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

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

\usepackage{epstopdf}


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

 
\usepackage[absolute,overlay]{textpos}


  
% for tikzpicture
\usepackage{tikz}
\usetikzlibrary{tikzmark,calc}




 
\usepackage{threeparttable}

%\usepackage{MnSymbol}%
% for smileys
\usepackage{wasysym}%
\usepackage{multirow}
% for subfloat figures:
\usepackage{subfig}
\usepackage{tabularx}
%used for truncated section title in headers
\usepackage[breakall]{truncate}
%\usepackage{caption}


\usepackage{ulem}
\usepackage{amsmath}
\usepackage{amsmath}
\usepackage{amssymb}
\newcommand\hmmax{0} % default 3
% solution from https://texfaq.org/FAQ-manymathalph
\newcommand{\bmmax}{3}
% \newcommand\bmmax{0} % default 4
\usepackage{bm}

\usepackage{IEEEtrantools}
\usepackage{setspace}
\usepackage{scalerel}


% 
% % for listing DSL
% \input{essi_listings_options.tex}
% 


      
\usepackage{multimedia}

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

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


%% ovo je za cirilicu
\input vuk.def
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% % for not showing eq numbers unless eq is references
% \usepackage[fleqn,tbtags]{mathtools}
% \mathtoolsset{
%   showonlyrefs
%   }

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


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


\usepackage{pause}
% or whatever
%\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.



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


\title[Plastic Energy Dissipation]
        {Plastic Energy Dissipation \\ 
         for Steel Building with BRBs   } 


%\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)
%\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
\author[Yang and Jeremi{\'c}] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c} \hspace*{5mm} and  \hspace*{5mm}  Han Yang}
%\\
%{\cyss Boris Jeremi\cj{}}
% }
% \\ 
%Han Yang, Hexiang Wang, Sumeet Kumar Sinha }


%\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\\
%{ University of California, Davis, CA, USA
{\hspace*{-10mm} University of California, Davis
%\\
\hspace*{20mm}
% Tianjin University, Tianjin, PRC}
Tianjin University}
% %  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 $5^{th}$ SEECCM
{
~\\ 
CIVIL-COMP 2023 
\vspace*{2mm} 
%\hspace*{5mm}
 \\ 
%28-31 August 2023
%          \\ ~ \\
         {P{\'e}cs, Hungary}}


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\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.



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

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

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


% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
    \setcounter{tocdepth}{1}
% \AtBeginSubsection[]
 \AtBeginSection[]
 {
   \begin{scriptsize}
   \begin{frame}<beamer>
     \frametitle{Outline}
%     \tableofcontents[currentsection,currentsubsection]
    \tableofcontents[currentsection]
   \end{frame}
   \end{scriptsize}
 }



% % Delete this, if you do not want the table of contents to pop up at
% % the beginning of each subsection:
% % \AtBeginSubsection[]
% \setcounter{tocdepth}{3}
%  \AtBeginSubsection[]
% % \AtBeginSection[]
%  {
%    \begin{scriptsize}
%    \begin{frame}<beamer>
%      \frametitle{Outline}
%      \tableofcontents[currentsection,currentsubsection]
% %    \tableofcontents[currentsection]
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%  }


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





\begin{document}

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\begin{frame}
  \titlepage
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\begin{frame}
  \frametitle{Outline}

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

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% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:

% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you
%   are going to talk about. So *simplify*!
% - In a 20min talk, getting the main ideas across is hard
%   enough. Leave out details, even if it means being less precise than
%   you think necessary.
% - If you omit details that are vital to the proof/implementation,
%   just say so once. Everybody will be happy with that.



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\section{Introduction}




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



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\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



 
\vspace*{1mm}
  \item[-] Safety and economy of infrastructure

%\vspace*{0.3cm}
 
%\vspace*{2mm}
%  \item[]  Improve  analysis of infrastructure objects
 
 
%  %\vspace*{1mm}
%  %  \item[-]  Analysis of Earthquakes and/or Soils and/or Structures and their Interaction
%  %  \item[-]  Analysis of Earthquakes, Soils, Structures and their Interaction
%  %  \item[-]  Soils, Structures and their Interaction, statics and dynamics
%    \item[-]  Soils, Structures, statics and dynamics
 

% \vspace*{1mm}
%  \item[]  Expert numerical modeling and simulation tool
% 
% \vspace*{1mm}
%   \item[]      Use of numerical models to
%   analyze statics and dynamics of soil/rock-structure systems
% 


