%             colorlinks=true,
%             linkcolor=webblue,
%             citecolor=webblue,
%             urlcolor=webblue,
%             linktocpage,
%             pdftex]{hyperref}



             

\title[Fully Coupled FEM Analysis]
        {Fully Coupled FEM Analysis}


%\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)
%\institute[\pgfuseimage{university-logo}] % (optional, but mostly needed)
%%{ Professor, University of California, Davis\\
{\small University of California, Davis
\\
~
\\
~
\\
Tongji University \\
Liquefaction Workshop
% \\
%Underground Structures in Liquefiable Ground 
}
% %  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 01Nov2023 
%        \\ ~
%        \\ ~
%        \\ 
%        ~  \vspace*{8mm}
%%        \\ ~
%        \flushleft{\hspace*{-10mm}\framebox{\tiny please use google chrome to view this PDF 
%                                   so that animation links work }}
%        \lstinline|please use google chrome to view this PDF!
        }


\subject{}






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

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

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




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


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








\begin{document}

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

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

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

\begin{frame}
  \frametitle{Outline}

   \begin{scriptsize}
  \tableofcontents
% You might wish to add the option [pausesections]
   \end{scriptsize}
\end{frame}

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

% 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.



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



% %  Introduction to Seismic Ground Motions. Participants will learn
% % about and develop free field seismic ground motions from:
% %
% %
%   Ground motions from given surface motions.
%
%   Ground motions from small and regional scale models.
%
% Ground Motions for ESSI Modeling. Participants will learn
% about, apply and propagate ground motions through the soil-structure system:
%
%  Input ground motion into FEM model,
%
%  Application of ESSI ground motions.
%
%  Develop hierarchy of input ground motions: 1D, 3x1D and 3D.
%
%  Control ground motion frequency content.






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Inelastic, Coupled Analysis}
\section{Introduction}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection*{Real-ESSI Simulator System}
%\subsection{Analysis Features}
\subsection{\ }




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

\frametitle{Engineering Analysis}

    \begin{itemize}

     \item[-]  Improve analysis and design for infrastructure

\vspace*{3mm}
     \item[-] All ESSI problems are three dimensional, 3D

\vspace*{3mm}
     \item[-] Simplifying assumptions $\rightarrow$ epistemic uncertainty

%\vspace*{3mm}
%     \item[-] 

\vspace*{3mm}
     \item[-] Design and assessment of infrastructure

\vspace*{3mm}
     \item[-] Predict and inform!

\vspace*{3mm}
    \item[-]  Engineer needs to know!

    \end{itemize}



\end{frame}




  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Long Lasting Infrastructure}
% 
% 
% 
% \begin{itemize}
%  
% 
% %\vspace*{0.3cm}
%   \item[] 
%  
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{-10mm}
% \includegraphics[height=2.8truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Aya-Sofia_03_1990.jpg}
% %\includegraphics[height=2.8truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
% %\hfill
% \hspace*{10mm}
% \includegraphics[height=2.8truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/ZhaozhouBridge.jpg}
% \\
% \vspace*{2mm}
% \includegraphics[height=3.2truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Four_Water_Wheels_Hama_Syria.jpg}
% %\hfill
% \hspace*{10mm}
% \includegraphics[height=3.2truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Hoover_dam.jpg}
% %\hspace*{-10mm}
% %
% %\vspace*{3mm}
% \end{center}
% \end{figure}
% %\vspace*{3mm
% 
% %
% %  
% %  
% 
% % 
% % \includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
% % \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Kuca_Bajina_Basta-Drina.jpg}
% % \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Four_Water_Wheels_Hama_Syria.jpg}
% % %%\hspace*{2mm}
% % %\hspace*{2mm}
% % 
% % 
% 
% 
% \end{itemize}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   





     

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Prediction under Uncertainty}


\begin{itemize}




%\vspace*{1mm}
%  \item    \underline{Modeling, Epistemic Uncertainties}, 
  \item[-]    Modeling, Epistemic Uncertainties
  
      \begin{itemize}

\vspace*{1mm}
      \item[] Modeling simplifications

\vspace*{1mm}
      \item[] Low, medium, high  sophistication modeling and simulation

\vspace*{1mm}
      \item[] Modeling sophistication level for confidence in  results

\vspace*{1mm}
      \item[] Verification and Validation

    \end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{2mm}
%  \item   \underline{Parametric, Aleatory Uncertainties},  
  \item[-]  Parametric, Aleatory Uncertainties  

  \begin{itemize}

\vspace*{1mm}
    \item[] ${M}  \ddot{u_i}  +  {C}  \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$ 

\vspace*{1mm}
    \item[] Uncertain: mass $M$, viscous damping  $C$ and stiffness $K^{ep}$


\vspace*{1mm}
    \item[] Uncertain loads, $F(t)$


\vspace*{1mm}
    \item[] Results are PDFs   and   CDFs  for  $\sigma_{ij}$,  $\epsilon_{ij}$,  $u_i$,  $\dot{u}_i$,  $\ddot{u}_i$

  \end{itemize}




\end{itemize}



% 
% 
% %Le doute n'est pas un {\'e}tat bien agr{\'e}able,\\ 
%        mais l'assurance est un {\'e}tat ridicule.  (Fran{\c c}ois-Marie Arouet, Voltaire)



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


% 

 
   



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Engineer, Analyst}

\begin{itemize}



 
%\vspace*{0.3cm}
 \item[-] Educated, Trained, Experienced
   

%\vspace*{1mm}
%  \item[-] From simple to sophisticated modeling
   

%\vspace*{2mm}
% \item[-] Simplified analysis 

% 
\vspace*{2mm}
  \item[-] Sound engineering judgement

\vspace*{2mm}
 \item[-] Assess various analysis  sophistication levels

%  % 
%  \vspace*{2mm}
%   \item[-] Expert engineering analyst
%  
%  \vspace*{1mm}
%   \item[-] Credibility of developed models
%  % 
%  % 
%  % 
%  \vspace*{1mm}
%   \item[-] Confidence in and credibility of analysis results
%  % 
%  
\vspace*{2mm}
  \item[-] Engineer is in full control of the model and the analysis
   

\vspace*{2mm}
 \item[-] Engineer uses models to assess design options

% 

\vspace*{2mm}
 \item[-] Confidence in all modeling choices

\vspace*{2mm}
 \item[-] Confidence in all analysis results 

% %\vspace*{2mm}
% % \item[-] Confidence in all model components
% 
% \vspace*{2mm}
%  \item[-] Confidence in all analysis results


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Expert Analyst, Engineer}
% 
% 
% 
% \begin{figure}[!h]
% \begin{center}
% %\vspace*{-2.5cm}
% %\vspace*{-1.0cm}
% %\hspace*{-1.5cm}
% {\includegraphics[height=3.0cm]{/home/jeremic/tex/works/Conferences/2022/IFNFEES02_01-02Jul2022/present/Hartford-Coliseum-failure-01.jpg}}
% \hfill
% {\includegraphics[height=3.0cm]{/home/jeremic/tex/works/Conferences/2022/IFNFEES02_01-02Jul2022/present/Hartford-Coliseum-failure-03.jpg}}
% \hfill
% {\includegraphics[height=3.0cm]{/home/jeremic/tex/works/Conferences/2022/IFNFEES02_01-02Jul2022/present/Hartford-Coliseum-failure-02.jpg}}
% %\hspace*{-1.5cm}
% %\vspace*{-1.5cm}
% %\vspace*{-5.0cm}
% \end{center}
% \end{figure}
% 
% {\tiny Hartford Coliseum Collapse, 1978 (Martin and Delatte, ASCE-JPCF (2001))}
% 
% % \begin{itemize}
% % 
% %     
% % 
% % \end{itemize}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Analysis Program}

\begin{itemize}



 

%\vspace*{0.3cm}
  \item[-] Hierarchy of model sophistication capabilities
%  \item[-] Hierarchy, levels of modeling capabilities
   

\vspace*{3mm}
 \item[-] Hierarchy of simulation/algorithmic capabilities

% 

\vspace*{3mm}
 \item[-] Full Verification !