%  
%  %\vspace*{1mm}
%    \item[-] Analysis to  predict and inform 
%  % rather than (force) fit


%\vspace*{1mm}
%  \item[-] Design, build and maintain sustainable objects
\vspace*{4mm}
  \item[-] Design, build and maintain sustainable infrastructure


    
\vspace*{4mm}
  \item[-] Responsible Engineer, with Executive Powers 

%\vspace*{1mm}
% \item[] Engineer with executive powers


%\vspace*{2mm}
\vspace*{4mm}
  \item[-] Engineer with versatile, quality assured analysis tool to

  \begin{itemize}
\vspace*{1mm}
%  \item[-] Explore various design concepts
  \item[-] Explore design concepts

\vspace*{1mm}
  \item[-] Assess infrastructure performance 

  \end{itemize}


% \vspace*{2mm}
%   \item[-]  Choice of analysis/modeling level of sophistication
% 
% \vspace*{1mm}
%   \item[] Modeling simplifications, Epistemic uncertainty
% 
% \vspace*{1mm}
%   \item[] Variable, random material and loads, Aleatory  uncertainty
% 



\vspace*{4mm}
  \item[-] Engineering Analysis to Predict and Inform



% 
%  
%  
%  \vspace*{1mm}
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  %\hspace*{-7mm}
%  %\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
%  %\hspace*{1mm}
%  \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2023/5_SEECCM_Vrnjacka_Banja_5-6Jul2023/present/Parthenon_on_Acropolis_June2023.jpg}
%  %\hspace*{2mm}
%  \hspace*{2mm}
%  \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Aya-Sofia_03_1990.jpg}
%  %\hspace*{2mm}
%  \hspace*{2mm}
%  \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/ZhaozhouBridge.jpg}
%  \hspace*{2mm}
%  %\hspace*{2mm}
%  \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Four_Water_Wheels_Hama_Syria.jpg}
%  \hspace*{2mm}
%  %\hspace*{2mm}
%  \includegraphics[height=1.2truecm]{/home/jeremic/tex/works/Conferences/2023/5_SEECCM_Vrnjacka_Banja_5-6Jul2023/present/Eiffel_tower_design_drawings/Eiffel_tower_02.jpg}
%  %
%  %\vspace*{3mm}
%  \end{center}
%  \end{figure}
%  %\vspace*{3mm}
%  
%  %\vspace*{1mm}
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  %\hspace*{-7mm}
%  %\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
%  %\includegraphics[height=1.8truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Aya-Sofia_03_1990.jpg}
%  %\hspace*{2mm}
%  \includegraphics[height=3.5truecm]{/home/jeremic/tex/works/Conferences/2023/5_SEECCM_Vrnjacka_Banja_5-6Jul2023/present/Eiffel_tower_design_drawings/Eiffel_tower_force_diagram_shape.jpg}
%  \hspace*{4mm}
%  \includegraphics[height=3.5truecm]{/home/jeremic/tex/works/Conferences/2023/5_SEECCM_Vrnjacka_Banja_5-6Jul2023/present/Eiffel_tower_design_drawings/Eiffel_tower_foundation.jpg}
%  %\hspace*{2mm}
%  %
%  %\vspace*{3mm}
%  \vspace*{-2mm}
%  \end{center}
%  \end{figure}
%  %\vspace*{3mm}



%
%
%
%  \vspace*{1mm}
%    \item[]  Follow  the  flow, input and dissipation,  of seismic  energy,

%  \vspace*{2mm}
%    \item[]
%  %System  for
%   {\bf Real}istic modeling and simulation of
%    {\bf E}arthquakes and/or
%    {\bf S}oils and/or
%    {\bf S}tructures    and    their
%    {\bf I}nteraction:\\
%     Real-ESSI
%   \hspace*{5mm}
%    \url{http://real-essi.us/}
%  % % %  \hspace*{25mm}
%  %     \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % %    \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % %  % \url{http://ms-essi.us/}
%  % %
%


%
%  
%  
%  \vspace*{1mm}
%    \item[]  Follow  the  flow, input and dissipation,  of seismic  energy, 

%  \vspace*{2mm}
%    \item[]  
%  %System  for 
%   {\bf Real}istic modeling and simulation of
%    {\bf E}arthquakes and/or    
%    {\bf S}oils and/or    
%    {\bf S}tructures    and    their    
%    {\bf I}nteraction:\\
%     Real-ESSI 
%   \hspace*{5mm} 
%    \url{http://real-essi.info/} 
%  % % %  \hspace*{25mm} 
%  %     \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % %    \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % %  % \url{http://ms-essi.info/}
%  % %  
% 




\end{itemize}
\end{frame}
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%  




  


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\begin{frame}
%\frametitle{ESSI Challenges}
\frametitle{Civil Engineering Analysis Challenges}
           

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%
\begin{figure}[!htb]
\begin{center}
% %\includegraphics[width=5cm]{Figure-files/_Chapter_Applications_ESSI_BOOK/Building_modeling_Issues_01_pdf.pdf}
%\vspace*{-3mm}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/Seismic_Motions_modeling_Issues_01_pdf.pdf}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/Seismic_Motions_modeling_Issues_02_pdf.pdf}
\\
%\vspace*{-2mm}
%\vspace*{-8mm}
\vspace*{2mm}
\includegraphics[width=2.8cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/NPP_Modeling_Issues_03.jpg}
\includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/SMR_Modeling_Issues_02_pdf.pdf}
\includegraphics[width=3.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/Building_modeling_Issues_03_pdf.pdf}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/Building_modeling_Issues_02_pdf.pdf}
\\
\vspace*{2mm}
\includegraphics[width=2.5cm]{/home/jeremic/tex/Classes/2020/Spring_semester_ETH/ESSI/Term_Projects_from_Students/Tunnel02.pdf}
\includegraphics[width=1.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/Dam_modeling_Issues_01_pdf.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/Dam_modeling_Issues_02_pdf.pdf}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_BOOK/Bridge_modeling_Issues_01_pdf.pdf}
% %\vspace*{-8mm}
% \caption{\label{ESSI_Models_and_Challenges}
% ESSI modeling and simulation challenges:
% Free field motions, 3C/6C vs 3$\times$1C;
% Nuclear Power  Plant structure -- soil/rock system, Small Modular Reactor structure -- soil/rock system;
% Low and High Building-foundation-soil system;
% Dam-Foundation-Fluid system;
% Bridge-soil  system;
% %
% Aspects of modeling:
% 1) Seismic motions,
% 2) Inelastic soil and rock,
% 3) Inelastic interface/contact/joints, foundation with soil/rock and
%    interfaces/contacts/joints within structure,
% 4) Inelastic structure, systems and components,
% 5) Solid, Structure -- Fluid interaction, external (reservoirs, fluid pools...) and internal
%    (fully saturated and partially, (un-)saturated soil, rock and concrete).}
\end{center}
\end{figure}

%
%  
%  \begin{itemize}
%  
%      \item[-] Linear elastic, all elements
%  
%  %\vspace*{1mm}
%      \item[-] Nonlinear elastic, solids
%  
%  %\vspace*{1mm}
%      \item[-] Soil, solids/3D, dry, saturated and partially saturated)
%  
%  %\vspace*{1mm}
%      \item[-] Rock, solids/3D, dry, saturated and partially saturated) 
%  
%  %\vspace*{1mm}
%      \item[-] Interface/Contact, soft, hard, gap, dry, saturated
%  
%  %\vspace*{1mm}
%      \item[-] Base isolator and dissipator 2-node/3D
%  
%  
%  %\vspace*{1mm}
%      \item[-] Concrete, solids/3D, wall/2D, beam/1D, ASR
%  
%  %\vspace*{1mm}
%      \item[-] Steel, beam/1D and solid/3D
%  %
%  
%  
%  %\vspace*{1mm}
%      \item[-] Seismic input, DRM
%  
%  %\vspace*{1mm}
%      \item[-]  Energy Dissipation
%  
%  
%  \end{itemize}


\end{frame}
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%\section{Engineering Analysis Methods and Tools}
\section{Plastic Energy Dissipation}

      
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% \subsection{Real-ESSI }



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


\frametitle{Real-ESSI Engineering Analysis System}
%\frametitle{Real-ESSI Simulator Analysis System}


\begin{itemize}


\vspace*{1mm}
  \item[-]
     Statics and dynamics of rock, soil, structures, fluids...