\vspace*{3mm}
 \item[-] Extensive Validation


\vspace*{3mm}
 \item[-] Confidence in analysis results


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






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{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/interface/joint elements: Bonded, Shear/Frictional; 
%  (EPP, EPH, EPS); 
Gap/Normal; linear, nonlinear, dry, coupled/saturated,

%\vspace*{1mm}
%  \item[-] Super element: stiffness and mass matrices

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

\vspace*{1mm}
  \item[-] Energy dissipation: elastic-plastic, viscous, algorithmic

\vspace*{1mm}
  \item[-] Solid/Structure-Fluid interaction, Internal and External 

\vspace*{1mm}
  \item[-] Intrusive probabilistic inelastic modeling, Forw. and Backw.

%
%\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{Simulation Features}



%\vspace*{-10mm}

\begin{itemize}

  \item[-] Static loading stages

\vspace*{1mm}
  \item[-] Dynamic loading stages

\vspace*{1mm}
  \item[-] Explicit and Implicit computations

\vspace*{1mm}
  \item[-] Restart, simulation tree

\vspace*{1mm}
  \item[-] Solution advancement methods/algorithms, \\
        on global and constitutive levels, \\
        with and without enforcing equilibrium


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

\vspace*{1mm}
  \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}


 
\vspace*{-60mm}
%\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
\end{flushright}
%\vspace*{-0.5cm}
%\end{figure}
%




 
\end{frame}



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


%\subsection{Verification  and Validation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - 
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  \begin{frame}
% -   \frametitle{Verification and Validation}
% -  \begin{itemize}
% -      
% -      
% -  
% -  
% -  
% -       \item[-]  {{  Verification:}  provides  evidence  that  the  model is solved
% -       correctly.} Mathematics issue.  Well developed 
% -       for the Real ESSI Simulator.
% -  
% -  \vspace*{4mm}
% -       \item[-]  {{  Validation:}  provides  evidence  that  the  correct  model is
% -       solved.} Physics issue. Work in progress.
% -          
% -  \vspace*{4mm}
% -     \item[-] {  Prediction:}  use  of  computational  model
% -     to  foretell  the  state  of  a  physical  system  under  consideration under
% -     conditions for which the computational model has not been validated.
% -    
% -  %   \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  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 and rather than (force) Fit
% -  % 
% -  % 
% -  
% -  
% -  
% -  \end{itemize}
% -  \end{frame}
% -  
% -  
% -  
% -  
% -  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  % \begin{frame}
% -  % \frametitle{V \& V Motivation}
% -  % 
% -  % 
% -  % 
% -  % \begin{itemize}
% -  % 
% -  % 
% -  % %\vspace*{0.5cm}
% -  % \item How much can (should) we trust  model implementations (verification)?
% -  % 
% -  % %\vspace*{0.5cm}
% -  % \item How much can (should) we trust numerical simulations (validation)?
% -  % 
% -  % %\vspace*{0.5cm}
% -  % \item How good are our numerical predictions?
% -  % 
% -  % %\vspace*{0.5cm}
% -  % \item    Can      simulation  tools  be used for improving safety and economy?
% -  % 
% -  % %   \vspace*{2.0truecm}
% -  %    \item  V  \&  V  procedures  are  the  primary means of assessing accuracy in
% -  %    modeling and computational simulations
% -  % 
% -  % %   \vspace*{1.0truecm}
% -  %    \item  V  \&  V  procedures  are the tools with which we build confidence and
% -  %    credibility in modeling and computational simulations
% -  % 
% -  % 
% -  % 
% -  % 
% -  % %\vspace*{2.5cm}
% -  % %\item How do we  use experimental simulations   to improve models
% -  % 
% -  % 
% -  % 
% -  % 
% -  % \end{itemize}
% -  % 
% -  % 
% -  % 
% -  % 
% -  % \end{frame}
% -  % 
% -  % 
% -  % 
% -     
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  
% -  
% -  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  % \begin{frame}
% -  %  \frametitle{Role of Verification and Validation}
% -  % 
% -  % 
% -  % 
% -  % \begin{figure}[!h]
% -  % \begin{center}
% -  % \hspace*{-2cm}
% -  % %{\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/ASME_V_and_V_symposium/presentetation/RoleVV_NEW_knowledge.pdf}}
% -  % {\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/RoleVV_NEW_knowledge.pdf}}
% -  % %{\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
% -  % {\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VandV_ODEN.jpg}}
% -  % \hspace*{-2cm}
% -  % \end{center}
% -  % \end{figure}
% -  % 
% -  % {Oberkampf et al. \hspace*{4cm}  Oden et al.}
% -  % %
% -  % %\item Models available (some now, some later)
% -  % %\vspace*{-2.0cm}
% -  % 
% -  % %
% -  % %\item Models available (some now, some later)
% -  % %\vspace*{-2.0cm}
% -  % \end{frame}
% -  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  
% -  
% -  
% -  \begin{frame}
% -    \frametitle{Fundamentals of Verification and Validation}
% -  
% -  
% -  
% -  %--
% -  
% -  
% -  \begin{figure}[!h]
% -  % \vspace*{-0.5cm}
% -  \hspace*{-8mm}
% -  %\begin{center}
% -  %{\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}}
% -  {\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VerifValidFund01.pdf}}
% -  %\end{center}
% -  \end{figure}
% -  
% -  
% -  \end{frame}
% -  
% -  
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  
% -  
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  \begin{frame}
% -  \frametitle{Important Sources}
% -  
% -  
% -  
% -  \begin{itemize}
% -  
% -  
% -  
% -  
% -  %\item {\it  Short Course on Verification and Validation in
% -  %Computational Mechanics}, by {\sc Dr. William Oberkampf}, Sandia National Laboratories
% -  %July 27th, 2003, Albuquerque, New Mexico.
% -  
% -  \item
% -  {\sc W.~L. Oberkampf, T.~G. Trucano, and C. Hirsch.}
% -  Verification, validation and predictive capability in computational
% -    engineering and physics.
% -  In {\em Proceedings of the Foundations for Verification and
% -    Validation on the 21st Century Workshop}, pages 1--74, Laurel, Maryland,
% -    October 22-23 2002. Johns Hopkins University / Applied Physics Laboratory.
% -  %{\href{http://sokocalo.engr.ucdavis.edu/~jeremic/UsefulReadings/Oberkampf-Trucano-Hirsch.pdf}
% -  %{PDF available here}}
% -  
% -  
% -  \item
% -  {\sc P.~J. Roache.}
% -   {\em Verification and Validation in Computational Science and
% -    Engineering}.
% -  Hermosa publishers, 1998.
% -  ISBN 0-913478-08-3.
% -  %
% -  
% -  
% -  % \item Material from {\it Verification and Validation in Computational Mechanics}
% -  % web site \texttt{http://www.usacm.org/vnvcsm/} at the USACM.
% -  
% -   \item  William L. Oberkampf and Christopher J. Roy. Verification and Validation
% -   in Scientific Computing. Cambridge University Press, 2010.
% -  
% -  
% -  
% -  \end{itemize}
% -  
% -  
% -  
% -  
% -  \end{frame}
% -  
% -  
% -  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  % 
% -  % 
% -  % 
% -  
% -  
% -  
% -  
% -  
% -  
% -  
% -  
% -  
% -  
% -  
% -  
% -  
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  \begin{frame}
% -   \frametitle{Verification}
% -  
% -  \begin{itemize}
% -  
% -  \item   Source code management
% -  \item   Source code verification
% -  
% -  \item  Constitutive integration
% -  \item   Static and dynamic behavior of single phase solids
% -  \item       Static  and dynamic behavior of fully and partially saturated, fully
% -  coupled, porous solid-pore fluid problems
% -  \item   Static and dynamic behavior of structural elements
% -  \item            Static    and    dynamic    behavior    of   special   elements
% -  (contacts-interface/gap-frictional/dry-saturated, isolators/dissipators)
% -  \item   Static and dynamic FEM solution advancement
% -  \item   Seismic wave propagation problems
% -  \item FEM Model verification, hierarchy of models
% -  %\item   Static and Dynamic Behavior of Soil-Structure-Interaction
% -  
% -  \end{itemize}
% -  
% -  \end{frame}
% -  
% -  
% -  
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Constitutive Integration Verification}
% 
% 
% \begin{itemize}
% 
%   \item Asymptotic regime of convergence
% 
%   \item Richardson extrapolation
% 
%   \item Grid convergence index
% 
% \end{itemize}
% 
% 
%  \begin{center}
%  \begin{figure}[!htbp]
% \vspace*{-3mm}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/asymptotic_regime.pdf}
%  \includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/asymptotic_nonassociate.pdf}
% \\
%  \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/error-map/DPAF_implicitErrMap.pdf}
%  \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/GCI/NonAssociate.pdf}
% \vspace*{-3mm}
%  \end{figure}
%  \end{center}
% 
% 
% 
% 
% 
% 
% 
% 
% \end{frame}
% 
% 
% 
% 
% 


% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Seismic Energy Input and Dissipation}
% 
% \begin{itemize}
% 
% \vspace*{1mm}
%      \item[] Seismic energy input, through a closed boundary (DRM)
% 
% 
% \vspace*{4mm}
%      \item[] Mechanical dissipation outside SSI domain:
%        \begin{itemize}
%          \item[] Reflected wave radiation
%          \item[] SSI system oscillation radiation
%        \end{itemize}
% %\vspace*{1mm}
%      \item[] Mechanical dissipation/conversion inside SSI domain:
%        \begin{itemize}
%          \item[] Inelasticity of soil and contact zone
%          \item[] Inelasticity/damage of structure and foundation
%          \item[] Viscous coupling of fluids and  soils and structure
% % %         \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{Energy Dissipation Verification: \\ Plastic Work $\neq$ Plastic Dissipation}
%  
% %\begin{itemize}
% %\item Negative incremental energy dissipation
% %\item Plastic work is NOT plastic dissipation
% %\end{itemize}
%  
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[height=4.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem.png}
% \end{center}
% \end{figure}
%  
%  \vspace*{-2mm}
% \begin{itemize}
% 
% \item[] Direct violation of the second law of thermodynamics
% 
% %\vspace*{3mm}
% \item[] 600 papers since 1990 (!?!) repeat this error
% 
% % \vspace*{3mm}
% % \item[] Important form of energy missing: {Plastic Free Energy}
% % 
% % \vspace*{3mm}
% % \item[] First described by Taylor and Quinney in 1934! 
% % 
% % \vspace*{3mm}
% % \item[] Plastic Work vs. {Plastic Energy Dissipation}
% 
% 
% %\vspace*{4mm}
% %\item[] However it seems to be forgotten
% 
% \end{itemize}
% 
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Dynamic Time Stepping Verification}
% 
% %\footnotesize
% Based  on  the  amplification  matrix ${\bf A}$,  to  calculate the analytical solution of
% damping ratios and period shift.
% 
% Example: Hilber-Hughes-Taylor $\alpha=-0.1$
% 
% \begin{figure}
% \hspace*{-5mm}
% \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/dynamic/hht/HHT-alpha-01-xi.jpg}
% \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/dynamic/hht/HHT-alpha-01-period-shift.jpg}
% \hspace*{-5mm}
% \end{figure}
% % HHT Integration $\alpha=-0.2$
% % \begin{figure}
% % \includegraphics[width=0.36\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/dynamic/hht/HHT-alpha-02-xi.jpg}
% % \includegraphics[width=0.36\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/dynamic/hht/HHT-alpha-02-period-shift.jpg}
% % \end{figure}
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Seismic Input Verification, DRM}
% % \begin{figure}
% % % \includegraphics[scale=0.35]{Present06_figs/3DModel.eps}
% %  \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/3DModel.eps}
% % \end{figure}
% 
% \begin{figure}
% %\hspace*{-5mm}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/90m_Northridge_EW.eps}
% \\
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/90m_Northridge_NS.eps}
% \\
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/90m_Northridge_UD.eps}
% \end{figure}
% 
% 
% 
% 
% % local
% % local% local
% % local%\vspace*{-2mm}
% % local\begin{center}
% % local\hspace*{-16mm}
% % local%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% % local\movie[label=show3,width=61mm,poster,showcontrols]
% % local  {\includegraphics[width=60mm]
% % local  {movie_ff_3d_mp4_icon.jpeg}}
% % local  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_3d.mp4}
% % local%\hspace*{-2mm}
% % local%\hfill
% % local%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% % local\movie[label=show3,width=61mm,poster,showcontrols]
% % local  {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}
% % local  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}
% % local\hspace*{-16mm}
% % local\end{center}
% % local% local  
% 
% 
% % online % online
% % online % online
% % 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   {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% % 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   {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% % online \end{center}
% % online % online
% % online % online
% % online % online
% % online 
% 
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification: ANDES Shell}
% 
%  \begin{center}
% % \includegraphics[width=0.6\textwidth]{./_Jose_Files/fig1_static_tests.pdf}
% \hspace*{-10mm}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/fig1_static_tests.pdf}
% % \includegraphics[width=0.6\textwidth]{./_Jose_Files/fig2_static_tests.pdf}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/fig2_static_tests.pdf}
% \hspace*{-10mm}
% \end{center}
% 
% \begin{flushleft}
%     \begin{tabular}{|l|l|}
%     \hline
%  $N_{\texttt{subd}}$   &      $u_z$ \\ \hline
%      2 &  96.2118 \\
%      7 & 100.096 \\
%    101 & 100.002 \\
%        &            \\ \hline
%     \end{tabular}
% \end{flushleft}
% 
% 
% \vspace*{-30mm}
% 
%  \begin{flushright}
% % \includegraphics[width=0.9\textwidth]{./_Jose_Files/Test_shell_andes_1_free_vibration_EigenMode1.png}
% %\hspace*{-10mm}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/Test_shell_andes_1_free_vibration_EigenMode1.png}
%  \\
% \vspace*{-8mm}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/Test_shell_andes_2_free_vibration_EigenMode1.png}
% \hspace*{-10mm}
% \end{flushright}
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
%  \frametitle{Verification: Irregular Solids and Poisson's Ratio}
% 
% 
% % \begin{itemize}
% %  \item Irregular Mesh
% %  \item Mesh Refinement
% % \end{itemize}
% 
%  \begin{figure}
% %  \hspace*{-25mm}
% %  \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_8brick.pdf}
% % % \hspace*{-25mm}
% % % \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_8brick_more_2.pdf}
%  \hspace*{-25mm}
%  \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_brick27_shape1_vertical.pdf}
%  \hspace*{-35mm}
%  \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_brick27_shape2_vertical.pdf}
%  \hspace*{-35mm}
%  \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_brick27_shape3_vertical.pdf}
%  \hspace*{-25mm}
%  \end{figure}
% 
% 
%  \vspace*{-6mm}
% 
% \begin{figure}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/irregular_shape.png}
% \end{figure}
% 
% % \begin{itemize}
% %  \item Verification Results of High Poisson's ratios
% % \end{itemize}
% 
%  \vspace*{-5mm}
% 
% \begin{figure}
% \hspace*{-9mm}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/error27brick_beam_different_poisson_ratio_disp_div100.jpeg}
% \hspace*{3mm}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/high_poisson.png}
% \end{figure}
% 
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Verification of Solid Shell/Plate}
% 
% 
% \begin{figure}
% \hspace*{-9mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/circular_plate1.pdf}
% \hspace*{-5mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/circular_plate3.pdf}
% \hspace*{-5mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/circular_plate4.pdf}
% \hspace*{-5mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/circular_plate6.pdf}
% \hspace*{-9mm}
% \end{figure}
% 
% \vspace*{-2mm}
% 
% \begin{itemize}
%  \item Simply supported and clamped ends
%  \item Timoshenko's analytic solutions 
% \end{itemize}
% 
% 
% 
% \vspace*{-3mm}
% 
% \begin{figure}
% \hspace*{-2mm}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/plate_error_plot.jpeg}
% \hspace*{3mm}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/plate_error_plot_clamped.jpeg}
% \end{figure}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification of Boussinesq Problem}
% 
% 
% \begin{figure}
% \hspace*{-9mm}
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/boussinesq/point_load_on_half_space.png}
% \hspace*{3mm}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/boussinesq/model3Dview.JPG}
% \end{figure}
% 
% 
% \vspace*{-3mm}
% 
% 
% \begin{figure}
% \hspace*{-9mm}
% \includegraphics[width=4.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/boussinesq/Boussinesq-8NodeBrick.jpeg}
% \hspace*{5mm}
% \includegraphics[width=4.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/boussinesq/Boussinesq-27NodeBrick.jpeg}
% \end{figure}
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification for Fully Coupled Problems}
% 
% 
% \begin{figure}
% \hspace*{-9mm}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2011/Verification_Coupled_Systems/FIGS/Gajo_comp.pdf}
% \end{figure}
% 
% 
% \end{frame}
% 
% 
% 
%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Wave Propagation, Mesh Size Effects}
% \begin{center}
% \begin{figure}
%  \includegraphics[scale=0.40]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present03_img/Vs1000_8Hz_10m.eps}
% \end{figure}
% {\small (Case 1, Vs = 1000 m/s, Cutoff Fq. = 8 Hz, E. Size = 10 m)}
% \end{center}
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Wave Propagation, Mesh Size Effects}
% \begin{center}
% \begin{figure}
%  \includegraphics[scale=0.40]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present03_img/Vs1000_8Hz_20m.eps}
% \end{figure}
% {\small (Case 1, Vs = 1000 m/s, Cutoff Fq. = 8 Hz, E. Size = 20 m)}
% \end{center}
% \end{frame}
% 
% %   
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Mesh Size Effects Analysis Results}
% % \begin{center}
% % \begin{figure}
% %  \includegraphics[scale=0.40]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present03_img/Vs1000_15Hz_10m.eps}
% % \end{figure}
% % {\small (Case 1, Vs = 1000 m/s, Cutoff Fq. = 15 Hz, E. Size = 10 m)}
% % \end{center}
% % \end{frame}
% % 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Mesh Size Effects Analysis Results}
% % \begin{center}
% % \begin{figure}
% %  \includegraphics[scale=0.40]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present03_img/Vs1000_15Hz_20m.eps}
% % \end{figure}
% % {\small (Case 1, Vs = 1000 m/s, Cutoff Fq. = 15 Hz, E. Size = 20 m)}
% % \end{center}
% % \end{frame}
% % 
% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{V \& V Summary}
% 
%     \begin{itemize}
%        
%       \item  V\&V most important for providing confidence in results
% 
% \vspace*{3mm}
%       \item Numerical modeling program(s) should not be used without extensive/full V\&V
% 
% \vspace*{3mm}
%       \item V\&V of FEM models is also essential
% 
% 
% \vspace*{3mm}
%       \item  Real  ESSI  Simulator has an extensive Verification database
% 
% % 
% \vspace*{3mm}
%       \item Validation database in development, TJU lab can help!
% 
% 
% %       \item    Education  is  the  key  to successful use of realistic nonlinear
% %       Earthquake Soil Structure Interaction modeling and simulation
% % 
% %     \item     Development     of    the    Real    ESSI    Simulator    system
% %     \href{http://real-essi.info}{http://real-essi.info}
% 
% %     \item Importance of using proper models correctly (verification, validation, level of sophistication)
% % 
% 
% 
%       
% 
% \end{itemize}
% 
% 
% 
% \end{frame}
%