\vspace*{1mm}
  \item[-]
     Linear, Nonlinear, Inelastic 


\vspace*{1mm}
  \item[-]
     Deterministic and Probabilistic 

\vspace*{1mm}
  \item[-]
     High Performance Computing, HPC


\vspace*{1mm}
  \item[-]
%     Reduction of modeling, epistemic uncertainty
     Reduction of Modeling Uncertainty

\vspace*{1mm}
  \item[-]
%     Propagation of parametric, aleatory uncertainty
     Propagation of Parametric Uncertainty


\vspace*{1mm}
  \item[-]
%     Quality assurance: verification and validation
     QA: Verification and Validation

\vspace*{1mm}
  \item[-]
     Infrastructure safety and economy
%     All models  available for civil engineers

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

\end{itemize}


 
\vspace*{-56mm}
%\begin{figure}[!hbpt]
\begin{flushright}
\hspace*{5mm}
\includegraphics[width=3.0cm]{/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}





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

\begin{frame}
 \frametitle{FEM for ESSI Analysis}
% \frametitle{Finite Element Method}


\begin{itemize}

      

%  \vspace*{2mm}
%   \item[-] Virtual displacements cannot be zero, they cancel out
%  
%  \vspace*{2mm}
% \item[-] Single Phase FEM
 \item[-] Single Phase FEM:
\hspace*{2mm}
% \\
%Final FEM equations:
%Single phase FEM
$
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*{2mm}
  \vspace*{4mm}
 \item[-] Two phase FEM, u-p-U:
{\footnotesize
% \hspace*{-25mm}
\begin{eqnarray}
 \hspace*{-15mm}
\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]
\nonumber
\end{eqnarray}
}
%

%\vspace*{4mm}
%  \item[-] Nonlinear FEM residuals, equilibrium:
 \vspace*{4mm}
  \item[-] Equilibrium:
\hspace*{2mm}
%  \\
$R = F_{external} - F_{internal}$ 

%$
%R_{Q} = 
%F_{Q}   -
%\left(
%M_{PQ}   \; \ddot{\bar{u}}_{P}
%+
%K_{PQ}   \; \bar{u}_{P}
%\right)
%$


\end{itemize}


\end{frame}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Energy Input and Dissipation in ESSI System}

\begin{itemize}

\vspace*{1mm}
     \item[] Energy input, forces/loads, static/dynamic


\vspace*{4mm}
     \item[] Energy dissipation outside SSI domain:
       \begin{itemize}
         \item[] SSI system oscillation radiation
         \item[] Reflected waves radiation
       \end{itemize}
\vspace*{2mm}
     \item[] Energy dissipation/conversion inside SSI domain:
       \begin{itemize}
\vspace*{1mm}
         \item[] Inelasticity of soil, interfaces, structure, dissipators
\vspace*{1mm}
         \item[] Viscous coupling with internal/pore and external fluids
% %         \item[] potential and kinetic energy
%          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\vspace*{1mm}
         \item[] Energy deflectors, meta-materials
       \end{itemize}                           



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




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\begin{frame}
\frametitle{Energy Dissipation within ESSI System}

\begin{itemize}



\vspace*{4mm}
\item[-] 
%Increment of 
Plastic energy dissipation:
%$\Phi =  \sigma_{ij} \dot{\epsilon}_{ij} - \sigma_{ij} \dot{\epsilon}_{ij}^{el} - \rho \dot{\psi}_{pl} \ge 0$
$\Delta  \Phi =  \sigma_{ij} \Delta {\epsilon}_{ij} - 
          \sigma_{ij} \Delta {\epsilon}_{ij}^{el} - 
%          \rho 
          \Delta {\psi}_{pl} \ge 0$
 

% %Following  the first and second laws of thermodynamics, the equation for plastic
% %energy  dissipation  in  decoupled  material models was presented by 
% %%\citeN7{Yang2017a}:
% %
% \begin{equation}
% \Phi =  \sigma_{ij} \dot{\epsilon}_{ij} - \sigma_{ij} \dot{\epsilon}_{ij}^{el} - \rho \dot{\psi}_{pl} \ge 0
% \label{equation_plastic_dissipation_final}
% \end{equation}
% %
% where  $\Phi$  is  the  rate  of  plastic  energy  dissipation  per unit volume,
% $\sigma_{ij}$  is  the stress  tensor,  $\epsilon_{ij}$  is  the strain tensor,
% $\epsilon_{ij}^{el}$  is  the  elastic  part of the strain tensor, $\rho$ is the
% mass  density of the material, ${\psi}_{pl}$ is the plastic free energy per unit
% volume.  
%






\vspace*{6mm}
\item[-] 
%Increment of 
Viscous energy dissipation/damping: \\
%dissipation $\Delta {D}_V$,  
$\Delta {D}_V =  C_{ij} \dot{u}_j \Delta {u}_i $

% 
% To  compute  the  energy  dissipation  due to viscous damping, we start with the
% general form of the equation of motion:
% %
% \begin{equation}
% M_{ij} \ddot{u}_j(t) + C_{ij} \dot{u}_j(t) + K_{ij}^{elpl}(t) u_j(t) = f_i(t)
% \label{equation_of_motion}
% \end{equation}
% %
% where  $u_j(t)$ is the vector of generalized displacements, $M_{ij}$ is the mass
% matrix,   $C_{ij}$   is   the   damping   matrix,   $K_{ij}^{elpl}(t)$   is  the
% inelastic  stiffness  matrix that generally evolves with time, $f_i(t)$ is
% the external load vector.
% %
% For linear viscous damping of the Rayleigh type, the damping matrix is
% expressed as
% %
% \begin{equation}
% C_{ij} = a_M M_{ij} + a_{K} K_{ij}^{el}
% \label{equation_damping_matrix}
% \end{equation}
% %
% where  $a_M$  and  $a_{K}$  are  damping constants with units of s$^{-1}$ and s,
% respectively.
% %
% 
%     
% %
% The incremental form of energy balance for a dynamic system with viscous damping can be expressed as
% %
% \begin{equation}
% \Delta {W}_{Input} = \Delta {E}_K + \Delta {D}_V + \Delta {W}_M
% \label{equation_energy_balance}
% \end{equation}
% %
% The left hand side of Equation~\ref{equation_energy_balance}  is the
% increment of external input work
% %
% \begin{equation}
% \Delta {W}_{Input}=  f_i \Delta {u}_i
% \label{equation_energy_balance_W_Input}
% \end{equation}
%
%
% %%
% The three terms on the right hand side of Equation~\ref{equation_energy_balance} are
% the  increment of kinetic energy $\Delta {E}_K$, the increment of viscous energy 
% dissipation $\Delta {D}_V$, and the increment of material work of the system $\Delta {W}_M$
% %
% \begin{equation}
% \begin{aligned}
% \Delta {E}_K &= M_{ij} \ddot{u}_j \Delta u_i \\
% \Delta {D}_V &=  C_{ij} \dot{u}_j \Delta {u}_i \\
% \Delta {W}_M &= K_{ij}^{elpl} {u}_j \Delta {u}_i = \Delta {E}_S + \Delta {E}_P + \Delta {D}_P
% \end{aligned}
% \label{equation_energy_balance_components}
% \end{equation}
% %
% Note  that  the term of material work $W_M$ can be separated into an elastic part
% and  a  plastic  part.
% These two components are known as  the elastic strain energy $E_S$ and the plastic
% work of the system, respectively.
% %
% Then,  as  mentioned  in  the  previous  section,  plastic  work can be further
% decomposed into plastic free energy $E_P$ and plastic energy dissipation $D_P$.


\vspace*{6mm}
\item[-] 
Algorithmic, numerical energy dissipation/production:
\\
 Newmark, Hilber-Hughes-Taylor, Houbolt, Bathe, Wilson...


%     


\end{itemize}






\end{frame}


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

\frametitle{Energy Dissipation Control}

\vspace*{3mm}
\begin{figure}[!H]
%\hspace*{-10mm}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
     \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
\end{figure}




\end{frame}

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


\vspace*{2mm}
 
% Single elastic-plastic element under cyclic shear loading
 
\begin{itemize}
\item[] Plastic work is NOT plastic dissipation !
\item[] Surface area of $F-\Delta$ or $\sigma-\epsilon$ is NOT plastic dissipation !
% \item[] Plastic dissipation always increases
\end{itemize}
 
%\vspace*{-7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



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

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


\vspace*{6mm}

Increment of  plastic energy dissipation:
%$\Phi =  \sigma_{ij} \dot{\epsilon}_{ij} - \sigma_{ij} \dot{\epsilon}_{ij}^{el} - \rho \dot{\psi}_{pl} \ge 0$
$\Delta \Phi =  \sigma_{ij} \Delta {\epsilon}_{ij}^{pl} - 
%          \sigma_{ij} \Delta {\epsilon}_{ij}^{el} - 
%           \rho 
           \Delta {\psi}_{pl} \ge 0$
 


\vspace*{6mm}


 Plastic Free Energy $  \Delta {\psi}_{pl} $ 

\begin{itemize}

\vspace*{4mm}
\item[-]  3D Drucker-Prager El=Pl, Armstrong Frederick (soil) \\
        $\Delta {\psi}_{pl}  
        = 
        \left(( 3/(2 h_a)) \alpha_{ij} \Delta  \alpha_{ij}  
        - 
        m_{ii}^{vol} \Delta \lambda \right) (-\sigma_{kk}/3 ) $
%        m_{ii}^{vol} \Delta \lambda \right) p $