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  
%  \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}
%  %
%  
%  
%  
%  
%  
%  % \vspace*{-5mm}
%  
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%   
%  
%  
%  
%  
%  
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




































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





















% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{High Performance Computing}
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Course Grained 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}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Parallel_Computing_in_Coputational_Geomechanics/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_Speedup01.pdf}
% \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{Inelastic, Coupled Analysis}


%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Numerical Formulation}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{FEM Formulation Assumptions}

\begin{itemize}

  \item[-] 3D Geometry

\vspace*{1mm}
  \item[-] Solids and Structures


\vspace*{1mm}
  \item[-] Material nonlinear, inelastic and/or elastic 

\vspace*{1mm}
  \item[-] Small deformations:
   \begin{itemize}
     \item[] small strain 
     \item[] small translations 
     \item[] small rotations
   \end{itemize}

%\vspace*{1mm}
%  \item[-] Dry, single phase material

\vspace*{1mm}
  \item[-] Fully or Partially/Un- Saturated, two phase material


\vspace*{1mm}
  \item[-] Mixture of pore fluid and porous solid

\vspace*{1mm}
  \item[-] Compressible pore fluid and compressible porous solid


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




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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Two Phase, Fully Coupled Systems}

\begin{itemize}





  \item[-] Based on: \\
O. C. Zienkiewicz and T. Shiomi. Dynamic behaviour of saturated porous media;
the generalized Biot formulation and its numerical solution. International
Journal for Numerical and Analytical Methods in Geomechanics, 8:71-96, 1984.



\vspace*{4mm}
  \item[-] Full coupling of internal, pore fluid with porous solid


\vspace*{1mm}
  \item[-] Full saturation and partial, unsaturated soils

\vspace*{1mm}
  \item[-] Statics and dynamics of coupled systems

%



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




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

\begin{frame}
 \frametitle{FEM Discretization, Approximation}


\begin{itemize}


\vspace*{1mm}
  \item[-] Displacement approximation:
   $u_i \approx \hat{u}_{a} = H_{I} \bar{u}_{Ia}$



\vspace*{6mm}
  \item[-]  Strain:
$
\epsilon_{ab} \; \approx \; \hat{\epsilon}_{ab}
=
\frac{1}{2}  \left(
\left( H_{I,b} \; \bar{u}_{Ia} \right)
+
\left( H_{I,a} \; \bar{u}_{Ib} \right)
\right)
$


\end{itemize}



%\vspace*{-5mm}

\end{frame}

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









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

\begin{frame}
 \frametitle{FEM Discretization, Stress-Strain}


%\begin{itemize}
%%
%
%\vspace*{1mm}
%  \item[-] Stress-strain relation: 
%\\
$
\Delta \hat{\sigma}_{ab}
=
E^{EP}_{abcd} 
\left( \Delta \hat{\epsilon}_{cd} - \Delta \epsilon_{cd}^{0} \right)
+
\Delta \sigma_{ab}^{0}
$

%\end{itemize}



%\vspace*{-5mm}

\end{frame}

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






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

\begin{frame}
 \frametitle{FEM Discretization, Stiffness Tensor Symmetries}


 \begin{itemize}
 
  
   \item[-] Minor  symmetry of stiffness tensor:
 $^{EP}E_{abcd} = E^{EP}_{bacd}= E^{EP}_{abdc}$

   \vspace*{5mm}
   \item[-] Major symmetry is not necessary, non-associated plasticity
 $^{EP}E_{abcd} \ne E^{EP}_{cdab}$

 
 
 \end{itemize}


\end{frame}

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



%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{FEM Discretization, Equation}
%  
%  
%  \begin{itemize}
%  
%        
%  
%  \vspace*{2mm}
%    \item[-] Virtual displacements cannot be zero, they cancel out
%  
%  \vspace*{2mm}
%    \item[-] Final FEM equations:
%  $
%  M_{AacB} \; \ddot{\bar{u}}_{Bc}
%  +
%  K_{AacB}   \; \bar{u}_{Bc}
%  =
%  F_{Aa}
%  $
%  %\\ \nonumber
%  %A,B &=& 1,2,\dots,\mbox{\# of nodes}
%  %\\ \nonumber
%  %a,c &=& 1,\dots,\mbox{\# of dimensions (1, 2 or 3)}
%  
%  
%  
%  \end{itemize}
%  
%  
%  \end{frame}
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{FEM Discretization, Tensors}
%  
%  
%  % \begin{itemize}
%  
%           
%  \vspace*{2mm}
%    \item[-] Final FEM equations:
%  $
%  M_{AacB} \; \ddot{\bar{u}}_{Bc}
%  +
%  K_{AacB}   \; \bar{u}_{Bc}
%  =
%  F_{Aa}
%  $
%  %\\ \nonumber
%  %A,B &=& 1,2,\dots,\mbox{\# of nodes}
%  %\\ \nonumber
%  %a,c &=& 1,\dots,\mbox{\# of dimensions (1, 2 or 3)}
%  
%  
%  \vspace*{3mm}
%    \item[-] Mass matrix/tensor:
%  $
%  M_{IacJ}
%  =
%  \int_{V^{m} } H_{J}  \; \delta_{ac} \; \rho  \;  H_{I} \;  dV^{m}
%  $
%  
%  
%  \vspace*{3mm}
%    \item[-] Stiffness matrix/tensor:
%  $
%   K_{IacJ}
%  =
%  \int_{V^{m} }  H_{I,b} \; E_{abcd} \; H_{J,d} \;  dV^{m}
%  $
%  
%  \vspace*{3mm}
%    \item[-] Load vector/tensor:
%  $
%  F_{Ia}
%  =
%  \int_{V^{m} } f^{B}_{a} \; H_{I} \; dV^{m}
%  +
%  \int_{S^{m} } f^{S}_{a} \; H_{I} \; dS^{m}
%  +
%  \int_{V^{m} } E_{abcd} \; \epsilon_{cd}^{0}   \; H_{I,b} \;  dV^{m}
%  +
%  \int_{V^{m} }  \sigma_{ab}^{0}  \; H_{I,b} \;  dV^{m}
%  $
%  
%  
%  
%  
%  \end{itemize}
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{FEM Discretization, Matrix Form}
%  
%  
%  \begin{itemize}
%  
%    
%  
%  \vspace*{4mm}
%    \item[-] FEM matrix form:
%  $
%  M_{PQ}   \; \ddot{\bar{u}}_{P}
%  +
%  K_{PQ}   \; \bar{u}_{P}
%  =
%  F_{Q}
%  $
%  
%  
%    
%  
%  
%  \end{itemize}
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{FEM, Matrix Form, Residuals, Equilibrium}
%  
%  
%  \begin{itemize}
%  
%    
%  \vspace*{4mm}
%    \item[-] Nonlinear FEM residuals, equilibrium:
%  
%  $
%  R_{Q} = 
%  F_{Q}   -
%  \left(
%  M_{PQ}   \; \ddot{\bar{u}}_{P}
%  +
%  K_{PQ}   \; \bar{u}_{P}
%  \right)
%  $
%  
%  
%  \vspace*{-2.5cm}
%  \begin{figure}[!hbpt]
%  \begin{flushright}
%  \includegraphics[width=3cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
%  %\caption{\label{loading_stages-increments_iterations} }
%  \end{flushright}
%  \vspace*{-0.5cm}
%  \end{figure}
%  %
%  
%  
%  \end{itemize}
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Notation}





%$\sigma_{ij}^{''} =  \sigma_{ij}  -  \alpha \delta_{ij} p $




%Notation
\begin{itemize}

\item[-] Effective stress $\sigma_{ij}^{''} =  \sigma_{ij}  -  \alpha \delta_{ij} p $

\item[-] $\sigma_{ij}$ - the total Cauchy stress in the mixture

\item[-] $\alpha=1-K_T/K_S \approx 1$

\item[-] $p$ -  the pore fluid pressure

\item[-] $u_i$ -  the displacement of the solid skeleton

\item[-] $w_i$ - disp. of fluid phase relative to the skeleton of solid

\item[-]   $\varepsilon_{ij}   =\frac{1}{2}(u_{i,j}+u_{j,i})$ -
 strain
increment of the solid phase,

%\item[] $\omega_{ij} =\frac{1}{2}(du_{i,j}-du_{j,i})$,  the rotation increment
%of the solid phase,