\vspace*{4mm}
\item[-]  1D steel fiber (BRB) \\
        $\Delta {\psi}_{pl}  = \frac{1}{2} 
         \left( 
            (\sigma + \sigma^{r})\Delta \epsilon) 
            +
            (\epsilon^{pl} - \epsilon^{r}) \Delta \sigma \right) $

\vspace*{4mm}



   \end{itemize}









\end{frame}


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% 








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\begin{frame}

\frametitle{ASCE-7, Steel Building with BRBs}

\vspace*{3mm}


\begin{figure}[!H]
\hspace*{-5mm}
%\hspace*{-10mm}
     \includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/ASCE-7-Steel-building-BRB_model.jpg}
\end{figure}




\end{frame}

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

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

\frametitle{ASCE-7, Steel Building with BRBs, Soil}


Parabolic Drucker-Prager with Armstong-Frederick rotational kinematic hardening

%\vspace*{3mm}
\begin{figure}[!H]
%\hspace*{-10mm}
     \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/ASCE-7-Steel-building-BRB_soil_profile.jpg}
\\
     \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/ASCE-7-Steel-building-BRB_upper_soil_response.jpg}
     \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/ASCE-7-Steel-building-BRB_lower_soil_response.jpg}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/from_Han_24Aug2023/}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/from_Han_24Aug2023/}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/from_Han_24Aug2023/}
\end{figure}




\end{frame}

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

\frametitle{ASCE-7, Steel Building with BRBs, Steel}


Giuffr{\'e}-Menegotto-Pinto 1D Fiber steel model

\vspace*{3mm}
\begin{figure}[!H]
%\hspace*{-10mm}
     \includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/ASCE-7-Steel-building-BRB_BRB_calibration.jpg}
\end{figure}




\end{frame}

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

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

\frametitle{Buckling Restrained Braces (BRB) Energy Dissipation}


%\vspace*{3mm}

\begin{flushleft}
\begin{figure}[!H]
\hspace*{-20mm}
%\hspace*{-10mm}
     \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/ASCE-7-Steel-building-BRB_BRB_elements.jpg}
\hspace*{50mm}
\end{figure}
\end{flushleft}

\vspace*{-12mm}
\begin{flushright}
\begin{figure}[!H]
\hspace*{42mm}
     \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/from_Han_24Aug2023/Plastic_Dissipation_Density_Time_History.jpg}
\end{figure}
\end{flushright}




\end{frame}

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% 





  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ASCE-7-21, Steel Building Energy Dissipation}


% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Thesis/HanYang/ASCE-7-21_low_building_energy_dissipation/ATC_Short_Building_PD.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/ASCE-7-21_low_building_energy_dissipation/ATC_Short_Building_PD.mp4}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/ATC_Short_Building_PD.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online  
   



\end{frame}
%\vspace*{10mm}  

     









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

\frametitle{Building Seismic Response}


\vspace*{3mm}
\begin{figure}[!H]
%\hspace*{-10mm}
     \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/from_Han_24Aug2023/response_acc_2.jpg}
     \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2023/CIVIL-COMP-28-31Aug2023/present/from_Han_24Aug2023/response_disp_2.jpg}
\end{figure}




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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Energy Dissipation for Design}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/2D_Frame_Model.pdf}
% \end{center}
% \end{figure}
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Design Alternatives}
% 
% 
% % local
% %\vspace*{-2mm}
% \begin{center}
% \hspace*{-16mm}
% %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% \movie[label=show3,width=61mm,poster, showcontrols]
%   {\includegraphics[width=60mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation_screen_grab.jpg}}
%   {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation.mp4}
% %\hspace*{-2mm}
% %\hfill
% %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% \movie[label=show3,width=61mm,poster, showcontrols]
%   {\includegraphics[width=61mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation_screen_grab.jpg}}
%   {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation.mp4}
% \hspace*{-16mm}
% \end{center}
% % local
% 
% 
% % online
% \begin{center}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Individual_Foundation.mp4}
% {\tiny (MP4)}
% %
% \hspace*{40mm}
% %
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Continuous_Foundation.mp4}
%  {\tiny (MP4)}
% \end{center}
% % online
% 
% 
% 
% 
% 
% \end{frame}
%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
       

% 


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

\frametitle{Important Infrastructure, 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,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}




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



\end{frame}

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

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