\item[-]  $\rho,\rho_s,\rho_f$ - densities of mixture, solid phase and water

\item[-] $n=V_{voids}/V_{total}$ - porosity,

\item[-] $\dot{w}_{i,i}$ - rate of change of volume of fluid / volume of mixture

\end{itemize}

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



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Governing Equations}




\begin{itemize}

\item[-] Equilibrium Equation of the Mixture:

$
  \sigma_{ij,j}-\rho \ddot{u}_i-\rho_f[\ddot{w}_i+
  \underline{\dot{w}_j\dot{w}_{i,j}}]+\rho b_i=0
$


$
\rho=\frac{M_t}{V_t}
     =\frac{M_s+M_f}{V_t}
     =\frac{V_s\rho_s + V_f\rho_f}{V_t}
     =\frac{V_f}{V_t}\rho_f+\frac{V_t-V_f}{V_t}\rho_s
     = n\rho_f+(1-n)\rho_s
 $




\vspace*{1mm}
\item[-] Equilibrium Equation of the Fluid

$
-p_{,i}- R_i - \rho_f \ddot{u}_i-\rho_f[\ddot{w}_i+
\underline{\dot{w}_j \dot{w}_{i,j}}]/n+\rho_f b_i=0
$
%

$R_i=k_{ij}^{-1} \dot{w}_j \qquad \textrm{or} \qquad
R_i=k^{-1} \dot{w}_i$



\vspace*{1mm}
\item[-] Flow Conservation Equation

$ %
\dot{w}_{i,i}+\alpha       \dot{\varepsilon}_{ii}+\frac{\dot{p}}{Q}+\underline{n
\frac{\dot{\rho_f}}{\rho_f}+\dot{s}_0}=0
$
%

$\frac{1}{Q}\equiv\frac{n}{K_f}+\frac{\alpha-n}{K_s}\cong \frac{n}{K_f}+\frac{1-n}{K_s}$


\end{itemize}



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





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Simplified Governing Equations}



\begin{itemize}

\item[-] Equilibrium Equation of the Mixture:
%
\begin{eqnarray}
  \sigma_{ij,j}-\rho \ddot{u}_i-\rho_f \ddot{w}_i+\rho b_i=0
  \nonumber
 \end{eqnarray}






\vspace*{3mm}
\item[-] Equilibrium Equation of the Fluid
%
\begin{eqnarray}
- p_{,i}- R_i -\rho_f \ddot{u}_i-\frac{\rho_f \ddot{w}_i}{n}+\rho_f b_i=0
  \nonumber
\end{eqnarray}


\vspace*{3mm}
\item[-] Flow Conservation Equation
%
\begin{eqnarray}
\dot{w}_{i,i}+\alpha \dot{\varepsilon}_{ii}+\frac{\dot{p}}{Q}=0
  \nonumber
\end{eqnarray}






\end{itemize}



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








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modified Governing Equations}


\vspace*{5mm}

$
U_i=u_i+\frac{w_i}{n}
$
\hspace*{10mm}
\includegraphics[width=2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_FEM_Formulation/tex_works_LectureNotes_Figures_Darcy_vs_Real_01.pdf}

%
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_FEM_Formulation/tex_works_LectureNotes_Figures_Darcy_vs_Real_01.pdf}
%  \end{center}
%  \end{figure}



\begin{eqnarray}
\sigma_{ij,j}^{''}-(\alpha-n) p_{,i}+(1-n) \rho_s b_i-(1-n) \rho_s \ddot{u}_i +
n R_i=0
\nonumber
\end{eqnarray}
%%
%
\begin{eqnarray}
-n p_{,i}+n \rho_f b_i-n \rho_f \ddot{U}_i
- n R_i=0
\nonumber
\end{eqnarray}
%
\begin{eqnarray}
-n \dot{U}_{i,i}=(\alpha-n) \dot{\varepsilon}_{ii}+\frac{1}{Q} \dot{p}
\nonumber
\end{eqnarray}



\begin{itemize}
\item[]
$u_i$: three solid displacement
\item[]
$p$: pore pressure
\item[]
$U_i$: three fluid displacement
\end{itemize}



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


















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

\begin{frame}
 \frametitle{FEM u-p-U Discretization}


%Detailed derivation in Lecture Notes, Part I, Chapter 102

{\small
\begin{eqnarray}
\left[ \begin{array}{ccc}
M_s & 0 & 0 \\
 0  & 0 & 0 \\
 0  & 0 & M_f
\end{array} \right]
\left[ \begin{array}{c}
\ddot{\overline{u}} \\
\ddot{\overline{p}} \\
\ddot{\overline{U}}
\end{array} \right]
+
\left[ \begin{array}{ccc}
C_1 & 0 & -C_2 \\
 0  & 0 &   0  \\
-C_2^T & 0 & C_3 \\
\end{array} \right]
\left[ \begin{array}{c}
\dot{\overline{u}} \\
\dot{\overline{p}} \\
\dot{\overline{U}}
\end{array} \right]
+ \nonumber \\
\left[ \begin{array}{ccc}
K^{EP} & -G_1 & 0 \\
-G_1^T  & -P & -G_2^T \\
 0  & -G_2 & 0
\end{array} \right]
\left[ \begin{array}{c}
\overline{u} \\
\overline{p} \\
\overline{U}
\end{array} \right] \nonumber
=
\left[ \begin{array}{c}
\overline{f}_s \\
0  \\
\overline{f}_f
\end{array} \right]
\nonumber
\end{eqnarray}
}
%
%
%
%

%\vspace*{-5mm}

\end{frame}

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


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

\begin{frame}
 \frametitle{FEM u-p-U Discretization, Index Form}


%Detailed derivation in Lecture Notes, Part I, Chapter 102



{\footnotesize
\begin{eqnarray}
\left[ \begin{array}{ccc}
(M_s)_{KijL} & 0 & 0 \\
 0  & 0 & 0 \\
 0  & 0 & (M_f)_{KijL}
\end{array} \right]
\left[ \begin{array}{c}
\ddot{\overline{u}}_{Lj} \\
\ddot{\overline{p}}_N \\
\ddot{\overline{U}}_{Lj}
\end{array} \right]
+
\left[ \begin{array}{ccc}
(C_1)_{KijL} & 0 & -(C_2)_{KijL} \\
 0  & 0 &   0  \\
-(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
\end{array} \right]
\left[ \begin{array}{c}
\dot{\overline{u}}_{Lj} \\
\dot{\overline{p}}_N \\
\dot{\overline{U}}_{Lj}
\end{array} \right]
\nonumber \\
+
\left[ \begin{array}{ccc}
(K^{EP})_{KijL} & -(G_1)_{KiM} & 0 \\
-(G_1)_{LjM}  & -P_{MN} & -(G_2)_{LjM} \\
 0  & -(G_2)_{KiL} & 0
\end{array} \right]
\left[ \begin{array}{c}
\overline{u}_{Lj} \\
\overline{p}_M \\
\overline{U}_{Lj}
\end{array} \right]
=
\left[ \begin{array}{c}
\overline{f}_{Ki}^{solid} \\
0  \\
\overline{f}_{Ki}^{fluid}
\end{array} \right]
\end{eqnarray}
}
%
%



\end{frame}

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

%



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

\begin{frame}
 \frametitle{FEM u-p-U Matrices/Tensors}



{\footnotesize
\begin{eqnarray}
\hspace*{-8mm}
\boldsymbol{M_s}=(M_s)_{KijL}=\int_{\Omega} H_K^u (1-n) \rho_s \delta_{ij} H_L^u d\Omega
~~ \mbox{;} ~~
\boldsymbol{M_f}=(M_f)_{KijL}=\int_{\Omega} H_K^U n \rho_f \delta_{ij} H_L^U d\Omega \nonumber\\
%
\boldsymbol{C_1}=(C_1)_{KijL}=\int_{\Omega} H_K^u n^2 k_{ij}^{-1} H_L^u d\Omega
~~ \mbox{;} ~~
\boldsymbol{C_2}=(C_2)_{KijL}=\int_{\Omega} H_K^u n^2 k_{ij}^{-1} H_L^U d\Omega \nonumber\\
\boldsymbol{C_3}=(C_3)_{KijL}=\int_{\Omega} H_K^U n^2 k_{ij}^{-1} H_L^U d\Omega \nonumber\\
%
\boldsymbol{K^{EP}}=(K^{EP})_{KijL}=\int_{\Omega} H_{K,m}^u D_{imjn} H_{L,n}^u d\Omega \nonumber\\
\boldsymbol{G_1}=(G_1)_{KiM}=\int_{\Omega} H_{K,i}^u (\alpha-n) H_M^p d\Omega
~~ \mbox{;} ~~
\boldsymbol{G_2}=(G_2)_{KiM}=\int_{\Omega} n H_{K,i}^U H_M^p d\Omega \nonumber\\
\boldsymbol{P}=P_{NM}=\int_{\Omega} H_N^p \frac{1}{Q} H_M^p d\Omega \nonumber
\end{eqnarray}
}
%
%
%
%

%\vspace*{-5mm}

\end{frame}

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


\begin{frame}
 \frametitle{FEM u-p-U Loads}



%\newpage

{\footnotesize
\hspace*{-8mm}
\begin{eqnarray}
\overline{f}_{Ki}^{solid}&=&(f_1^u)_{Ki}-(f_4^u)_{Ki}+(f_5^u)_{Ki} \nonumber\\
\overline{f}_{Ki}^{fluid}&=&-(f_1^U)_{Ki}+(f_2^U)_{Ki}  \nonumber\\
(f_1^u)_{Ki}&=&\int_{\Gamma_t} H_K^u n_j \sigma_{ij}^{''} d\Gamma \nonumber\\
(f_4^u)_{Ki}&=&\int_{\Gamma_p} H_K^u (\alpha-n) n_i p d\Gamma \nonumber\\
(f_5^u)_{Ki}&=&\int_{\Omega} H_K^u (1-n) \rho_s b_i d\Omega \nonumber\\
(f_1^U)_{Ki}&=&\int_{\Gamma_p} n H_K^U n_i p d\Gamma \nonumber\\
(f_2^U)_{Ki}&=&\int_{\Omega} n H_K^U \rho_f b_i d\Omega \nonumber
\label{eqn_69_u-p-U}
\end{eqnarray}
}
%


%\vspace*{-5mm}

\end{frame}

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



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

\begin{frame}
 \frametitle{Coupled FEM Discretization, Matrix Form}


\begin{itemize}

  


\vspace*{1mm}
  \item[-] Coupled FEM, full matrix form:
\begin{eqnarray*}
\left[ \begin{array}{ccc}
M_s & 0 & 0 \\
 0  & 0 & 0 \\
 0  & 0 & M_f
\end{array} \right]
\left[ \begin{array}{c}
\ddot{\overline{u}} \\
\ddot{\overline{p}} \\
\ddot{\overline{U}}
\end{array} \right]
+
\left[ \begin{array}{ccc}
C_1 & 0 & -C_2 \\
 0  & 0 &   0  \\
-C_2^T & 0 & C_3 \\
\end{array} \right]
\left[ \begin{array}{c}
\dot{\overline{u}} \\
\dot{\overline{p}} \\
\dot{\overline{U}}
\end{array} \right]
+
\\
+
\left[ \begin{array}{ccc}
K^{EP} & -G_1 & 0 \\
-G_1^T  & -P & -G_2^T \\
 0  & -G_2 & 0
\end{array} \right]
\left[ \begin{array}{c}
\overline{u} \\
\overline{p} \\
\overline{U}
\end{array} \right]
=
\left[ \begin{array}{c}
\overline{f}_s \\
0  \\
\overline{f}_f
\end{array} \right] 
\nonumber
\label{eqn_67_u-p-U}
\end{eqnarray*}
%


\vspace*{3mm}
  \item[-] Coupled FEM, generalized matrix form:
$
M_{PQ}   \; \ddot{\bar{u}}_{P}
+
C_{PQ}   \; \dot{\bar{u}}_{P}
+
K_{PQ}   \; \bar{u}_{P}
=
F_{Q}
$


  


\end{itemize}


\end{frame}


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

\begin{frame}
 \frametitle{Coupled FEM, Residuals, Equilibrium}


\begin{itemize}

  

\vspace*{6mm}
  \item[-] Nonlinear coupled FEM residuals, \\
           equilibrium:
%

%\begin{flushleft}
%\begin{eqnarray*}
$
R_{Q} = 
$
\\
$
F_{Q} -
\left(
M_{PQ}   \; \ddot{\bar{u}}_{P}
+
C_{PQ}   \; \dot{\bar{u}}_{P}
+
K_{PQ}   \; \bar{u}_{P}
\right)
$
%\nonumber
%\end{eqnarray*}
%\end{flushleft}



\vspace*{-3.5cm}
\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=3cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
%\caption{\label{loading_stages-increments_iterations} }
\end{flushright}
\vspace*{-0.5cm}
\end{figure}
%




\end{itemize}


\end{frame}



 

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



\subsection{Analysis Examples}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Coupled Analysis in Practice}

\begin{itemize}

\vspace*{2mm}
\item[-] The coupled u-p-U formulation is very powerful

\vspace*{4mm}
\item[-] The u-p-U formulation is useful for many problems


\vspace*{4mm}
\item[-] ESSI: internal fluids problems
%, porous solids -- pore fluid

\vspace*{4mm}
\item[-] ESSI: external fluid problems
%, porous solids -- pore fluid -- external fluid


% \vspace*{2mm}
% \item[-] 
% 
% 
% \vspace*{2mm}
% \item[-]
% 
% 
% \vspace*{2mm}
% \item[-]
% 
% 
% \vspace*{2mm}
% \item[-]
% 
% 

\end{itemize}


\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Liquefaction as Base Isolation}

\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=4.8truecm]{/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=6.0truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_01.jpg}
\end{center}
\end{figure}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Liquefaction, Stress-Strain Response}

\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_03.jpg}
\end{center}
\end{figure}

\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pile in Liquefiable Soil}

\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=2.5truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_FEmesh3D.pdf}
\hfill
\includegraphics[width=3.2truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_FEmeshPileBeam.pdf}
%\hfill
\includegraphics[width=4.7truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_SFSIModelSetup_upU_01.pdf}
\end{center}
\end{figure}


\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pile in Liquefiable Soil}

\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=6.7truecm]{/home/jeremic/tex/works/Conferences/2018/Oersted-DONG-Energy/present/Pile_in_liquefied_soil.jpg}
\end{center}
\end{figure}




\end{frame}




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

\begin{frame}

\frametitle{Buoyant Force Effects}

\begin{figure}[!H]
\hspace*{-10mm}
     \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/upU_element_type_annotation.pdf}
     \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}
\hspace*{-10mm}
\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{Building on Liquefiable Soil}



\vspace*{16mm}

\noindent
Plastic Strain \hspace*{40mm} Pore Fluid Pressures

\vspace*{-1mm}
% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-20mm}
\movie[label=show3,width=5.5cm,showcontrols]
%\movie[label=show3,width=61mm, showcontrols]
  {\includegraphics[width=59mm]
  {/home/jeremic/tex/works/Thesis/HanYang/Liquefaction_models_Nov-Dec2021/Plastic_Strain.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Liquefaction_models_Nov-Dec2021/Plastic_Strain.mp4}
%\hspace*{-2mm}
%\hfill
\movie[label=show3,width=5.6cm,showcontrols]
%\movie[label=show3,width=61mm, showcontrols]
  {\includegraphics[width=60mm]
  {/home/jeremic/tex/works/Thesis/HanYang/Liquefaction_models_Nov-Dec2021/Pore_Presure.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Liquefaction_models_Nov-Dec2021/Pore_Presure.mp4}
\hspace*{-16mm}
\end{center}
% local

\vspace*{-1mm}

% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/building_on_liquefiable_soil_ETH_model/Plastic_Strain.mp4}
{\tiny (MP4)}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/building_on_liquefiable_soil_ETH_model/Pore_Presure.mp4}
 {\tiny (MP4)}
\end{center}
% online

\end{frame}







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

\begin{frame}
 \frametitle{Solid/Structure-Fluid Interaction}

% local 
% local  
% local  %\vspace*{-5mm}
% local  \begin{center}
% local  % \hspace*{-15mm}
% local  \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% local  {\includegraphics[width=8.5cm]
% local  {/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/Solid-Fluid-Interaction.jpg}}
% local  {Solid_Fluid_Interaction.mp4}
% local  \end{center}
% local  
% local  
% local  
    
% online 
% 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/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
% online  \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_NEW.mpeg}
% online    {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction.jpg}}
% online  \end{center}
% online  % online 
% online 
% online  




 

%\vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=9cm,poster,autostart,showcontrols]
\movie[label=show3,width=9cm,showcontrols]
{\includegraphics[width=8.5cm]
{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/Solid-Fluid-Interaction.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction_NEW.mpeg}
\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/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%




\end{frame}

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

% -




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



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

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



% 
%   
%   
%   \subsection{Nonlinear FEM Analysis Process}
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   \begin{frame}
%   \frametitle{Nonlinear FEM Analysis Process}
%   
%   
%   \begin{figure}[!hbpt]
%   \begin{center}
%   \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
%   %\caption{\label{loading_stages-increments_iterations} }
%   \end{center}
%   \vspace*{-0.5cm}
%   \end{figure}
%   %
%   \end{frame}
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \begin{frame}
%   \frametitle{Nonlinear FEM Equilibrium Iterations}
%   
%   
%   
%   \begin{itemize}
%     
%     \item[-] Global, FEM equilibrium iterations, convergence
%   
%   
%   %  \item[-] Convergence criteria
%      \begin{itemize}
%         \item[-] Force, unbalanced, relative, abs. minimum check
%         \item[-] Force, unbalanced, average
%         \item[-] Force, unbalanced, absolute
%         \item[-] Displacement, incremental, relative, abs. minimum check 
%         \item[-] Displacement, incremental, average
%         \item[-] Displacement, incremental, absolute
%         \item[-] Energy, incremental, relative, abs. minimum check 
%         \item[-] Energy, incremental, average
%         \item[-] Energy, incremental, absolute
%      \end{itemize}
%   
%   
%   
%   \vspace*{3mm}
%     \item[-] Local, constitutive level equilibrium iterations
%   
%   
%   
%   \end{itemize}
%   
%   
%   \end{frame}
%   
%           
%   
%   
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Summary}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{\ }



% 
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%    \frametitle{Nonlinear FEM}
%  
%    \begin{itemize}
%  
%  \vspace*{-8mm}
%      \item[-] Nonlinear FEM, global level, iterations
%  
%  \vspace*{1mm}
%      \item[-] Nonlinear FEM, constitutive level, iterations
%  
%  
%  \vspace*{1mm}
%      \item[-] No equilibrium check, explicit
%  
%  \vspace*{1mm}
%      \item[-] Equilibrium check, implicit
%  
%  \vspace*{1mm}
%      \item[-] Explicit, no equilibrium on constitutive and \\
%       global levels
%  
%  \vspace*{1mm}
%      \item[-] Implicit, equilibrium on constitutive and \\
%       global levels
%  
%  
%  
%  \vspace*{1mm}
%      \item[-]  Gradually building confidence in inelastic modeling
%  
%  
%  \end{itemize}
%  
%  \vspace*{-5.5cm}
%  \begin{figure}[!hbpt]
%  \begin{flushright}
%  \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
%  %\caption{\label{loading_stages-increments_iterations} }
%  \end{flushright}
%  \vspace*{-0.5cm}
%  \end{figure}
%  %
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%    \frametitle{Model Verification and 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}
%  \\
%    \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 = 4cm]{/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{Analysis of  ESSI Systems }

\begin{itemize}

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


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


\vspace*{1mm}
    \item[-] Structure inelasticity/damage
       \begin{itemize}
         \item[-] Nonlinear/inelastic 1D fiber beam
         \item[-] Nonlinear/inelastic 3D shell/wall/plate element
       \end{itemize}


\vspace*{1mm}
     \item[-] Fluid-Solid interaction, open surface fluid



\end{itemize}

%
\end{frame}



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

 

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






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




%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Solid Elastic-Plastic Examples}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Contact Inelastic Examples}
% 












%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Summary}

%OVDE
  \begin{itemize}

    \item[-] Reduction of modeling uncertainty 

\vspace*{4mm}
    \item[-] Choice of analysis level of sophistication

\vspace*{4mm}
    \item[-] Numerical analysis to predict and inform

% \vspace*{1mm}
%     \item[-] Change of demand due to inelastic effects
% 
%       \begin{itemize}
%          \item[-] Reduction of dynamic motions
%          \item[-] Increase in deformations
%       \end{itemize}
% 

\vspace*{4mm}
    \item[-]  Engineer needs to know!

%
%\vspace*{4mm}
%    \item[-] Sophisticated analysiscarefully and in phases
%



% \vspace*{4mm}
%     \item[-]  Gradually building confidence in inelastic modeling
% 

%    \item    The    Real      ESSI    Simulator    system used for all the model
%     development, modeling/simulations and post-processing
% 
% 
\vspace*{4mm}
   \item[-]  The    Real        ESSI        Simulator system
 \\
 ~
 \\
\hspace*{30mm}   \href{http://real-essi.info}{http://real-essi.info}
% 
% 
% %\vspace*{1mm}
%     \item  Nonlinear/Inelastic Earthquake Soil Structure Interaction (ESSI)
%              short course offered this fall in San Francisco, more info at
%              \href{http://real-essi.info}{http://real-essi.info}




\end{itemize}



\end{frame}
%

















\end{document}


